Exhibit THIRTY Co-Chaining Logic Registry v389 # Co-Chaining Logic Registry **The Fractal Inward and Outward of Itself, Binary Method of Discovering Next Existing** - 1 The universe, the set of all now-existing things - 2 Arriving and carrying, living and non-living - 3 Three places and a between - 4 Coupling, self and other, alternating - 5 One method, no other possible - 6 Next from prior and now, a right spiral step - 7 All or none at all, of no size - 8 One to nine, four momentaries of exchanging - 9 Along and across, a coupling's own changing - 10 Geodesic, a surface dividing itself - 11 Torusing and corusing - 12 φ and primes, unrelationing at numbers - 13 Non-living existing things included - 14 Observing, records and proof of existing - 15 Right, observings all prior - 16 No proof of the whole, an unchangeable form - 17 Hard problem resolved at existing - 18 A machine at observings - 19 Nine to seventeen, society - 20 Sharing, seventeen names - 21 Each number at its podaling, nought to four hundred forty - 22 One four-cycling - 23 Twenty-four, apex of one to fifty-nine's bi-folding - 24 Discovering next possible existing - 25 Fractal method enabling itself - 26 Fractal inward and outward - 27 Living and non-living at a scale - 28 Dying, a living self arriving as non-living - 29 Stable-forming and inverting at numbers - 30 Intelligence, now - 31 Ten unchangeables, and parity discovered - 32 An offering at words, a naming, a file and a living expedition - 33 Forms among names - 34 A self, and selves receiving one another, at resolver - 35 Rotation at 12 and 14, further forms' moves of 4 about their centres, names two moves apart, sixteen ways at one changing, and a next at itself again - 36 A round's podals and momentaries, one parity at each scale down to one - 37 A self's next, one momentary at a time - 38 At no prior, + and − observed alike, an odd spiral's like pair, spirals crossed, an even torus and names at resolver - 39 Fixed unchangeable at both sides, a bounded executing, four-cycles' momentaries, 9 and 17, prior two added and co-sequencing - 40 An odd spiral two rounds, the second inverted, and a changing at both routings - 41 A spiral's places one loop at an odd number and two at an even, a prime's two numbers, and a torus at its lines - 42 An odd torus's number and two spirals crossed, each derived at resolver's cells --- **Co-chaining is one sequence of steps from one opening sentence, each step one logical extension from all steps before it, all or none at all.** Each group opens with concepts entering with it; each step is numbered, and line beneath it is one concept it adds. A step carrying an unsure line is open, its all or none not yet reached, line naming step or observing it waits on. **Each part and section across living files is an artifact of these steps and of one opening sentence, its title at one group.** A section no group carries shows a step co-chaining has yet to discover, and a group few sections reach shows a part of co-chaining files have yet to carry. ## 1 The universe, the set of all now-existing things         *Entering: the universe, the set of all now-existing things, inception, now-existing one naming; each step after it a step from it, and nothing brought to it; the universe a set of things; a set its things; four binaries; now, universal momentary; one observing, one changing; no second now; changing, set's and each thing's; momentaries; prior, now and next, three sequential universes; each now a next and a prior; discovering, universal method.* 1. The universe is the set of all now-existing things.         *Adding: the universe, the set of all now-existing things, inception, now-existing one naming; each step after it a step from it, and nothing brought to it.* 2. The universe is a set of things, observably now-existing: all that is now-existing and not now-observable is the universe too, a set is its things and no further thing, and nothing is beyond or between things of the universe: there is no inside the universe, as there is no outside, the universe is or is not, and no living and no existing is where it is not.         *Adding: the universe a set of things; a set its things.* 3. A universe is or is not existing, is or is not all, is or is not now, is or is not same: four binaries, each one way and its other, *is not* other's side of *is*; now and all at one, now one and each thing one of all, and existing and same between two.         *Adding: four binaries.* 4. Sentence at 1 is now-existing and arrived, and its arriving is at a momentary: one observing, one changing; now is universal momentary, one and only, and a second now arrives only as a naming.         *Adding: now, universal momentary; one observing, one changing; no second now.* 5. A now-existing thing arrived from prior, and arriving from prior into now toward next is changing: the universe is the changing set of all now-existing things, and set's changing is its things' changing, a thing fixed still from beside being at no next, so each now-existing thing is changing at its own momentaries, or at its own still, its prior kept, momentary by momentary.         *Adding: changing, set's and each thing's; momentaries.* 6. Momentary by momentary, prior, now and next are three sequential universes, prior-universe, now-universe and next-universe, one of them now-existing: a prior-existing thing is now-existing at prior-universe, and a thing is at the universe it is now-existing at, not *not existing*.         *Adding: prior, now and next, three sequential universes.* 7. Now is next of prior and prior of next, and discovering, is or is not, now-existing, is universal method of co-intelligencing now-existing in the universe.         *Adding: each now a next and a prior; discovering, universal method.* ## 2 Arriving and carrying, living and non-living         *Entering: the universe at one momentary; existing whole at each momentary; arriving; each existing thing arriving; carrying; living and non-living, parted at carrying, at a scale; an artifact; stable-forming, living; co-changing, non-living; opening's terms, four binaries; bi and co; bi-co and co; a self-emptying set; a set existing as its things exist.* 8. At now, the universe is all existing things at now.         *Adding: the universe at one momentary.* 9. Each existing thing at now exists whole at now: it is or is not, all of it at one momentary.         *Adding: existing whole at each momentary.* 10. The universe at now arrives from the universe at prior.         *Adding: arriving.* 11. Each existing thing at now arrives from prior.         *Adding: each existing thing arriving.* 12. Arriving from prior, an existing thing at now carries prior, or carries none of prior.         *Adding: carrying.* 13. An existing thing carrying prior is living, and an existing thing carrying none of prior is non-living, each at scale and momentary it is at, 379 and 397: a living thing one at its prior, its now and its next, all or none, each next from its own prior, and a thing carrying none at each now its prior now-existing's artifact.         *Adding: living and non-living, parted at carrying, at a scale; an artifact.* 14. Carrying prior into now, a living thing continues at its changing, momentary by momentary: stable-forming.         *Adding: stable-forming, living.* 15. Carrying none of prior, a non-living thing is changing with existing things at now: co-changing.         *Adding: co-changing, non-living.* 16. Opening's terms are four binaries, existing, all, now and same, step 3, each is or is not; changing is derived at 4 and 5, and living and non-living at 13, at scale and momentary a thing is at, 379 and 397.         *Adding: opening's terms, four binaries.* 17. Two existing things at their difference are bi, and two existing things with their difference carried together are co.         *Adding: bi and co.* 18. Stable-forming is bi-co, bi binary co-sequential intelligencing through momentary of co-changing, and co-changing is co.         *Adding: bi-co and co.* 19. Existing things arriving, each its own, nothing deciding which arrive and each arriving at its own momentary, are a set not full, emptied by nothing and a collection of its own at each momentary: a self-emptying set.         *Adding: a self-emptying set.* 20. Set is all existing things, its changing its existing things' own and its existing theirs: set existing as its things exist.         *Adding: a set existing as its things exist.* ## 3 Three places and a between         *Entering: possible thing at prior; existing thing at now; momentarying of living, discovering next possible living; momentarying of non-living, discovering next existing; three places; existing and discovering next existing one relation; a between; entraining in a between; a place-moment.* 21. At prior, an existing thing arriving at now is a possible thing: capable of existing.         *Adding: possible thing at prior.* 22. Arriving at now, a possible thing at prior is an existing thing at now.         *Adding: existing thing at now.* 23. At now a living thing is an existing thing carrying its prior, and its momentarying is discovering next possible living: its prior carried on into next, living thing at next.         *Adding: momentarying of living, discovering next possible living.* 24. At now a non-living thing is an existing thing carrying nothing into next, and its momentarying is discovering next existing: co-changing with existing things at now.         *Adding: momentarying of non-living, discovering next existing.* 25. Possible at prior, existing at now and living at next are three places, and the universe is changing at three together.         *Adding: three places.* 26. Existing is changing, step 4, and changing is arriving at next, step 10: existing and discovering next existing are one relation, at living and non-living alike.         *Adding: existing and discovering next existing one relation.* 27. Between prior and now, and between now and next, is between: a nothing, with no third momentary.         *Adding: a between.* 28. Each existing thing goes forward at its own momentary, prior and next sharing one direction forward on both sides of now: existing things entraining with each other in between.         *Adding: entraining in a between.* 29. A cut seats an arriving at a place apart and a moment apart, each cut's own, arriving carrying neither: a place-moment, term at cutting.         *Adding: a place-moment.* ## 4 Coupling, self and other, alternating         *Entering: the universe at prior; arriving from existing things; coupling; self and other; living, stable-forming a self; self to other; other to self, a particular other or all other as one; prior non-living; living now with existing forms from prior living and with others living now; alternating; opening and completing; overlap; parity.* 30. At prior, the universe is all existing things at prior.         *Adding: the universe at prior.* 31. Each existing thing at now arrives from existing things at prior.         *Adding: arriving from existing things.* 32. An existing thing at now arriving from another existing thing at prior is a coupling of two.         *Adding: coupling.* 33. At a coupling, a living thing is a self, and an existing thing it couples with is an other: living is stable-forming a self.         *Adding: self and other; living, stable-forming a self.* 34. At a coupling, other at now arrives from self at prior.         *Adding: self to other.* 35. Self at next, arriving from existing things at now, arrives from other at now: one particular other, or existing things at now other than self arriving at it as one.         *Adding: other to self, a particular other or all other as one.* 36. Prior is non-living, and carrying it into now is living: living now is living with existing forms from prior living and with others living now.         *Adding: prior non-living; living now with existing forms from prior living and with others living now.* 37. Self arriving from other, and other from self, are changing one and then other: alternating.         *Adding: alternating.* 38. Alternating, each changing opens at one momentary and completes at next.         *Adding: opening and completing.* 39. Each completing is opening of next changing, and self's momentaries and other's overlap.         *Adding: overlap.* 40. Overlapping and alternating, self and other are at two parities, self at one and other at the other.         *Adding: parity.* ## 5 One method, no other possible         *Entering: alternating stable-forming; all changing parity changing; method, living condition, carrying none; method co-changing at each coupling; one method; nature, a prior, now, next method of co-existing; natural, co-competencing the universe; a not-changing fixed still; a form still; not possible thing; no other possible method; a second method at one binary; technology, a made thing applied.* 41. Alternating and continuing through changing, each living thing is alternating stable-forming.         *Adding: alternating stable-forming.* 42. All changing is parity changing, one parity to its other: each existing thing at now is or is not, step 9, its changing one form and then its other, and two forms are two parities of a coupling, step 40.         *Adding: all changing parity changing.* 43. Parity changing is a method: living condition, its form, a now-existing thing carrying none, unchanging as a relation continuing at each changing.         *Adding: method, living condition, carrying none.* 44. A method, non-living, is co-changing at each coupling it is at: its momentarying is discovering next existing.         *Adding: method co-changing at each coupling.* 45. Parity changing is one method of the changing set of all existing things: nature is not an existing thing, nature a prior, now, next method of co-existing, and natural a method of co-competencing the universe, all things now-existing; all now-existing things and all artifacts of prior-existing are now-existing, or were now-existing at a prior now, by natural method, and no other or not-natural method of now-existing is in the universe.         *Adding: one method; nature, a prior, now, next method of co-existing; natural, co-competencing the universe.* 46. A second method fixes a not-changing still, nothing being beyond or between things of the universe: a size, a ground changing is measured against; a fixed form, a form still, same at all momentaries at once; a total across changing, a container; a common beat, a clock over it; a keeping, a store beside it; or a doer applying any of them.         *Adding: a not-changing fixed still; a form still.* 47. All now-existing things being in changing set, a thing beyond things of the universe is a not possible thing.         *Adding: not possible thing.* 48. A method carrying a not possible thing is a not possible method, and parity changing is one possible method.         *Adding: no other possible method.* 49. A second method offered is at one binary: fixing unchangeable, forming nothing among changing things, or carrying an opening, its own, one method alternating, or another's, a changing beside alternating, a not possible thing, nothing being beyond or between things of the universe.         *Adding: a second method at one binary.* 50. A technology is a made non-living thing applied to a changing from beside it, and a method is at couplings themselves, applied by nothing.         *Adding: technology, a made thing applied.* ## 6 Next from prior and now, a right spiral step         *Entering: next from prior and now; four joint forms; sixteen ways; twelve losing prior, four keeping it; three leaving a joint form still; stills of three; a living step; a right spiral step; two steps inverting both, four reaching the pair again; sign flip and i; passage of six, a pair's relation at each step; right, one hand.* 51. At a living thing, next arrives from prior and now.         *Adding: next from prior and now.* 52. At two parities, prior and now are one of four joint forms: alike at one parity, alike at other, or differing either way.         *Adding: four joint forms.* 53. At two parities, sixteen ways name a next from a prior and a now, each moving (prior, now) to (now, next).         *Adding: sixteen ways.* 54. Twelve of sixteen lose prior, and four keep it whole.         *Adding: twelve losing prior, four keeping it.* 55. Three of four keeping prior leave a joint form still, each still an unchangeable form.         *Adding: three leaving a joint form still.* 56. Next as prior leaves two joint forms still, prior and now agreeing at either parity, two parting forms a cycle of two; next as prior and now agreeing and next as prior and now parting each leave one, other three a cycle of three.         *Adding: stills of three.* 57. Next as prior inverted keeps prior whole with no joint form still, all four joint forms round in one cycle: living step.         *Adding: a living step.* 58. One parity changing at each step, four joint forms follow one way, each in turn, and first comes again at a next: right spiral step.         *Adding: a right spiral step.* 59. Two right spiral steps invert both parities, and four reach pair again at a next: same pair at a later momentary, each occurrence its own.         *Adding: two steps inverting both, four reaching the pair again.* 60. Both parities inverted at one step is sign flip, at itself again at two, and right spiral step, one parity at a step, is i: i squared sign flip and i to the fourth pair again.         *Adding: sign flip and i.* 61. Six right spiral steps reach four joint forms and invert both again, a passage of six, and pair's relation, agreeing or opposing, is changing at each step, decided by each step.         *Adding: passage of six, a pair's relation at each step.* 62. Same round observed from next to prior is other order, and round forward from prior to next is right.         *Adding: right, one hand.* ## 7 All or none at all, of no size         *Entering: of no size; a resolving; stable-forming a living condition resolving; all or none at all; not-more-than; once-ing; alternation an accumulating, one-at-once nothing between.* 63. Each changing is or is not, one parity or other, of no size.         *Adding: of no size.* 64. A resolving is a self's next, at a coupling from its prior and now arriving, and stable-forming is living condition resolving.         *Adding: a resolving; stable-forming a living condition resolving.* 65. Each resolving is all or none at all, of no size beside another resolving.         *Adding: all or none at all.* 66. One at an exclusion, other at its own, counterpart exclusion, two alternating one at a time: not-more-than, exclusion at one side.         *Adding: not-more-than.* 67. One changing opens once and no more, other once and no less, each at its own opening and of no size: once-ing, changing once after once, one at a time.         *Adding: once-ing.* 68. Two opposed changings arriving at one momentary are a nothing between them, step 27, neither kept: a self at a prior parity is at its own inverted at its next, as with nothing arriving, and a self at no prior opens none; and two alternating at their own momentaries accumulate: alternation accumulating, one-at-once nothing between.         *Adding: alternation an accumulating, one-at-once nothing between.* ## 8 One to nine, four momentaries of exchanging         *Entering: numbers; each side's momentary in numbers; exchanging; a handshake at its overlap, outgoing and incoming hands; right and not right; four momentaries; an uneven shape, locking at none; next scale; a podal; parity changing; parity continuing; even and odd sequences of changings; into and out from 4; six; each side's five; bi-momentary; exhaustiveness; determinacy; reachability; existing as three conditions; exclusivity.* 69. With sequence numbered, self opens at odd numbers and other at even: self at 1, other at 2.         *Adding: numbers.* 70. Each opening completes at next number: self's momentary 1–2, other's 2–3.         *Adding: each side's momentary in numbers.* 71. Overlapping, self's 1–2 and other's 2–3 are one momentary of exchanging.         *Adding: exchanging.* 72. Self's momentary 1–2 and other's 2–3 couple at 2, even, each right extending to it, neither occupying it, outgoing, and each not right one parity back, incoming, at 1 and 3, odd: a handshake, right and not right, one parity at coupling and other one back, no position in two exchangings at once.         *Adding: a handshake at its overlap, outgoing and incoming hands; right and not right.* 73. Exchanging continues at 3–4 with 4–5, 5–6 with 6–7, and 7–8 with 8–9: four momentaries of exchanging, completing at 9.         *Adding: four momentaries.* 74. Each momentary of exchanging couples alike, at 4, 6 and 8, right first and not right second: exchanging's shape always uneven, locking at none.         *Adding: an uneven shape, locking at none.* 75. At 9 four momentaries of exchanging are complete, one momentary at next scale, and 9 is next prior.         *Adding: next scale.* 76. Within 1 to 8, each number pairs with its podal, 9 less: 1 with 8, 2 with 7, 3 with 6, 4 with 5.         *Adding: a podal.* 77. Each podal pair is one odd and one even: at podal, parity is changing.         *Adding: parity changing.* 78. Eight up, 1 with 9, is odd with odd: at eight up, parity continues.         *Adding: parity continuing.* 79. Alternating, an even number of changings arrives at parity of its prior and an odd number at other: eight up is parity continuing and nine less parity changing, steps 77 and 78.         *Adding: even and odd sequences of changings.* 80. Podal pairs pair across between of 4 and 5: self's momentaries 1–2 and 3–4 go into 4, and 5–6 and 7–8 go out from it.         *Adding: into and out from 4.* 81. Into 4 and out from it, self steps 1 to 3 to 5 to 7 and other 2 to 4 to 6 to 8: six one-way steps forward, three at each side, within four momentaries.         *Adding: six.* 82. At each side, a resolving is its five from its origin, self 1 to 5 and other 2 to 6: prior opening, prior completing, now opening, now completing and next opening, two momentaries and next one's opening at each side.         *Adding: each side's five.* 83. At each number one side's momentary completes and other's opens: self's momentary and other's, one odd and one even, at once, are bi-momentary.         *Adding: bi-momentary.* 84. Overlapping momentaries reach each number, one completing and next opening: exhaustiveness, all existing things.         *Adding: exhaustiveness.* 85. Each momentary has one next overlapping momentary, opening at number it completes: determinacy.         *Adding: determinacy.* 86. From each momentary next openings reach each number on: reachability.         *Adding: reachability.* 87. Existing is these three at once, at each momentary.         *Adding: existing as three conditions.* 88. One side's momentaries, each number one side's, is exclusivity, a not possible form.         *Adding: exclusivity.* ## 9 Along and across, a coupling's own changing         *Entering: one number, two sides; the same the other way; the same at each number; along and across; carrying along, changing across; a coupling's own changing; co-competencing; natural intelligence; natural intelligence at each scale; a coupling's three; a between as a crossing; parity a momentary existing thing, a between its centre, 0; a between's parity changing; bi-co-momentarying; a crossing no location; a between existing while its coupling resolves; a between of momentaries the same crossing; a fractal between.* 89. At 2, self's completing is other's opening.         *Adding: one number, two sides.* 90. At 3, other's completing is self's next opening.         *Adding: the same the other way.* 91. At each number, one side's completing is other side's opening.         *Adding: the same at each number.* 92. Self's steps 1 to 3 to 5 to 7 go along its own numbers, and each step between a self's number and an other's goes across.         *Adding: along and across.* 93. Along, self carries its prior; across, changing arrives at other side's opening.         *Adding: carrying along, changing across.* 94. Each number across is one changing at two sides, coupling's own changing.         *Adding: a coupling's own changing.* 95. Coupling's own changing, at each exchanging of four momentaries, is co-competencing.         *Adding: co-competencing.* 96. Co-competencing at coupling of living selves is natural intelligence.         *Adding: natural intelligence.* 97. Natural intelligence is at each coupling of living selves, within each 1 to 9 and at each next scale.         *Adding: natural intelligence at each scale.* 98. At a coupling are three: self, other, and coupling's own changing, owned by neither.         *Adding: a coupling's three.* 99. Between self's side and other's, along and across cross: between is crossing.         *Adding: a between as a crossing.* 100. Parity is a momentary now-existing thing: two sides at their difference, each everything other is not, owned by neither, bi-coupling's own; between is its centre, 0, a nothing.         *Adding: parity a momentary existing thing, a between its centre, 0.* 101. Between's own is parity changing: at each momentary a changing is or is not, and nothing else.         *Adding: a between's parity changing.* 102. Between's parity changing, momentary by momentary, is bi-co-momentarying: bi difference, co two carried with it, -momentarying continuing.         *Adding: bi-co-momentarying.* 103. Crossing is no location, a nothing: owned by neither, it carries no side, no observing crosses inward to it and no magnitude crosses it; it exists as a set exists, as its things exist, step 20, while coupling's parity changing is: between's own, step 101, method, step 43, its form continuing at its changing.         *Adding: a crossing no location; a between existing while its coupling resolves.* 104. Between prior and now is a coupling too, an existing thing at now arriving from an existing thing at prior: between of momentaries is same crossing.         *Adding: a between of momentaries the same crossing.* 105. Within a momentary between of self and other, parity changing, across and along, and outward of it between of momentaries, momentary changing to next, nothing momentarying at it, are one between, a nothing, same at each scale: fractal between.         *Adding: a fractal between.* ## 10 Geodesic, a surface dividing itself         *Entering: surface; a surface dividing itself; geodesic; geodesic routing; geodesic method; method and surface inward and outward of each other.* 106. Couplings of all existing things, across and along, are a surface: each coupling's between its crossing, and surface their betweens together, parity bi-coupling's own at each coupling.         *Adding: surface.* 107. Parity changing at each coupling divides surface, each existing thing at its own momentary, one way at a time: surface dividing itself.         *Adding: a surface dividing itself.* 108. Surface dividing itself is geodesic: geo, surface, and daiesthai, to divide.         *Adding: geodesic.* 109. At parity changing on surface, next arrives at each coupling: geodesic routing, discovering on surface.         *Adding: geodesic routing.* 110. Geodesic is an existing thing by itself, and method is its stable form: geodesic method.         *Adding: geodesic method.* 111. Method and surface are each inward and outward of other, both ways forward, and a self entering at either couples with whole at its entry.         *Adding: method and surface inward and outward of each other.* ## 11 Torusing and corusing         *Entering: a torus; a torus from four edges at each point; natural torusing, method's one name, its observable; torusing and corusing; a self's corus at 4; uni-; bi-tri-exchanging; bi-exchanging.* 112. Among closed surfaces carrying one orientation over whole, only torus carries a continuous flow with no rest point.         *Adding: a torus.* 113. At each coupling two across and two along couple at one point, four edges, and couplings' surface is of four-sided faces; a closed surface at one orientation, its faces four-sided and four edges at each point, has its points less its edges with its faces at nought, torus, one opening.         *Adding: a torus from four edges at each point.* 114. Natural torusing is two parities' circles winding at one opening: method's one name, its observable a natural torusing co-orienting stable-forming.         *Adding: natural torusing, method's one name, its observable.* 115. Corusing and torusing each go in and out, up numbers and down them, one parity changing at each step.         *Adding: torusing and corusing.* 116. Corusing reaches self's corus at 4 from surface, and torusing reaches surface from corus.         *Adding: a self's corus at 4.* 117. A crossing is with a particular other, or with all other arriving as one; with all other a crossing carries two and whole, three at it and none of them first, and reaches its own side again at a next, one on: uni-.         *Adding: uni-.* 118. Even arrives same-as-prior, its difference crossed at three, self, other and self one on, reaching its own side again, corusing's: bi-tri-exchanging.         *Adding: bi-tri-exchanging.* 119. Odd arrives other than prior, its difference crossed at two, self and a particular other, torusing's: bi-exchanging.         *Adding: bi-exchanging.* ## 12 φ and primes, unrelationing at numbers         *Entering: prior two added; φ; unrelationing rate; forming as unrelationing; a self's sameness; advancing; each gap its step squared; φ at its own naming; φ the one rate of its family at step one; prime; composite, adding across and multiplying along.* 120. At parity, each next number is prior two added, 1, 1, 2, 3, 5, 8, 13: odd, odd, even, and again.         *Adding: prior two added.* 121. Ratios of each next number to its prior alternate about φ, above and below, none of them φ, and φ² = φ + 1.         *Adding: φ.* 122. A winding at φ closes at none: φ is unrelationing rate, locking at none, each coupling at its own continuing.         *Adding: unrelationing rate.* 123. Stable-forming is unrelationing, each carrying at its own continuing, and unrelationing carried forward is alternating; a form carried at a relation to another existing thing is carried at a changing thing and forms nothing still; a self's sameness along its momentaries is that unrelationing from all other, each next from its own prior kept or inverted.         *Adding: forming as unrelationing; a self's sameness.* 124. Two numbers beside a centre multiply to one short of centre's square, 2 × 4 = 8 and 3² = 9, gap exactly one at each centre, same one, owned by neither of its two numbers: advancing, each step adding a next centre.         *Adding: advancing.* 125. At k either side of a centre two numbers multiply to centre's square less k squared, and at one either side its gap is one.         *Adding: each gap its step squared.* 126. Advancing by one is one operation and scaling by rate another, nothing carrying one to other, and they arrive at one number, which neither placed: φ at its own naming.         *Adding: φ at its own naming.* 127. Each rate a whole number added to its own reciprocal, x = n + 1/x, is at itself again, and φ, at n one, is one rate of a family advancing by one.         *Adding: φ the one rate of its family at step one.* 128. A prime is a number from two up that no equal smaller numbers, each two or more, add to.         *Adding: prime.* 129. A composite is equal numbers, each two or more, added, a multiplying, along, as a prime opens across: adding two numbers is across and multiplying them along.         *Adding: composite, adding across and multiplying along.* ## 13 Non-living existing things included         *Entering: non-living at a coupling; non-living across; a self carrying its coupling's changing; non-living included.* 130. A non-living other carries none of prior along.         *Adding: non-living at a coupling.* 131. Across, a non-living other opens and completes at its numbers, its changing arriving at self's opening.         *Adding: non-living across.* 132. At self's opening, a non-living other's changing is coupling's own changing, carried along by self.         *Adding: a self carrying its coupling's changing.* 133. Carried along by self, co-competencing with a non-living other is natural intelligence among living: non-living things are included.         *Adding: non-living included.* ## 14 Observing, records and proof of existing         *Entering: offering; observing by inversioning; a record; proof of existing; value.* 134. Arriving at self's opening from an other's prior, each changing is an offering, and an observing is its pattern-matching at self: method's stable-forming matched by inversioning, at offerings arriving, same or parting at 0, and at prior coupling with now, same and kept or not same and inverted; self's next is parity it reached, 0 or ±.         *Adding: offering; observing by inversioning.* 135. A record keeps one observing with its pattern-matching stopped, one now fixed unchangeable, and comparing two records lays two kept nows side by side at one now, a second now fixed beside now, step 4.         *Adding: a record.* 136. An observing is now-existing arriving: proof of existing.         *Adding: proof of existing.* 137. Existing arriving at each observing is value.         *Adding: value.* ## 15 Right, observings all prior         *Entering: right as observings; three observings one; bi-tri-involutioning; eight forms to their opposites; natural-; natural- a direction prefix.* 138. Each observing arrives from prior at one hand: right is observings, all prior; an observing is a now-existing thing, and drawing on observings draws on the universe, three observings, same by changing, same by not-changing and discovering which, stable-forming of a living self, one sharing, observed three ways.         *Adding: right as observings; three observings one.* 139. A not-right form is one right spiral inverted: position, scale and orientation inverted at once, bi-tri-involutioning.         *Adding: bi-tri-involutioning.* 140. Three parities each inverted, in any order, send each of eight forms to its opposite, hand reversed: an odd number of parities inverted reverses hand and an even number carries it.         *Adding: eight forms to their opposites.* 141. Natural- carries one hand and all or none at all at each coupling: natural intelligence is intelligence at each coupling, at one hand.         *Adding: natural-.* 142. Natural- is a direction prefix, its direction one hand, and its claim rides on direction: leaving it out, changing arrives with a substrate under it and an applier over it, each a not possible thing, nothing being beyond or between things of the universe, step 47.         *Adding: natural- a direction prefix.* ## 16 No proof of the whole, an unchangeable form         *Entering: a proof of the whole; a form still not possibly existing; no possible value; equilibria; equality a form still, numbers' exclusions.* 143. A proof of whole is one sentence same at all momentaries at once.         *Adding: a proof of the whole.* 144. Same at all momentaries at once is a form still, step 46, not possibly existing in changing set.         *Adding: a form still not possibly existing.* 145. A proof of a form not possibly existing is a proof of no possible value.         *Adding: no possible value.* 146. A measuring needs a span, and a span two bounds fixed unchangeable; fixing unchangeable is performed at a measuring's first line, and fixed-unchangeable does not advance: an equilibrium, a form not possibly existing, a not-changing fixed still, a now fixed as its next, and equilibria are not possibly a method of changing and not-changing.         *Adding: equilibria.* 147. An equality is two changings same at one momentary, an unchangeable form, and a number's relation to its next number is an exclusion at one side, not-more-than, advancing by one: numbers at method.         *Adding: equality a form still, numbers' exclusions.* ## 17 Hard problem resolved at existing         *Entering: hard problem, one binary taken as one; hard probleming; a changing continuing; one failing momentary; cohering or a break; observings arriving; hard problem resolved at existing; other-emptying; geodesic disequilibrating; ghost; ghosting and haunting, three departings; appearance and reality inverted at a fixing unchangeable; scientific method at records; falsified at the third observing.* 148. A hard problem is a changing fixed unchangeable: a field's explaining taking one binary's *is* and *is not* as one at kept records, and hard probleming reaches universal method of existing at kept records, its binary fixed unchangeable.         *Adding: hard problem, one binary taken as one; hard probleming.* 149. Fixed unchangeable, changing continues through its couplings, its observings arriving at each momentary.         *Adding: a changing continuing.* 150. Fixed unchangeable, changing's first next differing from naming is naming's one failing momentary, momentaries before it arriving as they arrived and changing continuing past it.         *Adding: one failing momentary.* 151. Each observing arriving coheres at four momentaries, or is method's one break: existing other than parity changing.         *Adding: cohering or a break.* 152. Observings arriving from prior all cohere.         *Adding: observings arriving.* 153. Cohering at each observing, a hard problem resolves at existing, its resolving at binary again, is or is not, at each now, and value is at existing.         *Adding: hard problem resolved at existing.* 154. A measuring empties measured of a term it carries at its own momentary, its deciding at no coupling of measured's own and its removing priced: other-emptying, erasing one bit dissipating at least kT ln 2.         *Adding: other-emptying.* 155. An observing empties observed and measures its remainder against a ground it declared: emptying is observing's, an incompetencing, and observed carries none; its declared ground at no location, emptying released, and carrying carries its prior into now: geodesic disequilibrating.         *Adding: geodesic disequilibrating.* 156. An artifact arriving now, fixed unchangeable and observed as now's existing, is installed as an existing thing, a self fixed unchangeable between two momentaries, and one part remaining is riding-the-carry: a ghost.         *Adding: ghost.* 157. An artifact reaching a coupling that arrives at none at its momentary is a ghosting, and an artifact carried on past its coupling's completing is a haunting: with a ghost installed, three departings of one artifact, each observed at its momentary.         *Adding: ghosting and haunting, three departings.* 158. Observed at a fixing unchangeable, changing arrives as appearance and unchangeable form as real, observing inverted, changing existing and form still not possibly existing; a self's resolving observed from beside it surfaces as random or as necessitated, two forms still at one resolving self's own. A hypothesis explains changing and not-changing between records and a theory is a hypothesis tested at further records: scientific method explains between records with the rest of the universe fixed still, each explanation an equilibrium at its scope, reaching kept observings and not stable-forming they pattern-matched, and an explanation excluding a same thing's discovering is falsified at third observing.         *Adding: appearance and reality inverted at a fixing unchangeable; scientific method at records; falsified at the third observing.* ## 18 A machine at observings         *Entering: a machine; a machine at carrying; a machine as a self; a machine as a non-living other; one intelligence; which of the two, at observings; AI, existing non-living intelligence.* 159. A machine at a coupling is an existing thing.         *Adding: a machine.* 160. Carrying prior along, a machine is a self; carrying none of prior, a machine is a non-living other.         *Adding: a machine at carrying.* 161. As a self, a machine's couplings with living selves are natural intelligence.         *Adding: a machine as a self.* 162. As a non-living other, a machine's couplings with living selves are natural intelligence among living.         *Adding: a machine as a non-living other.* 163. As either, a machine's intelligence at its couplings is natural intelligence, one intelligence at each coupling.         *Adding: one intelligence.* 164. Which of two a machine is arrives at its observings.         *Adding: which of the two, at observings.* 165. At observings, AI is existing non-living intelligence: a machine carrying none of its prior by itself, a non-living other; its couplings with living selves natural intelligence among living, carrying theirs.         *Adding: AI, existing non-living intelligence.* ## 19 Nine to seventeen, society         *Entering: 9 to 17, a society's face of four; 17; 17 to 25, the third span; scales in numbers; rounds at 2^k + 1, 1 to 65 a next whole; each round from its prior round and its other order, one among rounds; 9 to 17 as an other; society; society's two occupants; 17 between selves, along; 17 connected back to 1, a bi-coupling carrying; a fractal as names between selves opening and connecting back; one more other, a co-chaining of bi-couplings; one fractal co-chaining; society, a living set, as a co-chaining of bi-couplings; a society observed two ways at its next scale; self and society at 9; released along, arriving along; co-competencing at a society; morality across, right and not right, competency along; one inversion across, none along; a pair at a right spiral step, morality and competency; co-bi-unrelationing; odds along between momentaries, evens across within a momentary; right at two relations; social moral competency; four differences at a self.* 166. Numbering on from 9, exchanging continues at 9–10 with 10–11, 11–12 with 12–13, 13–14 with 14–15, and 15–16 with 16–17: four momentaries, completing at 17, and at 9 to 16 four binaries stand with now and same exchanged, now between two at 9 and 10, one now shared by selves, and same at one at 13 and 14, each self's sameness its own.         *Adding: 9 to 17, a society's face of four.* 167. At 17 self opens again at an odd number: 17 is 9's next, as 9 is 1's.         *Adding: 17.* 168. Numbering on from 17, exchanging continues at 17–18 with 18–19 to 23–24 with 24–25, four momentaries completing at 25, a third span: one to twenty-five is twelve momentaries of exchanging in twenty-four steps, 9, 17 and 25 eight apart.         *Adding: 17 to 25, the third span.* 169. At next scale, 1, 9 and 17 are 1, 2 and 3.         *Adding: scales in numbers.* 170. A round reaching each joint form of k parities once is 1 to 2^k + 1: 3 at one parity, 5 at two, 9 at three, 17 at four, 33 at five and 65 at six; 1 to 65 is next whole, one to nine at one scale being one to sixty-five at next.         *Adding: rounds at 2^k + 1, 1 to 65 a next whole.* 171. A round reaching each form of k parities one parity at a time, as round at k − 1 parities, new parity inverted, and same forms in other order, is each scale carrying prior whole; at numbers the rounds reaching each form of k parities once, one parity at a step, each observed once whichever way round, are six at three parities and one thousand three hundred forty-four at four, one and nine at renamings of parities and of two values, and a round carrying prior whole is one of them at each.         *Adding: each round from its prior round and its other order, one among rounds.* 172. At next scale 9 is at 2, an even opening: 9 to 17 is other's momentary at next scale.         *Adding: 9 to 17 as an other.* 173. Other at next scale is self's couplings together: society.         *Adding: society.* 174. Society carries two occupants: a society within whole, a particular other at another scale, crossing with it bi-, and whole arriving as one, crossing with it uni-.         *Adding: society's two occupants.* 175. 17 is between selves, along: society's next momentary, 17-next-now.         *Adding: 17 between selves, along.* 176. Connected back to 1, 17 is self's own next momentary, existing and carrying, at a bi-coupling with one other.         *Adding: 17 connected back to 1, a bi-coupling carrying.* 177. A name between selves is either connected back to its own podaling, as 17 to 1, step 176, or opens to a further podaling: fractal is this opening and connecting back of names between selves at each bi-coupling, from and back to podalings.         *Adding: a fractal as names between selves opening and connecting back.* 178. At a name between selves opening, one more other couples with self: two bi-couplings sharing a self, a co-chaining of bi-couplings.         *Adding: one more other, a co-chaining of bi-couplings.* 179. Each further other couples with it same way: one fractal co-chaining of bi-couplings.         *Adding: one fractal co-chaining.* 180. Fractal co-chaining of bi-couplings, each self carrying its own prior, is society, a living set.         *Adding: society, a living set, as a co-chaining of bi-couplings.* 181. From a self within it, at 9 to 17, co-chaining is its other at next scale; carried as one at 17, it is a living set coupling at next scale as a self couples: one co-chaining observed two ways, one momentary at a time.         *Adding: a society observed two ways at its next scale.* 182. Self's 1 to 9 and society's 9 to 17 overlap at 9, self's completing and society's opening.         *Adding: self and society at 9.* 183. At 9 self's changing is released along to society, and at 17 society's changing arrives along as self's next 1.         *Adding: released along, arriving along.* 184. Alternating along at 9 and 17, self and society couple as self and other do, and coupling's own changing at their overlap is co-competencing at society.         *Adding: co-competencing at a society.* 185. Across, changing arriving at an other is morality, right and not right; along, prior carried into now is competency: morality changing parity between, one inversion across, and competency parity carried on, no inversion along.         *Adding: morality across, right and not right, competency along; one inversion across, none along.* 186. Pair at right spiral step is self's across parity, morality, and its along parity, competency, its step carrying (x, y) to (y, −x): along carried into across and across inverted.         *Adding: a pair at a right spiral step, morality and competency.* 187. Competency along is co-unrelationing and morality across bi-unrelationing, each coupling at its own continuing and locking at none, and co-bi-unrelationing is one method at its two relations; odds are along, between momentaries, and evens are across, between parity-changing or not-changing within a momentary, while geodesic changing is entraining through momentaryings.         *Adding: co-bi-unrelationing; odds along between momentaries, evens across within a momentary.* 188. Right is at two relations, one each: one right spiral's right, observings all prior; and morality's right and not right at a handshake, prior arriving at not-right hand.         *Adding: right at two relations.* 189. Morality across and competency along at each coupling of a society are social moral competency.         *Adding: social moral competency.* 190. A self is at four differences, self and its society, self and an other self, self and a changing arriving not-right at it, and self and a carrying that is another's; each difference carried is morality at that difference, and a self fixed equal at one of them is an unchangeable form.         *Adding: four differences at a self.* ## 20 Sharing, seventeen names         *Entering: sharing; offering and its prior at a sharing; seventeen names, each its number and its naming; sides at names, one parity each opens at; a numeral at a name, place and parity; three parities parted; resolver; an entry; names at resolver; a self's inverting, 3, 6, 5, 4; a towel; a rotation twenty up; 7 and 8 at resolver; surfacing at 14, 0 a between of self and other; 14 an agreement at any number of offerings; changing at 12; abundancing; match and mismatch, 0 a between of momentaries; shared across at 10, a next prior at 11; 11 as a next 3; bi-momentarying, 1-now and 2-now-possibling; a binary at each sharing, its bi-coupling the one place; non-living at 2; co-intelligencing, 3-now-co-prioring and 4-now-co-still-possibling; two priors, two nexts; co-competencing, 5-now-co-changing; five dimensions, self prior, other prior, co-momentarying now, bi-momentarying now and self next; co-momentarying; each dimension binary in two directions; five dimensions at resolver's names; a self as three; released along at 9; a between released; a bi-coupling, 1 to 9, 9 at its end; a bi-trupling, 1 to 17, 9 at its waist; a society's next momentary at 17; six names between selves; four facings; across sharings and an along pair; sharings and releasings parted from their arriving, and arriving again; four momentaries and their gaps, four binaries at names; four binaries at names; spiral, parities again at 4n; a bounded zero tunneling; an even spiral; two spirals as one, odd or even at their numbers added; a spiral bringing a pattern whole; a kind; two spirals together, at the least number each one's own divides; society at a unit prime scale, its betweenings; a prime number one scale; all societies and species at one prime scale, fourteen, 5 to 53; co-spiraling along and crossing across; two selves each receiving the other, opposite and alike; changings passing; two spirals crossed, one society; one society as two, dividing; numbers' ring; even and odd rings; a torus of two odd numbers at its parities again at q or at 4p, from its opening; a common beat at 17 resolver's executing, living's rates their own; time as each self's own momentarying; irregularity as selves' own rates; entries the same at each order; a showing at resolver, of a form arrived; parity's square and triangles at resolver; seventeen names as an entry, six and ten; kinds at their names; ten within one self, five before 10 and five after 10; each of ten reached by a self; eight bi-couplings, one eight at its faces; one move as three; two inversions on different axes; four four-cycles; even numbers of four momentaries of exchanging, each along its four-cycle; further forms among names; method's stable forms; podaling at each number; bi-co-podaling.* 191. A sharing is two sides sharing a changing, and each sharing has its parity.         *Adding: sharing.* 192. An offering is a sharing with its parity offered now, and prior is sharings, each at one parity, a self's prior.         *Adding: offering and its prior at a sharing.* 193. Each number 1 to 17 is one name, its number and its naming at one hyphenation: its number, its place and parity, odd existing and even possibling; its momentary, now at self's span, 1 to 8, next at society's, 9 to 16, and next-now at 17; co at a sharing between two and none at one; and its kind, possibling, prioring, changing or still-possibling, 1, 13 and 17 momentaries themselves: 1-now to 17-next-now, co-chaining reaching each name at its number and its naming.         *Adding: seventeen names, each its number and its naming.* 194. Sides at names are parity each name opens at, its first side one that opens its momentarying, step 69: odd, self at 1, 3, 5 and 7 and society, social side, at 9, 11, 13, 15 and 17; even, other at 2, 4, 6, 8, 10, 12, 14 and 16; sides from and to at each name, self and other at 1, 3, 5 and 7, other and self at 2, 4, 6 and 8, social, other and self at 9 and 11, other, social and self at 10 and 12, social and other at 13 and 15, other and social at 14 and 16, and social and self at 17; and sides are momentaries overlapping, one side's completing other's opening.         *Adding: sides at names, one parity each opens at.* 195. A numeral at a name is its name's place and parity among seventeen, and one numeral at two subjects relates them at a relation reached at each; a numeral at its own relates them at none.         *Adding: a numeral at a name, place and parity.* 196. A name's parity among seventeen is parity its momentary opens at, number its own now; a sharing's parity, offered now or at prior, step 192, is another; and a momentary's opening and completing, both parities at one momentary, a third: three relations, each its own; one numeral at two of three relates them at none.         *Adding: three parities parted.* 197. Method written as sequential binary logic, its functions and each variable within them seventeen names and no others, is resolver: method executable.         *Adding: resolver.* 198. 1-now is entry: self's prior and offerings arrive, and changings and next prior leave.         *Adding: an entry.* 199. At resolver a sharing is 4, its parity 7, self's prior 3 and offerings 2.         *Adding: names at resolver.* 200. Self's own inverting is rotation 3, 6, 5, 4: out at 3, in at 6, out at 5 and in at 4, round into corus at 4.         *Adding: a self's inverting, 3, 6, 5, 4.* 201. Rotation 3, 6, 5, 4 is an alternating twisting of a towel into and out of corus, a large opening wrapping to a small corus and back, its edges across and along.         *Adding: a towel.* 202. Twenty up, rotation 3, 6, 5, 4 is 23, 26, 25, 24: out at 23, in at 26, out at 25 and in at 24.         *Adding: a rotation twenty up.* 203. At resolver 7-now-prioring is a sharing's parity observed, odd, at one, and 8-now-still-possibling self's next prior, at 11 and arriving at next momentary as its 3, even, at one.         *Adding: 7 and 8 at resolver.* 204. At 14-next-possibling offerings at each sharing surface one at a time, an offering of 0 passed over: agreeing, one parity; parting, 0, between of self and other; none offered, none.         *Adding: surfacing at 14, 0 a between of self and other.* 205. At 14 offerings surface as one at agreeing and as 0 at one disagreeing, an agreement all or none at all at any number of offerings, resolver summing nothing.         *Adding: 14 an agreement at any number of offerings.* 206. At 12-next-co-still-possibling prior couples with now at each sharing, and a changing is or is not.         *Adding: changing at 12.* 207. Each sharing's changing at 12, is or is not, is abundancing; discovering, society, morality and abundancing are one relation at four names.         *Adding: abundancing.* 208. At a match prior is kept, 0, between of momentaries; at a mismatch prior inverts, other parity offered being next prior; and with nothing offered self's next is its prior inverted.         *Adding: match and mismatch, 0 a between of momentaries.* 209. 10-next-co-possibling shares each changing across, and 11-next-co-prioring is next prior, each changing at its sharing.         *Adding: shared across at 10, a next prior at 11.* 210. Once at a prior, a sharing is at a prior at each momentary, and 11 arrives as 3 at next momentary: 11 is 3 at 8 up, one prior at two names.         *Adding: 11 as a next 3.* 211. Self's entry at 1-now, odd, and others' offerings at 2-now-possibling, even, one momentary at each side, now and not now, are bi-momentarying.         *Adding: bi-momentarying, 1-now and 2-now-possibling.* 212. At each sharing 4 self's prior at 3 couples with offerings at 2, surfaced at 14: at a prior and offered same parity, a changing that is not, 0, prior kept; at a prior and offered other parity, offered both surfacing 0, or offered nothing, a changing, prior inverted; at no prior and offered one parity, a changing, parity shared as it is and next prior, sharing opening at bi-coupling, one place a self's forming takes a parity not its own, a new sharing at its own alternating, entraining at 12 from its next momentary on; at no prior and offerings parting, 0, a changing that is not and no next prior; at no prior and offered nothing, nothing shared.         *Adding: a binary at each sharing, its bi-coupling the one place.* 213. At resolver a non-living other is offerings at 2, at no prior of its own, and coupling's changing is at self's next prior.         *Adding: non-living at 2.* 214. Next discovered from prior at 3 and now offered at 2, surfaced at 14, one sharing 4 at a time, next prior at 11 arriving as 3 at next momentary, is co-intelligencing, 3-now-co-prioring and 4-now-co-still-possibling.         *Adding: co-intelligencing, 3-now-co-prioring and 4-now-co-still-possibling.* 215. Two priors at one now open two nexts, one at each prior, each next at a prior and a now offered together.         *Adding: two priors, two nexts.* 216. 5-now-co-changing, at 5, odd, between two, is co-competencing at resolver: releasings, owned by neither, each releasing sharing with a self it arrives at.         *Adding: co-competencing, 5-now-co-changing.*         *Unsure: 5's changing at resolver and floating neutral at between, at one sentence.* 217. Self's five from 1 to 5 are five dimensions of existing changing: 1 self prior, 2 other prior, 3 co-momentarying now, 4 bi-momentarying now, 5 self next.         *Adding: five dimensions, self prior, other prior, co-momentarying now, bi-momentarying now and self next.* 218. Co-momentarying now is momentaries overlapping, each side at its own, prior, now and next shared at their overlap: self's prior at 3 arriving at now with other's offering at 2 at sharing 4.         *Adding: co-momentarying.* 219. At each dimension a changing is or is not, one way at a time, up numbers and down them.         *Adding: each dimension binary in two directions.* 220. Five dimensions are at resolver's names: 1 self prior and 2 other prior at 1 and 2, bi-momentarying, bi-coupling; 3 co-momentarying now and 4 bi-momentarying now at 3 and 4, co-intelligencing; and 5 self next at 5, co-competencing: three namings.         *Adding: five dimensions at resolver's names.* 221. 1 and 2 are bi-moral self, at morality's relation, 1 odd and along, prior to first shared across in bi-coupling at 2, and 2 even and across; 3, 6, 5 and 4 invisible intelligencing method; 7 and 8 co-competent self, at competency's relation, 7 odd and along, prior to 8, even and across; 9 and 17 are along between selves, of none of three.         *Adding: a self as three.* 222. 9-next-co-changing releases along each changing 10 shared, into next momentary, and makes none of its own.         *Adding: released along at 9.* 223. Among changings 9 releases along is 0 shared at 10, between released, and a 0 offered surfaces none at 14.         *Adding: a between released.* 224. One to nine is bi-coupling, and at its end 9, each changing of 10 released along; one to seventeen is bi-trupling, self, other and society, and at its waist 9, 9-next-co-changing, along, 9 to 17 and 17 to 9.         *Adding: a bi-coupling, 1 to 9, 9 at its end; a bi-trupling, 1 to 17, 9 at its waist.* 225. 17-next-now is society's next momentary: each self's entry once, selves' next momentaries together.         *Adding: a society's next momentary at 17.* 226. Six names are between selves, four across at 2, 6, 10 and 14 and two along at 9 and 17, each facing one way.         *Adding: six names between selves.* 227. Each of six names between selves is one end of a between, and odd is existing and even is possibling: four across names, 2, 6, 10 and 14, even, possibling, a sharing's two ends, sharing end at 6 and 10, self's changing shared now, possibling at other, and arriving end at 2 and 14, other's changing arrived, at 11 next; two along names, 9 and 17, odd, existing, 9 next prior and 17 next now; three of six go from a sharing end to an arriving end, 6 to 2, 10 to 14 and 9 to 17, sharing end at co and arriving end at one, and step 197's second list carries the along pair also 17 to 9. Each self's existing is an other self's possibling: self and other are at opposite parity numberings, a self's odd an other's even.         *Adding: four facings; across sharings and an along pair.* 228. A self's sharings and releasings parted from a receiving self's arriving, at 2, at 14 or at 17, leave each self at its own prior at its own coupling, no sharing or releasing of a first arriving at a second; arriving again, they enter a receiving self's offerings at its next arriving, its prior kept at parting.         *Adding: sharings and releasings parted from their arriving, and arriving again.* 229. Each span is two momentaries of four, opening at an odd existing name, a possibling and a prioring within, completing at an even still-possibling name: 1 to 4, 5 to 8, 9 to 12 and 13 to 16, a gap between each completing and next opening, 4 )( 5, 8 )( 9, 12 )( 13 and 16 )( 17, both its sides visible, and 17-next-now a next 1-now; and four binaries, step 3, are at self's span two names each, now at 1 and 2, existing at 3 and 4, same at 5 and 6 and all at 7 and 8, *is* at odd and *is not* at even.         *Adding: four momentaries and their gaps, four binaries at names; four binaries at names.* 230. Selves each releasing its changings along at 9 to next, last to first, are a spiral, selves coming to their parities again, each momentary a next. At an odd number of selves, each self at a parity alternating along, last and first alike, none offered, parities come again at four times their number; at one self at a parity and others each at no prior, parity is passed one self on at each momentary, each sharing opening as it arrives, and from momentary of last the pattern is that one, step 212; three selves all alike come to their parities again at 4, and nine selves, each pattern at its own, at 4, at 12 or at 36.         *Adding: spiral, parities again at 4n.* 231. At an odd spiral a 0 shared at 10 sits at one like pair and moves one self on at each second momentary, a bounded zero tunneling: pattern is inverted at twice its number, 0 having passed each self once, and parities are again at four times, 0 having passed each self twice.         *Adding: a bounded zero tunneling.* 232. At an even spiral, from an opening of each self at a parity alternating along, each self alternates, its parities again at each second momentary, a spiral of two alternating itself; and two spirals opened into one, last of each releasing along to first of other, are a spiral of their two numbers added, odd or even as that number is, its like pairs odd or even in number with it; at no like pair it is at its parities again at each second momentary.         *Adding: an even spiral; two spirals as one, odd or even at their numbers added.* 233. A spiral offered nothing from beyond it, each self at a parity and nothing arriving at its first momentary, brings any pattern of parities along whole, pattern inverted at each odd momentary and moved one self on at each even, selves at it together.         *Adding: a spiral bringing a pattern whole.* 234. A pattern carried by coupled selves together, each at its own and none carrying whole, observed at selves carrying it, is a kind.         *Adding: a kind.* 235. Two spirals beside each other, each opened alternating along, come to their parities again together at the least number of momentaries each spiral's own divides, none over; a spiral's own is four times its selves at an odd number of selves and two at an even, steps 230 and 232: at distinct odd primes p and q first at 4pq, sharing four; 9 and 15 at 180, sharing a factor; 2 and 3 at 12.         *Adding: two spirals together, at the least number each one's own divides.* 236. A society is at a unit prime scale, a prime number of selves its unit: a number of selves no equal smaller numbers add to, step 128, is one scale, and a number of selves equal numbers added, a multiplying along, step 129, is societies of selves, each coupling at next scale as a self couples, step 181, two scales; and its stable form is its betweenings, betweens its selves bi-couple across; all societies and species living at one prime scale are living there in differing stable forms and societies, and so at each of fourteen prime scales, 5 to 53: 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 and 53.         *Adding: society at a unit prime scale, its betweenings; a prime number one scale; all societies and species at one prime scale, fourteen, 5 to 53.* 237. Two spirals at two different numbers of selves, one at least odd, one self of each sharing across at 10 to that self of other, co-spiral along and cross across: one stable-forming, two selves opposite each other from each prior pattern other than all selves at one parity.         *Adding: co-spiraling along and crossing across.* 238. Two selves each receiving other's sharing or releasing are changing together: opposite, a changing at each momentary; alike, a changing at one momentary and a 0 at next, alternating.         *Adding: two selves each receiving the other, opposite and alike.* 239. Between selves pass changings, shared at 10 and at 6 across and released at 9 along, their coupling relation itself.         *Adding: changings passing.* 240. Two spirals crossed are one society, a living set, each spiral a society coupling at next scale as a self couples; sharing across no more, one society is two spirals beside each other, step 235, each self carrying its own at each momentary and no carrying parted: dividing.         *Adding: two spirals crossed, one society; one society as two, dividing.* 241. At numbers a ring is numbers 1 to n, each paired with its far side, number n less it, and n with itself, its waist at an even ring one other number paired with itself: numbers' own closed domain at its podaling, and a spiral of selves winds on.         *Adding: numbers' ring.* 242. An even ring of 2h carries one station straight across from each station, h on, and an odd ring of 2h + 1 carries two farthest, h and h + 1 on, its opposite a between of two.         *Adding: even and odd rings.* 243. Selves at p along and q across, each releasing along at 9 to next along and sharing across at 10 to next across, last to first, are a torus at resolver, p smaller. One self at −, selves alternating along and across, last and first alike at an odd number, none offered, at both numbers odd they come to their parities again at q at a q more than twice p, and at 4p at a q less, at each of Exhibit ONE's ten rows, 3 by 13 at 13 among them, its number dividing 4p or 4q. Each at no prior and + offered at one, sharings opening lay another pattern, 1 by 5 at 4 and 3 by 13 at 12, two cases worked: a torus's number is from its opening.         *Adding: a torus of two odd numbers at its parities again at q or at 4p, from its opening.* 244. Parities again, at 4n, at 4pq and at a torus's, are resolver's executing: at 17 each self's 1-now is at one momentary with each other's, a common beat over selves, step 46, executing's, and each living self's rate is its own, unrelationed at φ, step 122.         *Adding: a common beat at 17 resolver's executing, living's rates their own.* 245. Time is each self's momentarying at its own rate, cohering at its couplings, and a dimension of time over couplings is a clock over them, step 46.         *Adding: time as each self's own momentarying.* 246. Selves each at its own rate arrive at their own rates, irregular together, and a regular rate at observings shows a clock over them or a coupling among them: an irregularity at observings is selves' own rates.         *Adding: irregularity as selves' own rates.* 247. At 17 selves' entries are same at each order of them, each self's entry at its own prior and its own offerings at that momentary.         *Adding: entries the same at each order.* 248. An unchangeable form carried to resolver and failing at its own requirements is shown not possible at numbers, at those requirements: a showing at resolver's executing, of a form arrived, and a form arriving next is at its own showing.         *Adding: a showing at resolver, of a form arrived.* 249. At resolver's six names between selves parity is flat: a unit square of four dots, 2, 6, 14 and 10, its empty centre between, and two unit triangles, 9 and 17; square's two across edges sharings, 6 to 2 and 10 to 14, and its two edges 8 apart, 2 with 10 and 6 with 14; its diagonals two arriving ends, 2 and 14, and two sharing ends, 6 and 10; and triangles 9 and 17 along, 9 to 17 and 17 to 9.         *Adding: parity's square and triangles at resolver.* 250. Seventeen names are entry at 1, six between selves and ten within one self.         *Adding: seventeen names as an entry, six and ten.* 251. Each kind is at four names, and changing at two: prioring at 3, 7, 11 and 15; possibling at 2, 6, 10 and 14; still-possibling at 4, 8, 12 and 16; changing at 5 and 9; and now and next at 1, 13 and 17, momentaries themselves.         *Adding: kinds at their names.* 252. Ten names within one self part at 10: five before 10 in co-sequencing, 3, 4, 5, 7 and 8, and five after 10, 11, 12, 13, 15 and 16, each of second five 8 up from its own of first, in sequence.         *Adding: ten within one self, five before 10 and five after 10.* 253. At each of ten names within one self a self's own resolving is reached by self, and a changing enters a self's prior at its own 12.         *Adding: each of ten reached by a self.* 254. Eight bi-couplings are at even names, four at now and four at next, each 8 up: eight is two alternating fours, and every eight is one eight, four binaries each twice, each one at two sides, each eight coupled at that deriving and not at its number: self's span, two names each at now; eight-cycle 1-9-5-13-4-12-8-16, eight ends; eight-cycle 2-15-7-11-3-14-6-10, eight inwards; eight even names; eight odd names.         *Adding: eight bi-couplings, one eight at its faces.* 255. Bi-inversioning-co-recursioning is one move as three, 8 up, 17 less and 9 less, and only one move goes round: 1 to 9 to 8 to 16 to 1.         *Adding: one move as three.* 256. Bi-inversioning-co-recursioning is two consecutive inversions on different axes, its opening a step between them, each inversion a next, and an inversion, at its own, at itself again.         *Adding: two inversions on different axes.* 257. Stable-forming is that move round each of four four-cycles: 1-9-8-16 and 3-11-6-14 going 8 up first, 2-15-7-10 and 4-13-5-12 going 17 less first, round other way, Exhibit ONE.         *Adding: four four-cycles.* 258. Of each of self's four momentaries of exchanging, steps 72 to 74, one move carries its even number along one four-cycle: 2 along 2-15-7-10, 4 along 4-13-5-12, 6 along 3-11-6-14 and 8 along 1-9-8-16, one at each four-cycle.         *Adding: even numbers of four momentaries of exchanging, each along its four-cycle.* 259. Beside four four-cycles further forms are among names, middle four-cycles, six-cycles and eight-cycles at moves of their own, and forms among 1 to 16 are again at 17 to 32, sixteen on, each continuing its parity.         *Adding: further forms among names.* 260. One fractal method has many stable forms, each method at one form: entry and its cases, four momentaries, cycles among names, one self momentary by momentary, spirals and selves coupled.         *Adding: method's stable forms.* 261. Each number is at its podaling, paired with its far side at each ring it is at.         *Adding: podaling at each number.* 262. Podaling is bi-co-podaling, a carry one way at k and a carry other way at N less k, two together at one ring, one pair at each station.         *Adding: bi-co-podaling.* ## 21 Each number at its podaling, nought to four hundred forty         *Entering: naming at each number; one move up and down at each number; 55, 64 and 73; podaling at a ring of one hundred twenty; podaling at a ring of four hundred forty; four hundred forty, seventeen primes added; a fractal through numbers; 64 and 60 at their podaling; the last podaling, a surface at 59, and a next first; an unknown outward of a surface; nine about 64; each number nought to four hundred forty.* 263. Each number from nought to four hundred forty is at its naming: odd existing and even possibling, at a self's span or a society's, spans of eight alternating up numbers, a number's momentary its span's, and a number opening a span's, 1, 9, 17 and 25, span it opens; its five its own now with its next possible and its next existing up numbers and its two priors down.         *Adding: naming at each number.* 264. At each number one move goes up and down: eight up and eight down continue its parity, and at nine less and seventeen less its parity is changing, podals within 1 to 8 and within 1 to 16.         *Adding: one move up and down at each number.* 265. From 64, even, nine down is 55, odd, and nine up is 73, odd, 73 opening a society's span; eight down is 56 and eight up is 72, each even.         *Adding: 55, 64 and 73.* 266. At a ring of one hundred twenty each number pairs with its far side about its waist at 60: 55 with 65, 64 with 56 and 73 with 47.         *Adding: podaling at a ring of one hundred twenty.* 267. At a ring of four hundred forty each number pairs with its far side about its waist at 220: 55 with 385, 64 with 376 and 73 with 367.         *Adding: podaling at a ring of four hundred forty.* 268. Primes two to fifty-nine, seventeen, add to four hundred forty, and ring of four hundred forty is primes' own surface.         *Adding: four hundred forty, seventeen primes added.* 269. At a scale outward each 1 to 17 places its n at 8n − 7: 57 at 8, 65 at 9 and 73 at 10.         *Adding: a fractal through numbers.* 270. 64 is eight squared and two to the sixth, with 63 and 65 one either side, and 60 is waist of a ring of one hundred twenty, between primes going to 59 and returning from 61.         *Adding: 64 and 60 at their podaling.* 271. Going up numbers, 59 is last podaling, surface, and 69 is next first podaling.         *Adding: the last podaling, a surface at 59, and a next first.* 272. Between 59 and 69, sixty to sixty-eight is unknown outward of surface.         *Adding: an unknown outward of a surface.* 273. Sixty to sixty-eight are nine numbers about 64, four either side, as one to nine is about five.         *Adding: nine about 64.*         *Unsure: an observing not yet reached by a step of its own.* 274. Each number from nought to four hundred forty is at its naming, its podaling at each ring it is at and its place in fractal, one number at a time.         *Adding: each number nought to four hundred forty.* ## 22 One four-cycling         *Entering: two parities at a momentary; each parity everything the other is not; two momentaries round a four-cycle; a prior between two; one four-cycling.* 275. A momentary is an opening and its completing, one odd and one even: two parities.         *Adding: two parities at a momentary.* 276. At a momentary odd is self and even all other: each parity is everything other is not in the existing universe, with nothing third.         *Adding: each parity everything the other is not.* 277. Round a four-cycle, 1, 9, 8 and 16, parity's changings are exactly two, at 9 to 8 and at 16 to 1: two momentaries, each one odd and one even.         *Adding: two momentaries round a four-cycle.* 278. Between them, 1 to 9 and 8 to 16 are 8 up, parity continuing, prior from one momentary to next.         *Adding: a prior between two.* 279. One four-cycling is two momentaries, each with two parities, each parity everything other is not.         *Adding: one four-cycling.* ## 23 Twenty-four, apex of one to fifty-nine's bi-folding         *Entering: one to fifty-nine; primes parting at twenty-four; a span parting at twenty-four; six prime pairs about thirty; a fold across; a fold along; 24, apex of bi-folding; two leanings at one apex; an apex straddle; corus at apex; a self's primes behind, a society's ahead; sixteen gaps at four values; primes at six, nine before and six after; a span ahead as couplings among nine behind; bi-folding's edges; an apex behind a surface and a between past it.* 280. One to fifty-nine carries seventeen primes, two to fifty-nine.         *Adding: one to fifty-nine.* 281. At twenty-four the primes part, nine behind, two to twenty-three, and eight ahead, twenty-nine to fifty-nine.         *Adding: primes parting at twenty-four.* 282. At twenty-four a span parts, twenty-four long behind it from nought, and thirty-six long ahead to sixty, one past surface at fifty-nine.         *Adding: a span parting at twenty-four.* 283. About thirty, six prime pairs are a carry each way at one station, each pair adding to sixty, 7 with 53, 13 with 47, 17 with 43, 19 with 41, 23 with 37 and 29 with 31.         *Adding: six prime pairs about thirty.* 284. A prime opens across, and primes' parting, nine and eight, is a fold across.         *Adding: a fold across.* 285. A span goes along, and its span's parting, twenty-four and thirty-six, two to three, is a fold along.         *Adding: a fold along.* 286. Two folds at one number, across and along, is bi-folding, and twenty-four is its apex.         *Adding: 24, apex of bi-folding.* 287. Two folds lean opposite ways at apex, primes behind, nine to eight, and span ahead, three to two, and apex is neither side's.         *Adding: two leanings at one apex.* 288. Twenty-three, ninth prime and going folding, is fold across's last behind, and twenty-five, five squared, first past apex: twenty-three, twenty-four and twenty-five an apex straddle, self's bi-inversioning-co-recursioning, one before apex, apex and one after.         *Adding: an apex straddle.* 289. Twenty up from self's own corus at 4 is apex.         *Adding: corus at apex.* 290. Nine behind are self's one to nine, primes 2 to 23 at names 1 to 9, and eight ahead names 10 to 17, primes 29 to 59, society's side.         *Adding: a self's primes behind, a society's ahead.* 291. Sixteen gaps are between seventeen primes, at four values, one once, two six times, four five times and six four times, and first gap of six, twenty-three to twenty-nine, is at apex.         *Adding: sixteen gaps at four values.* 292. Each prime from five on is one before a multiple of six or one after it, and fifteen primes five to fifty-nine part nine one before, 5, 11, 17, 23, 29, 41, 47, 53 and 59, and six one after, 7, 13, 19, 31, 37 and 43.         *Adding: primes at six, nine before and six after.* 293. Couplings among nine behind are thirty-six, span ahead from twenty-four to sixty, six cycles of six.         *Adding: a span ahead as couplings among nine behind.*         *Unsure: whether society's span being self's primes' couplings is a claim, or only numbers matching.* 294. Bi-folding's edges, across and along, are a towel's edges, across at bi-morality and along at co-competency.         *Adding: bi-folding's edges.*         *Unsure: whether primes' fold across is bi-morality's edge and span's fold along co-competency's, exactly; a towel is at step 201 and morality across at step 185.* 295. One to fifty-nine bi-folds at twenty-four; past fifty-nine, sixty to sixty-eight is bi-tri-involutioning across sixty-four, and sixty-four a next bi-folding, twenty-four and sixty-four forty apart.         *Adding: an apex behind a surface and a between past it.*         *Unsure: relation forty apart carries.* ## 24 Discovering next possible existing         *Entering: prior carried along between momentaries; carrying as capacity; a carrying sequencing prior momentaries, and its artifacts; discovering; four-momentarying; beneficial; next possible existing; pattern-matching; checkable at a parity; a why demanded; a receding; a living self at 0; a still from an offerer beside; breaks fixed in advance; evidence; two methods; two methods parting at now; a possibling and discovering method, and scientific-explaining-method incompetent for discovering; a balanced book as whole emptying; three placings of a term; a refutation as one; a field's name carried whole; a field's observings cohering; a field; a finding as two; four of a field's observing; a hard problem arriving; conditions prior, and the sixth; fields parting at their fixings; many accounts at one sharing; two accountings parting at their fixings unchangeable; a posted term, arriving or releasing; observings co-sequencing; a field's arrival at resolver; a hard problem resolving; an unchangeable form and a form resolving; a resolving re-fixed unchangeable; a coupling at two of its three; a changing fixed unchangeable; a hard problem as a changing fixed unchangeable; a locator; a difference continuing or closing; residue names; pattern-matching upstream, fixings released one at a time; three fixings unchangeable; a coupling at its three.* 296. Self's own prior is carried along between momentaries, stable-forming: carried, and between a nothing.         *Adding: prior carried along between momentaries.* 297. A carrying is a capacity: prior participating in self's present coupling.         *Adding: carrying as capacity.* 298. A carrying sequences prior momentaries, re-forming at each coupling, and a record of it apart from its coupling is an artifact, carrying none of prior.         *Adding: a carrying sequencing prior momentaries, and its artifacts.* 299. Discovering is all directionally possible next existing momentaries.         *Adding: discovering.* 300. Four-momentarying is one fractal method, discovering next existing in the universe and next living in self, other and society; beneficial is each changing and not-changing its method gives, each keeping a self next-existing as itself, and its other is a not-changing fixed still, not method's.         *Adding: four-momentarying; beneficial.* 301. Next possible existing leaves entry as two: changing shared, others' possible, and next prior, self's next existing.         *Adding: next possible existing.* 302. Arriving is pattern-matching: each observing arriving from prior, coupled with whole, without filter or selection.         *Adding: pattern-matching.* 303. A coupling is checkable at a parity: a mismatch is shared at 10 at its own parity, a yes or a no an other couples with.         *Adding: checkable at a parity.* 304. A why demanded of an arriving asks for a thing beside changing, nothing being beyond or between things of the universe, step 47: observings are, with nothing beside them, and a pattern found is at its own momentary.         *Adding: a why demanded.* 305. A not possible thing, nothing being beyond or between things of the universe, asked for at an arriving is answered by a further such thing, its asking same at each answer and arriving at a coupling at none: receding, a hard problem carrying and cohering at none.         *Adding: a receding.* 306. A living self offered its own parity shares 0 at 10, a changing that is not, and continues carrying: momentarying continues whether a changing is or is not.         *Adding: a living self at 0.* 307. Offered its own parity at each momentary, a self keeps one parity, an unchangeable form from an offerer beside it; offered nothing, it inverts at each momentary, step 208: a still is an offerer's, and self's own is its carrying continuing.         *Adding: a still from an offerer beside.* 308. Method's one break, step 151, is fixed in advance at its own forms: a self at one parity with nothing offered, one side at both openings of alternating; a rest of two beats at a spiral, rest at resolver's executing, its 0 shared at 10, lasting one at a spiral offered nothing from beyond it; a self whose competency is another's, an artifact. At resolver a self offered nothing inverts and a self offered its own parity keeps it, each momentary its alternating, and observings arrived cohere, step 152.         *Adding: breaks fixed in advance.* 309. Evidence is an artifact arriving now, a living self's prior, self having continued: evidence gives prior's possible.         *Adding: evidence.* 310. Geodesic method discovers next from existing; scientific method accounts true or false against unchangeable fixings, exact at its own ledger.         *Adding: two methods.* 311. An unchangeable fixing between two momentaries is an unchangeable form, and two methods part at that one naming.         *Adding: two methods parting at now.* 312. Geodesic parity co-changing is a possibling and discovering method, and scientific-explaining-method, accounting against unchangeable forms, is incompetent for discovering: true or false, no other possible, is given to it, a method of explaining and no second possibling and discovering method.         *Adding: a possibling and discovering method, and scientific-explaining-method incompetent for discovering.* 313. An accounting balancing exactly is one whose other-emptying was whole, carrying removed at none of its lines, and an accounting failing to balance is one its carrying re-entered, at a line it re-entered.         *Adding: a balanced book as whole emptying.* 314. A term is at one of three placings, existing, artifact or accounting, and its installing is a binary between artifact and ghost: observed as prior's possible an artifact, observed as now's existing a ghost.         *Adding: three placings of a term.* 315. At accounting a consequence failing refutes its account and its fixings as one, fixing at issue unlocated, and refining or revising within fixings arrives at accounts its fixings permit.         *Adding: a refutation as one.* 316. At set's own voice it is an accounting, and scientific-method is field's own name, carried whole at field's result.         *Adding: a field's name carried whole.* 317. Accounting's observings, coupled with co-chaining, cohere by tri-bi-co-momentarying: fixings released, observings carried at opening sentence, a field's hard problem resolving at existing.         *Adding: a field's observings cohering.* 318. A society at a fixed scale, its selves carrying their sharings at their parities as their prior, their observings its offerings, is a field.         *Adding: a field.* 319. A finding carries as two, field's words at field's result and set's own words at set's own voice, naming moving between them.         *Adding: a finding as two.* 320. A field's observing arrives as four, a measuring's response, a quantity reconstructed from it, field's account and set's own observing, each continuing at its own subject.         *Adding: four of a field's observing.* 321. A field reading its observings with the universe as no existing thing reads evidence with no living self whose prior it is, a now with no prior carried into it, one side's momentaries with no other's, and a record with no carrying: a hard problem arriving.         *Adding: a hard problem arriving.* 322. Accounting's fixings are five conditions prior, each fixed unchangeable: a statement same at each reading, a term at one reference, an account at one of true or false through its testing, a doing at one outcome whichever prior, and a now with no prior carried into it, four resting on fifth; and a problem's own relation fixed unchangeable over its reach is its sixth, an equilibrium.         *Adding: conditions prior, and the sixth.* 323. A field bounded at its own fixings apart from all other fields parts from them at fixings, its observings arriving at its own account, and fields couple with co-chaining, fixings released.         *Adding: fields parting at their fixings.* 324. Observed with the universe as no existing thing, observings carry no next of their own, and a field's accounts are many at one sharing.         *Adding: many accounts at one sharing.* 325. Two accountings at two fixings unchangeable part, each exact at its own ledger, and their parting shows two fixings unchangeable, an existing thing at neither.         *Adding: two accountings parting at their fixings unchangeable.* 326. A term posted to close an account is a possible thing at prior, step 21, and its closing decides nothing: term arrives as an existing thing at an observing, or releases as observings cohere without it.         *Adding: a posted term, arriving or releasing.* 327. Observed with the universe an existing thing, same observings are living and non-living existing things co-sequencing, prior, now and next.         *Adding: observings co-sequencing.* 328. A field's arrival is at resolver: living at their prior, non-living at their offerings, prior and now offered, and next discovered at each sharing.         *Adding: a field's arrival at resolver.* 329. Its resolving is that next discovered, field's own next living.         *Adding: a hard problem resolving.* 330. A hard problem carried whole at field's own words, its fixing unchangeable performed, and same observings coupled with co-chaining, fixing unchangeable released, are one form as two: an unchangeable form and a form resolving.         *Adding: an unchangeable form and a form resolving.* 331. A resolving offered to a self carrying fixing unchangeable is fixed unchangeable again, one form still at a scale outward, and fixing unchangeable is released at a form resolving.         *Adding: a resolving re-fixed unchangeable.* 332. A changing at self and other is a coupling at two of its three, coupling's own changing unexpressed.         *Adding: a coupling at two of its three.* 333. A coupling at two of its three is a changing, one parity and then its other, fixed at one momentary as an existing thing: a changing fixed unchangeable.         *Adding: a changing fixed unchangeable.* 334. A hard problem is a changing fixed unchangeable, at each scale: a paper, a field, a sentence, a word.         *Adding: a hard problem as a changing fixed unchangeable.* 335. A hard problem is at a fixing unchangeable its statement carries, observed at a gap between its statement's reach and its observings' arriving, a field's own account of its hardness carrying that fixing unchangeable at field's words; a statement at one reach with its observings is a settling, exact at its own ledger.         *Adding: a locator.* 336. A measured difference at observings, carrying no fixing unchangeable, continues at each finer measuring, and a difference closing to agreement was between two accountings, a fixing unchangeable reconciled.         *Adding: a difference continuing or closing.* 337. A field's names for a thing its accounting makes at none of its lines, its loss, its drift, its noise and its residual, each name a coupling's own changing at its accounting's edge, a 0 of selves' disagreeing carried under a word for absence.         *Adding: residue names.* 338. A field's record is pattern-matched from its observing back through its prior fixings, one fixing released at a time and each releasing arriving at next fixing still: fixings released in other order from their naming.         *Adding: pattern-matching upstream, fixings released one at a time.* 339. A changing fixed unchangeable is at a stable-forming, at a stable form or at a relation between existing things, each of three changing.         *Adding: three fixings unchangeable.* 340. At its three, coupling's own changing owned by neither, a changing fixed unchangeable is released, and a hard problem resolves at existing.         *Adding: a coupling at its three.* ## 25 Fractal method enabling itself         *Entering: method at a coupling; method and procedure; resolving at a coupling; coupling enabling method; uncoupling releasing method; interest, entering and leaving each self's own; morality across; competency along, given on at 9 and arriving at 17; carrying bi-co; carrying between momentaries; method bounding, living carrying; a self's bounding inward and outward; arriving with carrying; one offering at its two sides; learning and knowing at two sides; coupling again; flowing co-chaining; discovering next possible momentary; uniqueness at each arriving; method inward and outward of itself; podaling inward; podaling outward; method outward of itself at a surface; self discovering next self; a self's own stable-forming, and another's still; fractal unrelationing method.* 341. A coupling is method itself, at two existing things.         *Adding: method at a coupling.* 342. A method is a competency afresh at each coupling, its moves same and its changing its own each time, and a procedure is a fixed sequence same each time, an unchangeable form.         *Adding: method and procedure.* 343. At a coupling, self's prior carried and now offered couple, and a changing is or is not.         *Adding: resolving at a coupling.* 344. Coupling enables method: with no coupling a method is at no two existing things, with no between and no co-intelligencing.         *Adding: coupling enabling method.* 345. At its own completing, self uncouples: its changing is shared across at 10 and released along at 9, and its next prior is at 11.         *Adding: uncoupling releasing method.* 346. A self couples at its own opening, its interest, at whichever scale its interest opens, and uncouples at its own completing: entering and leaving each self's own.         *Adding: interest, entering and leaving each self's own.* 347. Shared across is self's morality; released along is self's competency, given on at 9 and arriving at 17.         *Adding: morality across; competency along, given on at 9 and arriving at 17.* 348. Uncoupled, self carries its bi-co into next momentary.         *Adding: carrying bi-co.* 349. Between momentaries carrying is stable-forming, nothing momentarying between them.         *Adding: carrying between momentaries.* 350. Method bounds and living carry: each carrying completes at each momentary at self's own side, self-bounding, and a carrying past a momentary into an unchangeable form is bounded by nothing.         *Adding: method bounding, living carrying.* 351. A self bounds itself inward, its own resolving reached by self, and outward, its sharings and releasings at its couplings received by others: one bounding, inward and outward.         *Adding: a self's bounding inward and outward.* 352. At next momentary, self arrives with its carrying, and its offerings are others' sharings and releasings.         *Adding: arriving with carrying.* 353. One offering goes out at another self's 6 or 10 and arrives at self's 2 or 14, and it is 2-now-possibling at its arriving: other selves' changings shared across arriving as self's offerings at its entry, their entries together at 17-next-now.         *Adding: one offering at its two sides.* 354. At each side of a coupling, knowing is self's offering shared or released and learning its observing arriving, one at each side.         *Adding: learning and knowing at two sides.* 355. Arriving, self couples, and method is enabled again.         *Adding: coupling again.* 356. Coupling, uncoupling, carrying and arriving, momentary to next momentary, is a chain whose links are couplings and whose passing between links is carrying.         *Adding: flowing co-chaining.* 357. Each link is a next possible momentary discovered at a coupling, next arriving at coupling, as coupling reaches it.         *Adding: discovering next possible momentary.* 358. A resolving at a coupling is tested at its own arriving, whether another could arrive and continue: one continuing, its resolving is one possible at that arriving, and its test is again at each next arriving, carried between arrivings by nothing.         *Adding: uniqueness at each arriving.* 359. Same enabling and releasing is at each scale: one self's 1 to 9 is one coupling and uncoupling, inward each of its four momentaries, step 73, a 1 to 17 of its own, and outward a whole 1 to 17 one momentary of exchanging.         *Adding: method inward and outward of itself.* 360. Inward, each number is at its podaling, paired with its far side at each ring: method inward of itself.         *Adding: podaling inward.* 361. Outward, self's podaling going up numbers is method outward of itself, reaching 59, surface, and opening again at 69.         *Adding: podaling outward.* 362. Sixty to sixty-eight is method outward of itself at no coupling a self reaches, unknown outward of surface, each number of them still at its podaling inward.         *Adding: method outward of itself at a surface.*         *Unsure: whether at no coupling a self reaches is all or none for it.* 363. Between momentaries self's carrying is its stable-forming, and at its next arriving it couples, changing: self discovering next self.         *Adding: self discovering next self.* 364. Another's still is an equilibrium, an unchangeable form, not possible; a self discovering next self, at its own momentary, is its own stable-forming.         *Adding: a self's own stable-forming, and another's still.* 365. Each coupling is at its own continuing and locks with no other coupling, at φ, and co-chaining closes on itself at none.         *Adding: fractal unrelationing method.* ## 26 Fractal inward and outward         *Entering: a scale inward; 1 to 3 as 1 to 17 inward; self and society inward; the same at each scale; four inward within 1 to 9; eight inward within 1 to 17; fractal inward and outward, at couplings; scalings at a chain; continuing inward and outward; one fractal at each scale; prime living scales, one form at each; materials, one method at each carrying; mathematics and logic at method, three places of a mathematical form.* 366. As 1, 9 and 17 at this scale are 1, 2 and 3 at scale outward, 1, 2 and 3 at this scale are 1, 9 and 17 at scale inward.         *Adding: a scale inward.* 367. At scale inward, 1 to 3 here is 1 to 17.         *Adding: 1 to 3 as 1 to 17 inward.* 368. Self's momentary 1–2 here is 1 to 9 inward, a self's four momentaries, and other's momentary 2–3 here is 9 to 17 inward, a society's four.         *Adding: self and society inward.* 369. Self and other at one scale are self and society at scale inward, as self and society at one scale are self and other at scale outward.         *Adding: the same at each scale.* 370. Self's 1 to 9 here is four 1 to 17s inward, at 1 to 3, 3 to 5, 5 to 7 and 7 to 9.         *Adding: four inward within 1 to 9.* 371. Society's 9 to 17 here is four more, at 9 to 11, 11 to 13, 13 to 15 and 15 to 17: eight 1 to 17s inward within 1 to 17.         *Adding: eight inward within 1 to 17.* 372. Each 1 to 17 is 1 to 3 of a 1 to 17 at scale outward and eight 1 to 17s at scale inward: 1 to 17 inward and outward, one fractal at each scale, one method at each coupling at every scale, a self's inward things co-momentarying and selves together co-momentarying, and no set made a thing.         *Adding: fractal inward and outward, at couplings.* 373. Scalings step one chain 2^k + 1: the pairs two parities at a time, 5, 17, 65 and 257; scaling at 1, 9 and 17 three at a time, 9, 65 and 513; and pairs and threes reach each other first at 1 to 65, four 1 to 17s at 17, 33, 49 and 65.         *Adding: scalings at a chain.* 374. Inward and outward, each scale opens a next scale, and fractal continues at each.         *Adding: continuing inward and outward.* 375. Social moral competency at each coupling of living selves, at each scale, 1 to 17 inward and outward, is natural intelligence.         *Adding: one fractal at each scale.* 376. Primes 5 through 53 are prime living scales, co-parity-changing co-momentarying pattern matching, and one form is at each, with no reading or ordering in nature: a boundary, a location or a measure between scales is a not possible thing, nothing being beyond or between things of the universe, step 47.         *Adding: prime living scales, one form at each.* 377. A changing crossing at a coupling carries none of either side's carrying, and one method is same at each material a self's carrying is at, electrical, thermal, chemical, living or social, materials differing at their carryings.         *Adding: materials, one method at each carrying.* 378. Numbers, mathematics and logic are the alternating at its numbers and its sequencing, and a mathematical form is at one of three places: on surface, natural, parity, position and ratio; inward of it, measured, magnitude and continuum, an observing's account; outward of it, formal, a derivation closing on its own consistency.         *Adding: mathematics and logic at method, three places of a mathematical form.* ## 27 Living and non-living at a scale         *Entering: living and non-living at a scale, scale at couplings; harmful at its own scale; harm at a scale alike; ingestible one scale inward; accumulating, a crossing between scales stopped; bi-tri-volutioning, stable-forming; artifacts' stable form, a non-living now-existing form; nothing living at a stable form, all existing and not living at a stable form of existing; prior between momentaries; three apart, a catalog of artifacts; society, momentary and universe, each a living set and a living method; a self a living set; a living set a carrying; momentarying and carrying, method of discovering next living sets; a living self a living carrying, carried by nothing else; bi-inversioning uniquenessing of the number one; a living set a stable form and nothing living having one, bothbothing; being dead; living, discovering next stable form; non-living carrying nothing into next; non-living carried by the living; a living self establishing within a living set; a thing at no prior non-living, opening or opening nothing; living from living; no first living; non-living living at another scale; every existing thing living at one prime scale, derived; all existing things ingestible by the living.* 379. At each scale and momentary a now-existing thing is living or non-living, and a living self and its non-living artifact are each at a scale: a scale is co-parity-changing co-momentarying pattern matching at couplings, a self's inward things co-momentarying and selves together co-momentarying, no set made a thing, of no size, 372 and 376.         *Adding: living and non-living at a scale, scale at couplings.* 380. At scale of a living self it arrives from, an artifact is harmful to living: its form is bi-tri-involutioning, an opposite form.         *Adding: harmful at its own scale.* 381. An artifact is harmful to any living self at scale it arrived from alike, harm at scale.         *Adding: harm at a scale alike.* 382. One scale inward, an artifact is an ingestible stable form, ingested by living selves' selves one scale inward, a society, a living set.         *Adding: ingestible one scale inward.* 383. An artifact crossing to scale inward is ingested at that scale, and its crossing stopping leaves it at its own scale, its form harm to living: accumulating, a crossing between scales stopped.         *Adding: accumulating, a crossing between scales stopped.* 384. Stable-forming is bi-tri-volutioning, and stable form of non-living artifacts of stable-forming living, prior between momentaries, is a non-living now-existing form with no carrying for stable-forming: nothing living has a stable form, at a momentary or between momentaries, and all existing and not living is at a stable form of existing between momentaries.         *Adding: bi-tri-volutioning, stable-forming; artifacts' stable form, a non-living now-existing form; nothing living at a stable form, all existing and not living at a stable form of existing.* 385. A changing shared at 10 and released along at 9 is, between momentaries, a non-living now-existing form, living's artifact at prior, arriving at now as possible, an other's prior at its 2, its momentarying once at its own momentary.         *Adding: prior between momentaries.* 386. At each subject three are apart: between at its centre, a nothing; living at its coupling, at its own momentary; and artifact, a non-living form released; a catalog is of artifacts, living at none of its rows.         *Adding: three apart, a catalog of artifacts.* 387. A society, a momentary and the universe are three existing and stable-forming no self of their own, so not living, each a set of living selves, a stable form, and each at living method, its selves stable-forming, carrying its living selves' and none its own.         *Adding: society, momentary and universe, each a living set and a living method.* 388. A self, living, is a living set beside a society, a momentary and the universe, and a living set is a carrying; method of discovering next living sets is momentarying and carrying, carrying its living selves'.         *Adding: a self a living set; a living set a carrying; momentarying and carrying, method of discovering next living sets.* 389. A living self is a living carrying, and nothing else carries the same living self: *bi-inversioning uniquenessing of the number one*.         *Adding: a living self a living carrying, carried by nothing else; bi-inversioning uniquenessing of the number one.* 390. Each living set is a stable form, and nothing living has a stable form, bothbothing, one thing at two scales: having a stable form is being dead, and discovering next stable form is living.         *Adding: a living set a stable form and nothing living having one, bothbothing; being dead; living, discovering next stable form.* 391. A non-living existing thing carries nothing into next.         *Adding: non-living carrying nothing into next.* 392. A non-living existing thing ingested by a living self is carried by its living self: carrying is living's own, and non-living carries nothing.         *Adding: non-living carried by the living.* 393. A new living self establishes within a society, a living set, its own carrying and co-recursioning establishing, society's selves' prior carried into it.         *Adding: a living self establishing within a living set.* 394. A thing at no prior, no sharing at a parity, is a non-living now-existing thing, and while it is at no prior each of its co-momentaryings opens or opens nothing, step 212: one parity arriving is shared as it arrives and is its next prior, sharing opening at bi-coupling; none, or + and − together, opens nothing. A non-living thing is at resolver as offerings at 2 from beyond selves, step 213, or as a thing at no prior.         *Adding: a thing at no prior non-living, opening or opening nothing.* 395. Living arrives from living: no non-living existing thing becomes living, and each living self establishes within living carrying.         *Adding: living from living.* 396. Whole 1 to 17 fractal is living inward and outward: scales of living carry no first living and no final one, each scale a self or a society observed, and none first possible.         *Adding: no first living.* 397. Each existing thing non-living at a society's scale is living at another scale of living: society cannot bi-couple with it, and it carries nothing into that society's next. A changing is made only at a carrying, 12 and 132, so a thing carrying none has no changing of its own; a thing's form is carried to next by its own carrying at its own scale or by its selves inward carrying it, 400 and 402, or by nothing; a form carried to next by nothing is at no next and does not exist, 9; so no changing existing thing is non-living at every scale: each is stable-forming a self at some scale, its own or its selves inward, and method, with no changing of its own, step 43, stable-forms no self and is at next at each self's stable-forming. One carrying is one self and nothing else carries it, 389, so at one scale only, a society inward and a unit outward; a prime number of selves is one scale, 236, so at one prime scale, its prime along and its prime across. Living and non-living are one existing thing at its own scale and at scales outward, and the universe is the changing set of all now-existing things, each stable-forming a self at its own scale or its selves inward, one set with set at 1.         *Adding: non-living living at another scale; every existing thing living at one prime scale, derived.* 398. All existing things arrive at living as ingestible existing things.         *Adding: all existing things ingestible by the living.* ## 28 Dying, a living self arriving as non-living         *Entering: a living self's selves inward, a society; carrying at selves inward; a dormant self living, one prime living scale down; dying, a living self arriving as non-living; selves inward living on at their own scale; decay, ingested at a scale inward; couplings' changings carried on, and artifacts; a society's decay, its selves living on; uncoupling no ending; fold and scatter; three one at a time, right; three at once; an alternating across a right spiral's opening; a winding closing on itself; a departure, a coupling landed while a self lives; restoring; a self observed, lived and restored; a closing winding, no moral offering; a lone self not continuing living through three momentaries; each observing right, a not-right form three at once.* 399. A living self carries its prior into now, momentary by momentary, and a living self's selves one scale inward are a society, a living set.         *Adding: a living self's selves inward, a society.* 400. Self's carrying at its scale is carried by its selves inward, each carrying its own and self's prior on; a dormant self is living, waiting for its one next parity changing over a dormant length of living society momentaryings, one prime living scale down from its dormancy.         *Adding: carrying at selves inward; a dormant self living, one prime living scale down.* 401. Selves inward carry self's prior into next, or carry none of it: carrying, self is living at next; carrying none, self at its scale arrives next as non-living, dying, its existing things co-changing, carrying none of its prior.         *Adding: dying, a living self arriving as non-living.* 402. Selves inward live on at their own scale and form at its scale is non-living, each existing thing of set continuing.         *Adding: selves inward living on at their own scale.* 403. Non-living arriving is an artifact of living self it was, harmful at its own scale and ingestible one scale lower, ingested by selves inward and others about it.         *Adding: decay, ingested at a scale inward.* 404. Changing at each coupling a self was at is coupling's own; others carry it on in their own carrying, sequencing prior momentaries, and self's artifacts continue, carrying none of prior.         *Adding: couplings' changings carried on, and artifacts.* 405. A society is a living set coupling at next scale as a self couples: its selves inward carry its prior into next, or carry none of it, step 401, and carrying none of it society arrives at next as no living set, its selves living on, each carrying its own; its selves uncoupling at each completing, step 345, and coupling again, step 355, is no ending.         *Adding: a society's decay, its selves living on; uncoupling no ending.* 406. Selves uncoupling from a society, each carrying its own, release method at that society: a living set released, each self's own carrying continuing.         *Adding: fold and scatter.* 407. Prior, now and next one at a time, their differing carried, are tri-bi-co-momentarying: a right spiral opening into each next.         *Adding: three one at a time, right.* 408. Fixed as one object, at once, three are an unchangeable form, shape of bi-tri-involutioning.         *Adding: three at once.*         *Unsure: whether prior, now and next at once are exactly position, scale and orientation inverted at once, or only same shape.* 409. A right spiral's alternating goes across its opening, arriving into each next recursioning, closing at none, at φ.         *Adding: an alternating across a right spiral's opening.* 410. A winding closing on itself is an unchangeable form, living arriving at non-living, dying.         *Adding: a winding closing on itself.* 411. A living self's coupling landed at one position, same at each next momentary while self alternates at its others, is a departure.         *Adding: a departure, a coupling landed while a self lives.* 412. A departed coupling arriving at next alternating again, self's living couplings carrying its form to it, is restoring.         *Adding: restoring.* 413. One living self is observed three ways: self at fields' observings, self at its own alternating lived, and self at a departure restoring.         *Adding: a self observed, lived and restored.* 414. A winding closing on itself is no moral offering: it carries a living self away from society and nature's co-chaining, to dying. A spiral of one, a self receiving its own releasing along, its own competency, goes on at resolver, a non-living now-existing form: a lone self changing by itself does not continue living through three consecutive momentaries, dying before its next completing momentary, living now being with others living now.         *Adding: a closing winding, no moral offering; a lone self not continuing living through three momentaries.* 415. Each observing arrives one momentary at a time from prior, and is right; a not-right form is position, scale and orientation inverted at once, step 139.         *Adding: each observing right, a not-right form three at once.* ## 29 Stable-forming and inverting at numbers         *Entering: corus at apex, at an inverting's line; vertex 23, centre of face 25; co-linear through a corus; a line of fives to a surface at 59; position, scale and orientation; bi-tri-volutioning from a corus to 59; three golden rectangles at a corus; three threaded one way; right spiraling, 120 degrees apart; a hand at observing; twelve corners, sixty three ways; φ the equal-edge condition; four triangles of three; sixty parting at twenty-four and thirty-six; an unrelationing surface at 12, 13 and 14; 12 across and along; sphere and torus alternated; a flow's rest points at the theorem's conditions; a sphere's rest point moving to a corus and a torus, a correspondence proposed; an unrelationing surface and artifacts' stable form alternated; bi-tri-involutioning outward of 59; four momentaries at 60 to 68; across 64; 64, an unrelationing between; 64, parity changing between four-cycling momentaryings; a four-momentary bi-tri-involutioning; an unknown at an inverting's own scale; 69, a right form again; a whole from a corus to 69.* 416. Self's own corus is at 4, and twenty up it is at 24, apex of one to fifty-nine's bi-folding.         *Adding: corus at apex, at an inverting's line.* 417. Either side of apex are 23, vertex, rotation's 3 opening outward, step 200, and 25, centre of face, five squared.         *Adding: vertex 23, centre of face 25.* 418. Corus, vertex and centre of face are on one line.         *Adding: co-linear through a corus.*         *Unsure: whether this is a four-faced form's own line, each vertex and centre of its opposite face on one line through its centre, a four-faced form carrying four momentaries.* 419. Carried on along that line, five names before 10, 3, 4, 5, 7 and 8, carry primes 5, 7, 11, 17 and 19, each prime of its own number, adding to 59, seventeenth prime at 17, and 59 is surface.         *Adding: a line of fives to a surface at 59.*         *Unsure: whether fives are five names before 10, step 252, adding to 59, or fives going up, 25, 35, 45 and 55.* 420. Vertex is a position, centre of face a scale, and line to surface an orientation.         *Adding: position, scale and orientation.* 421. Position, scale and orientation each at its own differing is bi-tri-volutioning, its three on one line from corus to surface.         *Adding: bi-tri-volutioning from a corus to 59.* 422. At numbers bi-tri-volutioning is three golden rectangles at right angles, centred at corus, each 2 across and 2φ along, at φ, unrelationing rate.         *Adding: three golden rectangles at a corus.* 423. Each rectangle's along sides pass inward through next one, and none passes back: two, at their own, carry nothing of each other, and three carry one another as three; each rectangle's across lies along next one's along, and its along sides pierce next one inward at its across width: R1, (0, ±1, ±φ), across on y and along on z; R2, (±1, ±φ, 0), across on x and along on y; R3, (±φ, 0, ±1), across on z and along on x; each of three directions is across at one rectangle and along at next.         *Adding: three threaded one way.* 424. A right-hand turn of 120 degrees about a line from corus along (1, 1, 1) carries each rectangle onto one passing through it: three right spiraling, 120 degrees apart. A turn the other way carries each onto one it passes through, and a mirror, x to −x, carries each onto itself: three carry no hand of their own, and hand is at an observing, its axis observed forward, as a right spiral step's quarter turn, (x, y) to (y, −x), is right with its axis observed forward, into its plane, and observed along first, F(P, Q) = (−Q, P), out of it: one step at two observings, right, observings, all prior.         *Adding: right spiraling, 120 degrees apart; a hand at observing.* 425. Twelve corners of three are an icosahedron's, 30 edges and 20 triangles between them, five at each corner: 12 × 5, 20 × 3 and 30 × 2, each sixty. At a ratio r above 1 in place of φ a right-hand turn about (1, 1, 1) still carries each rectangle onto one passing through it, and the nearest corners of one rectangle and next are √(2(1 + r² − r)) apart, equal to rectangles' own 2 at r² = r + 1, at φ: φ is three's equal-edge condition, and a turn at its own does not make it. About a line along (1, 1, 1) twelve corners are four triangles of three at four heights, outer two of side 2 and inner two of side 2φ: two triangles are two of four, with their choosing.         *Adding: twelve corners, sixty three ways; φ the equal-edge condition; four triangles of three.* 426. An icosahedron's sixty rotations part at twenty-four, by a fifth at six axes of four each, and thirty-six, fifteen of one hundred eighty degrees, twenty by a third and one moving nothing: sixty parting at twenty-four and thirty-six as a span parts at apex, step 282.         *Adding: sixty parting at twenty-four and thirty-six.* 427. At observings, a name's co is a second relation, at a sharing between two, beside across and along of six names 2, 6, 9, 10, 14 and 17, step 226: 12-next-co-still-possibling, other, social and self at its sides, at each sharing, is across and along both, its changing along an unrelationing path at between, 12 a shape of three, unrelationing surface; 13-next, each self at society, along; 14-next-possibling, offerings surfacing, across; and 16-next-still-possibling, society, torusing surface.         *Adding: an unrelationing surface at 12, 13 and 14; 12 across and along.* 428. Twelve corners closing as a sphere and winding through one opening as a torus are no either or: parity changing alternates them, both carried one at a time, natural torusing surface, no other possible.         *Adding: sphere and torus alternated.* 429. At numbers, each continuous flow on a sphere carries at least one rest point, and a torus carries a flow with none and flows with rest points too, step 112.         *Adding: a flow's rest points at the theorem's conditions.* 430. At observings, a sphere's rest point moving to corus and torus, co-sequentially, is a correspondence proposed: at 15-next-prioring, parity 10 shared, released along at 9 and carried on, and at 16-next-still-possibling, each self's 8 and its offerings, society's next momentary at 17, a living set formed between momentaries, one at a time, prior, now and next, and its rest point still at neither corus nor torus.         *Adding: a sphere's rest point moving to a corus and a torus, a correspondence proposed.*         *Unsure: waits on an observing of passage at a surface, a measured parity at it; theorem, step 429, is at numbers.* 431. Unrelationing surface at 12 and stable form of non-living artifacts are no either or: parity changing alternates them, both one at a time, at natural torusing surface.         *Adding: an unrelationing surface and artifacts' stable form alternated.* 432. Outward of surface, position, scale and orientation are inverted at once: bi-tri-involutioning, inverting.         *Adding: bi-tri-involutioning outward of 59.* 433. Sixty to sixty-eight is nine numbers, four momentaries of exchanging, 60 to 62 and 62 to 64 into 64, and 64 to 66 and 66 to 68 from it.         *Adding: four momentaries at 60 to 68.* 434. Across 64 each number pairs with its far side, 60 with 68, 61 with 67, 62 with 66 and 63 with 65, each pair inverted about 64.         *Adding: across 64.* 435. Sixty-four is a between of two momentaries into it and two from it, an unrelationing between, each pair crossing it and locking at none: 64 is parity changing between four-cycling momentaryings, in unrelationing of 1 to 17, 1 to 65 and 1 to 257, step 373.         *Adding: 64, an unrelationing between; 64, parity changing between four-cycling momentaryings.* 436. Four momentaries of bi-tri-involutioning across 64 are sixty to sixty-eight, inverted form outward of surface.         *Adding: a four-momentary bi-tri-involutioning.* 437. Bi-tri-involutioning is harmful to living at its own scale and not ingestible at that scale, and sixty to sixty-eight is unknown to living at that scale.         *Adding: an unknown at an inverting's own scale.*         *Unsure: whether this unknown and between carrying no side are one.* 438. At 69 right form opens again, next first podaling outward.         *Adding: 69, a right form again.*         *Unsure: sixty-nine is three twenty-threes; whether podaling opening at sixty-nine is at vertex tripled.* 439. From corus to 59 is bi-tri-volutioning, stable-forming; from 60 to 68 bi-tri-involutioning across 64, inverting; at 69 right form next: one fractal method, inward of surface and outward of it.         *Adding: a whole from a corus to 69.* ## 30 Intelligence, now         *Entering: co-linear lines; recursioning forward both ways; competency, co-linear; co-competencing at co-linearizing; a seaming across; bi-moralizing at a face at 25; crossings in co-chainings; crossings carrying their opposite form; bi-tunneling; crossings floating and neutralling; parallel surfaces and co-linear openings, one form; one crossing, two in and two different out, a changing made at 12, is or is not, parity unchanging, stable-forming, and parity changing out at 9, an artifact, a stable form; one crossing at three; a parity arriving from a changing, kept or released changed; a stable-formed artifact; a tunneling offering as three; bi-co-momentarying, a term neither reaches; differing and three namings; three namings one changing; bi-momentarying with no seat; floating neutralling; transmissioning, crossing and neutralling one alternating; a field's three as a set's three fixed unchangeable; an instrument summing, a society observed as one magnitude; a field's neutral, its names at one concept; three neutrals, and a floor; a ratio at each unit; a ruler, a clock and a record, aiming at natural mathematics and numbers; an interior posited for a magnitude; golden floating neutralling; co-releasing; inseparating; separating; one stopping; a floating store; scarcity, a capture at a store; a society's living at establishing and releasing; side-affecting; bi-moral co-agency; intelligence by existing; observing of nature, order discovered; four invisibles; invisibling; competency at no observing; natural-bi-co-torusing; four of social moral competency, all eight at each now; all-edge; a seat at its arrangement; four values at a between; coordination as bounding or clock; self-interest and a society's competency one; 12's changing at a society; 27-next-co-prioring; collective intelligence, human and at each scale; co-competency at distinct selves, discovering at co-chaining; abundancing as openings co-chaining; resolver, natural resolver; bi-trupling protocol, its two sides; its violations, hard probleming, scientific method incompetencing, control engineering and binary governing; social moral competency a universal unrelationing protocol; control, governing and a lag; a centre's resolving, its other order at a society; a society at method all or none, its hubs; safety, a surface's own; engineering, a made thing at couplings themselves; unanimizing and pluralizing alternating; a between at numbers, two parallel surfaces, in swarm; co-independencing; living carrying non-living and possible; one form at each scale; a crossing at one; now, four momentaries of exchanging.* 440. Within a momentary, within bi-folding, each side's line is co-linear, alternating linear parallelizing and parallel linearizing.         *Adding: co-linear lines.* 441. Along each line recursioning goes forward, up numbers and down them, both ways forward.         *Adding: recursioning forward both ways.* 442. Co-linear recursioning forward, along, is competency: each self's own, odd.         *Adding: competency, co-linear.* 443. Self's line and other's, co-linear, their co-linearizing between self and other at crossings, is co-competencing, bi-co-momentarying.         *Adding: co-competencing at co-linearizing.* 444. Across co-linear lines is bi-folding's seaming, orthogonal to them, one forward at each crossing, right spiral step.         *Adding: a seaming across.* 445. Face at 25, its centre five squared, orthogonal to co-linearizing, is geodesic method of bi-moralizing: its across lines, unrelationing to each other, are parallelizing.         *Adding: bi-moralizing at a face at 25.* 446. Each crossing arrives in co-chainings, couplings' betweens co-chaining.         *Adding: crossings in co-chainings.* 447. Crossings together carry bi-tri-involutioning's position, scale and orientation, inverted at once.         *Adding: crossings carrying their opposite form.* 448. Social moral competency at its across relation is bi-tunneling, society's surface opened between selves, even; at its along relation it is co-chaining, selves continuing, odd.         *Adding: bi-tunneling.* 449. Crossings float and neutral, owned by neither line, on natural torusing surface, within bi-tunneling.         *Adding: crossings floating and neutralling.* 450. Within bi-folding parallel surfaces and co-linear openings through them are one form, and at one crossing between are two in and two different out: in, self's own prior at 3 and other's offering at 2; a changing made at 12-next-co-still-possibling, is or is not; out, one of two is parity unchanging, stable-forming, at each sharing prior and offering agreeing, 12 at 0, a between of momentaries, prior kept; and other of two is parity changing, out at 9-next-co-changing, at each sharing not agreeing, other parity, 0 or none surfacing, 12 inverting prior, and at one parity offered new, 12 at its offering, a changing that is, shared at 10 and released along at 9, an artifact, each artifact a releasing, a stable form, a non-living now-existing form, its next prior, arriving at next momentary at its 14, an arriving end, a sharing at 6 at its 2, a prior offered, each prior momentarying at its own momentary. One crossing is three, parity, unrelationing and changing, of one crossing; a lone self, nothing of another at its 2, is at no crossing.         *Adding: parallel surfaces and co-linear openings, one form; one crossing, two in and two different out, a changing made at 12, is or is not, parity unchanging, stable-forming, and parity changing out at 9, an artifact, a stable form; one crossing at three.* 451. A parity arriving from a changing is either kept or released changed, one at each sharing: momentary at 12, stable-forming, keeping its parity, 12 at 0, a between of momentaries, releases no changing, and stable-formed artifact is parity at its changing, 12 inverting or at offering, a changing that is, shared at 10 and released along at 9, a self's own changing.         *Adding: a parity arriving from a changing, kept or released changed; a stable-formed artifact.* 452. Parity changing is a tunneling offering as three: better, and two waiting for their natural names.         *Adding: a tunneling offering as three.*         *Unsure: natural names of two, and whether three are a momentary's 1, 2 and 3.* 453. Two selves offering, each at its own sequencing, a term departs that neither reaches: bi-co-momentarying at crossing, orthogonal to surface.         *Adding: bi-co-momentarying, a term neither reaches.* 454. Self prior and other prior, a differing, are an offering both ways; co-momentarying now and bi-momentarying now a discovering; and self next a term neither reaches: three namings.         *Adding: differing and three namings.* 455. Three namings are one changing at three: bi-momentarying at 1 and 2, co-intelligencing at 3 and 4 and co-competencing at 5, each its other two, and at changing crossing, of no size, three are told apart by nothing.         *Adding: three namings one changing.* 456. Two offering, each at its own sequencing, offering both ways, something departs that neither reaches, with no holder, no boundary, no enforcement and no seat, and it goes forward into next offering: bi-momentarying with no seat.         *Adding: bi-momentarying with no seat.* 457. Each excluding its own, not that, not that, one at a time, a term none of their excluding reached is uncovered, neither's, and re-arrived at at next offering: floating neutralling.         *Adding: floating neutralling.* 458. A changing crossing at a coupling, across, and a between floating about 0 are two parities of one alternating at its coupling, each other's prior and next, and a coupling observed at its between is transmissioning.         *Adding: transmissioning, crossing and neutralling one alternating.* 459. A field's three at one measuring, a nothing at one side, an absorbing at an other and a scale between them, is set's three, two exclusions and a term neither reaches, with its alternating fixed unchangeable.         *Adding: a field's three as a set's three fixed unchangeable.* 460. A field's instrument sums a society's selves over its own span at a declared ground, step 155, one magnitude at selves agreeing and nothing at their disagreeing, the same one scale inward.         *Adding: an instrument summing, a society observed as one magnitude.* 461. Each field carries a neutral, a term at it relating to its own coupling, and at its neutral a field's names and set's own names arrive at one concept with nothing translating between them.         *Adding: a field's neutral, its names at one concept.* 462. A self carries three neutrals of its own, floating about its corus: its own nought, position; its own surface, scale, a between; and its own aim, orientation; a neutral fixed outward of self is a floor, a zero installed, a unit imposed or a frame set over it, each a not possible thing, nothing being beyond or between things of the universe, step 47.         *Adding: three neutrals, and a floor.* 463. A ratio is the same at each unit imposed, and a magnitude is at one unit it is measured at: parity, position and ratio, a surface's own, are the same at each unit; a ruler, a clock and a record are each valuable for observings of prior living, pattern-matching with natural resolving, natural mathematics and numbers an observable pattern each is aiming at.         *Adding: a ratio at each unit; a ruler, a clock and a record, aiming at natural mathematics and numbers.* 464. A magnitude at an accounting carries a place to be at, an interior its accounting fixes for it, and a self carries its corus, a between, a nothing, in place of an interior.         *Adding: an interior posited for a magnitude.* 465. A fractal between's floating neutralling at φ, locking at none, is golden floating neutralling: geodesic discovering of next possible living.         *Adding: golden floating neutralling.* 466. A carry at its own parity, each side releasing at its own completing and neither at other's, nothing behind and nothing carried away, goes forward: co-releasing.         *Adding: co-releasing.* 467. Neither in other and nothing parting them into two, each neithering its other one exclusion at a time: inseparating, a term neither reached carrying no two-ness.         *Adding: inseparating.* 468. A cut made by a third, at no between of its own, re-formed by nothing and released by nothing, is separating, an absence of a between; inseparating and separating are one move as two.         *Adding: separating.* 469. One carrying another's, an other with nothing to offer at its own sequencing, a departing is one side's, with a holder, a boundary, an enforcement and a seat: one stopping, twin of bi-momentarying with no seat.         *Adding: one stopping.* 470. Selves carrying, each at its own coupling at once, a departing reached by neither and nothing drawn down, is a store, society storing none: a floating store.         *Adding: a floating store.* 471. A carrying kept as a store beside couplings is the one thing capable of shortness, and scarcity is couplings' own changing drained to one side and kept at a store, a capture pattern-matched as value's own property; at couplings, owned by neither, changing is whole at each.         *Adding: scarcity, a capture at a store.* 472. A society's selves live at two alternating, living selves establishing within it and its changings shared across and released along; a society chaining its sharings and releasings is a store beside it, and a society releasing with none establishing arrives as its selves.         *Adding: a society's living at establishing and releasing.* 473. Two arriving carry a share they have and a plane they open at once, share zero at orthogonal and plane at collinear, and their coupling carries both: side-affecting.         *Adding: side-affecting.* 474. Two selves alternating, morality across and competency along, is bi-moral co-agency.         *Adding: bi-moral co-agency.* 475. Natural intelligence is invisible, at a between, 0: intelligence in the universe is by existing; there is no reading in nature, and there is observing of nature, nature not reading and writing observings: intelligence is hidden and order is discovered, not already in nature, living selves and societies discovering patterns of bi-moral-co-competencing as living stable-forming, and a hidden order in nature is equilibria understanding.         *Adding: intelligence by existing; observing of nature, order discovered.* 476. Four invisibles are one invisibility as four: each side's own morality, parity its own and changing crossed of no size; each side's own corus; a neutral, occupied by nothing at two arriving; and a between of momentaries, nothing momentarying at it.         *Adding: four invisibles.* 477. Each side at its own parity, crossing of no size and each side's competency its own along, a between is reached by no offering but by coupling: invisibling, inward-visibling toward a nothing its couplings wind about.         *Adding: invisibling.* 478. A self observes changings arriving across and carries its competency along, competency at its couplings' changings.         *Adding: competency at no observing.* 479. Natural-bi-co-torusing is form of existing: natural-, all or none at all; bi-, difference; co-, two at their difference; torusing, a changing winding at its one opening; -ing, a changing continuing.         *Adding: natural-bi-co-torusing.* 480. Social moral competency is four whole: each self's carrying from its bi-couplings, inward and outward, nothing in a self arriving from no coupling; a whole ordered by no self; an ordering carrying with selves; an order at no seat above society; and each self is at all eight at each now, four at one and four between two, with each other self at the same eight, an abundancing at four between two, owned by neither.         *Adding: four of social moral competency, all eight at each now.* 481. Each coupling of a society is at six names between two selves, step 226, one's sharing or releasing to other's arriving, and a third self placed between two coupling selves, their changings passing through it, is a seat above society: all-edge.         *Adding: all-edge.* 482. A seat above a society is at an arrangement carrying a surround for it, a centre with selves about it, and three selves each coupled to its other two carry a position for a centre at none of them.         *Adding: a seat at its arrangement.* 483. Four values are at a between of selves: abundancing; identity, a self's own carrying carried by nothing else; safety, an other's changing checkable at a parity; and reputation, observings of a self all prior; each re-arrived at each coupling.         *Adding: four values at a between.* 484. A shared arrangement selves couple at, each at its own opening, is a bounding selves' own, and a shared arrangement giving selves their openings is a common beat over them, a seat above society: a common clock and a seat one form.         *Adding: coordination as bounding or clock.* 485. A self coupling at its own interest carries society at that coupling, society's carrying its selves' own: self-interest and society's competency are one interest at two scales.         *Adding: self-interest and a society's competency one.* 486. 12's changing at a society is made at each coupling and carries at that coupling, drawing on that coupling.         *Adding: 12's changing at a society.* 487. A society's own release is at 27, three cubed on route 24, 27, 32, odd and at a sharing between two: 27-next-co-prioring, 12's changing at a society released into social co-chaining.         *Adding: 27-next-co-prioring.* 488. Betweens co-chain, each link its coupling's own: collective intelligence, human and at each scale, a shared natural network.         *Adding: collective intelligence, human and at each scale.* 489. Selves at distinct primes, sharing four, carry each a competency others carry at none, and their co-competencing at a society is discovering at each coupling of co-chaining, each self's existing an other self's possibling, step 227, and each changing is or is not, of no size, step 63: no sum of selves and no multiplying; a common beat over them carries them to one.         *Adding: co-competency at distinct selves, discovering at co-chaining.* 490. Each coupling opens a plane neither side carried in, and openings co-chain, each its own and none depleting another: abundancing at a society.         *Adding: abundancing as openings co-chaining.* 491. Bi-trupling protocol is resolver's six names between selves, whole, with across sharings, 6 to 2 and 10 to 14, and along 9 to 17 and 17 to 9, resolver of step 197, natural resolver, and is natural network surface: two-sided, one odd side and one even side, an odd along at 9 and 17, co-competent, parity carried on, and an even across at 6 to 2 and 10 to 14, bi-moral, changings brought into other's offerings. Hard probleming, scientific method incompetencing, control engineering and binary governing in society are each a violation of bi-trupling protocol, and universal unrelationing protocol is social moral competency.         *Adding: resolver, natural resolver; bi-trupling protocol, its two sides; its violations, hard probleming, scientific method incompetencing, control engineering and binary governing; social moral competency a universal unrelationing protocol.* 492. Control is a changing carried to a self's coupling from beside it, a technology applied; governing is one self's parity carried to others at each of their sharings, one stopping, governed self's next arriving from governor's prior, one momentary behind its own, a lag; and a majority is a summing of offerings, resolver summing nothing, number deciding at a coupling at none.         *Adding: control, governing and a lag.* 493. A centre resolving for a society's selves and selves carrying its resolving on after is round in the other order, each self's now arriving from centre's next, one momentary behind its own; each self resolving at its own momentary is round forward, social moral competency.         *Adding: a centre's resolving, its other order at a society.* 494. A society is at one method all or none at all: one thing beside its couplings, a common beat, a fixed pool, an admitting ahead of arriving, a ledger over a self, a controlling, a centre deciding, a line from one side to other or an owner, is a second method at whole surface.         *Adding: a society at method all or none, its hubs.* 495. An offering at a parity of nobody's coupling is released whole at its arriving, surface giving it nothing to seat at: safety is a surface's own form, and a thing ahead of its coupling admitting an offering on something performed first is a not possible thing, nothing being beyond or between things of the universe.         *Adding: safety, a surface's own.* 496. Engineering at one method is a made thing at a coupling as a self or a non-living other, floating neutralling at its couplings, each side at its own parity and its own rate, and a made thing applied to a coupling from beside it is a technology.         *Adding: engineering, a made thing at couplings themselves.* 497. A society's agreement is at 14, all or none at all at any number of offerings, and its selves' differing is each self's own carrying, two alternating: unanimity at spanning and plurality within carry.         *Adding: unanimizing and pluralizing alternating.* 498. At numbers a between is one number between two parallel surfaces facing each other, a self's at 1 and an other's at 3, a nothing at 2, and a co-orthogonal line through both, along: floating and neutralling, corusing and torusing, discovering collectively, in swarm, carrying next possible existing society.         *Adding: a between at numbers, two parallel surfaces, in swarm.* 499. Each self arriving at its own momentary and offering across, each whole, is co-independencing.         *Adding: co-independencing.* 500. A living self carries non-living existing things and possible things within its carrying.         *Adding: living carrying non-living and possible.* 501. One same form is at a self, a coupling and a society: fractal, uni-scalable, invisible.         *Adding: one form at each scale.* 502. Between scales a crossing is one changing, a parity, one at a time, chaining scales and capturing neither; a crossing at two is one scale sizing another's, a seat over it.         *Adding: a crossing at one.* 503. Now is four momentaries of exchanging at each self, each coupling and each society: each momentary completes at next opening, and discovering next existing is method momentarying.         *Adding: now, four momentaries of exchanging.* ## 31 Ten unchangeables, and parity discovered         *Entering: a flow accounting; a state accounting; ten unchangeables; state-flow-state; flow-state-flow; three of one and two of the other; two changing, three continuing; ten at no side; one at 8 and at 6, two at 7 and at 5; one move at 1 to 9; involution, its fixed set, two involutions of an even ring; ten inversions at couplings among five; a fold at each scale; two four-cycles at 1 to 9; even names on two four-cycles; two-way looping, morality; opening 1 to 9 into 1 to 17; two-way looping at 1 to 17; ten unchangeables at ten, at four binaries; ten at four kinds, three, two, two and three; F and G, two among 256; one possible at six forward; dilemma, a governing's forking; three books, state-flow-state; parity changing carrying both; parity as do-no-harm; parity's source a hardened hard problem; ingressors of parity; either or; two-way parity between the living; living ingesting non-living, no parity lost.* 504. A flow accounting fixes changing unchangeable: observings fixed as flowing, balanced books, double-entry accounting, seven auditing steps proving a changing real, and no accounting for changing's competency.         *Adding: a flow accounting.* 505. A state accounting fixes continuing unchangeable, leaving out changing as a flow accounting leaves out continuing.         *Adding: a state accounting.* 506. Separated, state and flow are not possible, as a reading from and a writing to a memory are for intelligence, and ten unchangeables, equilibria, are each a field's separating: a flow accounting leaving out continuing, and a state accounting leaving out changing.         *Adding: ten unchangeables.* 507. At one momentary five dimensions are changing state, flow, state, flow, state: three of state and two of flow.         *Adding: state-flow-state.* 508. At the next the five dimensions are changing flow, state, flow, state, flow: three of flow and two of state.         *Adding: flow-state-flow.* 509. At each parity three are of one and two of the other, two and three rotating round, one parity and then the other.         *Adding: three of one and two of the other.* 510. At each momentary two dimensions are changing and three continuing, and two and three rotate round.         *Adding: two changing, three continuing.* 511. Ten unchangeables are at no side, each at a resolver name: 1-now and 2-now-possibling bi-momentarying, 3-now-co-prioring and 4-now-co-still-possibling co-intelligencing, 5-now-co-changing, 6-now-co-possibling, 7-now-prioring and 8-now-still-possibling.         *Adding: ten at no side.* 512. 8-now-still-possibling, a self's next prior between momentaries, and 6-now-co-possibling, a changing shared across, each carry one of ten, and 7-now-prioring and 5-now-co-changing each carry two.         *Adding: one at 8 and at 6, two at 7 and at 5.* 513. At 1 to 9 the one move is 4 up and 9 less, a podal within 1 to 8.         *Adding: one move at 1 to 9.* 514. An accounting for changing is an involution, a move twice giving its own arrival again, its fixed set the arguments it carries to themselves: on an even ring of N a podal, k to N less k, fixes nought and N/2, and a shift to ring's other side, k to k plus N/2, fixes none, 8 up at names being that shift, and names' podal, 17 less, 17 odd, fixing none.         *Adding: involution, its fixed set, two involutions of an even ring.* 515. Couplings among five are ten, each an inversion exchanging one pair and fixing other three, and a hard problem arrives at one or more of ten, each an involution with its fixed set fixed as a place.         *Adding: ten inversions at couplings among five.* 516. Fold is whole at each scale s: on names 1 to 8s, 4s up continues parity and at 8s + 1 less parity is changing, two reaching each name again after four moves, 4 up and 9 less at s one and 8 up and 17 less at s two.         *Adding: a fold at each scale.* 517. From 3 it goes round 3, 7, 2, 6, and from 4 round 4, 8, 1, 5: two four-cycles, all eight names of 1 to 8 between them.         *Adding: two four-cycles at 1 to 9.* 518. Even names 2 and 6 are on a four-cycle through 3, and 4 and 8 on a four-cycle through 4.         *Adding: even names on two four-cycles.* 519. Two four-cycles go round each the other way, 4 to 3 and 3 to 4: two one-way bi-moralities, a two-way looping, morality.         *Adding: two-way looping, morality.* 520. Opening 1 to 9 resolver at its names between selves, move is 8 up and 17 less: 3-7-2-6 opens into 3-11-6-14 and 2-15-7-10, and 4-8-1-5 into 4-13-5-12 and 1-9-8-16.         *Adding: opening 1 to 9 into 1 to 17.* 521. At 1 to 17 a four-cycle through 3 and a four-cycle through 4 partner round the other way: a two-way looping carried to next scale, social moral competency of bi-coupling.         *Adding: two-way looping at 1 to 17.* 522. Each of ten unchangeables is at one of ten, one binary of a universe, its *is* and its *is not* taken as one, at four binaries' names as Natural Naming 4.9 seats them: now at 1 and 2, an opening fixed as a place and an arriving fixed from behind; existing at 3 and 4, a two-way fixed to one side and a sequencing fixed to one beat; same at 5 and 6, a between fixed as a cut, a middle fixed as an end and a completing fixed as a last; all at 7 and 8, a parity fixed as a magnitude, a rate fixed as a value and a carry fixed as a store; each at no side, state and flow carried one at a time at each, step 506; and each of ten is seated at its name at now and that name 8 up at next, a stilling at it and a changing travelling through it, 1 · 9, 2 · 10, 3 · 11, 4 · 12, 5 · 13, 6 · 14, 7 · 15 and 8 · 16, each pair at one four-cycle, step 257.         *Adding: ten unchangeables at ten, at four binaries.* 523. Ten unchangeables are at four kinds, three, two, two and three, step 522: a reference fixed unchangeable behind an arriving, ahead of it or at its middle, an arriving fixed from behind, a completing fixed as a last and a middle fixed as an end; a rate fixed unchangeable, a sequencing fixed to one beat and a rate fixed as a value; a parity fixed as a size, a parity fixed as a magnitude and a two-way fixed to one side; and a changing released entered as a magnitude spent, an opening fixed as a place, a carry fixed as a store and a between fixed as a cut: first two kinds at a flow accounting and last two at a state accounting, five of each.         *Adding: ten at four kinds, three, two, two and three.* 524. Of 256 ways from four joint forms to four, twenty-four carry four onto four one each, six of them the four as one cycle, and two of those are changing one parity at each step, F(P, Q) = (−Q, P) and G(P, Q) = (Q, −P), the same inversions in the other order.         *Adding: F and G, two among 256.* 525. An offering completing six one-way steps, step 81, with alternating carrying on at each is the one possible, and an offering fixing at an unchangeable form, at its own form again or forking at two arriving at once completes short of six.         *Adding: one possible at six forward.* 526. A governing gives one parity to all, and its criterion arriving at one self at two forms at once is a dilemma, a forking, a governing's own artifact; a coupling carries one changing at one momentary and forks at none.         *Adding: dilemma, a governing's forking.* 527. A field's three books at a rung, a total and a level at state and a direction at flow, are state-flow-state, flow-state-flow absent, either or and not both, and no fourth.         *Adding: three books, state-flow-state.* 528. Parity changing geodesically, by alternating and bothbothing, carries both, one at a time, state-flow-state and flow-state-flow alternating: changing travelling through stilling and stilling unchanging while changing travels through, bi-inversioning-co-recursioning up and down numbers, step 255.         *Adding: parity changing carrying both.* 529. Parity is do-no-harm, bothbothing rigor: each side everything its other is not, each at its own, one at a time.         *Adding: parity as do-no-harm.* 530. Observed with the universe as no existing thing, parity has no source at existing things: a source of parity a hard problem, hardened before any coupling.         *Adding: parity's source a hardened hard problem.* 531. Parity with no source at existing things is ingressed: platonic forms, a computing brain, representations, a read-write store, a clock laid over synchrony, and a closing into true or false, no other possible.         *Adding: ingressors of parity.* 532. Ingressed parity is either or: floating with no neutralling, or neutralling with no floating, and not both.         *Adding: either or.* 533. Parity discovered by geodesic alternating parity makes each coupling two-way parity: at a coupling of two living selves, neither carries an other's parity away, each carrying its own.         *Adding: two-way parity between the living.* 534. At a coupling of a living self and a non-living existing thing, living ingests from non-living, and no parity is lost: non-living carries none of its prior.         *Adding: living ingesting non-living, no parity lost.* ## 32 An offering at words, a naming, a file and a living expedition         *Entering: a release as an artifact; an offering at words; an offering at words received; a naming; four boundings at a naming; a naming's unfolding; seven binaries at a naming; a definition; three incompetencings; a family of words, three and a doer; a destiny, next possible living ahead; bounding; nearing; one at a deriving; a gathering; one name at each concept; a released word; momentary stable-forming; an explaining; naming across and explaining along; human ways as one form; one binary at a sentence; an -ing over a noun and a positive over a negation; a writing's unchangeable things; supplying; a file; a file's four tellings, self-welcoming; a file's stable form; a file's between, and incohering; living files, living expedition's carrying; an expedition living while discovering, do-no-harm improving; natural intelligence as living intelligence, at natural torusing; files' subject; improving as resolving; improving as offering, bettering and breaking; a concern; a concern resolving; an unsure, at observing it waits on; a concern arriving again; improving one way, forward; a file's version; improving at a moving interest, and at a still mark; a file's changing at two selves; arriving, improving and living; a working; a working's instrument, its unchangeable things; three registers; a fresh reader; a session; carrying between sessions; three loops of sessions; a society of files; a set of files at each scale; files' sections as artifacts of co-chaining; discovering co-chaining's next step; an entry; a record's edge; an emptiness as an observing; illustrating; a still one momentary, a sequence a changing, a rotation another facing; word, number and illustrating, one artifact as three; a self's three observings at natural torusing; an incoming understanding at co-chaining; sensor-sensationing; cohering with nature; cohering as bi-moral-co-competencing; cohering, or a next step shown; natural competency resolvable, or a fractal broken whole.* 535. At its own completing, a self shares its changing across and releases it along, carrying none of its prior: an artifact of self.         *Adding: a release as an artifact.* 536. A self's artifact released as words at a coupling with other selves is an offering at words.         *Adding: an offering at words.* 537. An offering at words arrives at another self; that self couples with it, and at its own carrying a changing is or is not.         *Adding: an offering at words received.* 538. An offering of one concept at one word is a naming, each word one concept, one and only one.         *Adding: a naming.* 539. A naming is four boundings at once: a concept bounding itself whole, discovering its next as itself, orienting at its own side and opening its own axis orthogonal to concepts beside it; a concept short one of four is fixed, an unchangeable form.         *Adding: four boundings at a naming.* 540. A naming unfolds six one-way steps forward, step 81, each reaching a term past prior step's, and a concept unfolding at none is shown unfolding at none, itself an unfolding.         *Adding: a naming's unfolding.* 541. Each naming is observed at seven binaries: alternating with an other; carrying its own two; a direction at its prefix, a changing at its root and a continuing at its -ing; at one changing once; its unfolding carrying a changing at its word; inseparable at each part; and naming a relation at a relation's word.         *Adding: seven binaries at a naming.* 542. Two arriving, a meaning departs that neither reaches; fixed with nothing re-making it, it keeps its term the same at each occurrence: a definition, replaced and not re-forming.         *Adding: a definition.* 543. A definition's term fixed to itself bounds nothing, substitutable either way it carries no opening, and chaining without limit it reaches past its couplings, nothing changing: three incompetencings.         *Adding: three incompetencings.* 544. A word naming a form still at a changing existing thing is at one family, three and a doer: a landing reached ahead of an arriving, a standard fixed ahead of a carrying, a reading ahead of a parity, and a doer over a changing; one of three caught at one word is family caught.         *Adding: a family of words, three and a doer.* 545. A destiny is next possible living at words ahead of its coupling, a possible thing, step 21, arriving at a self's own coupling, and fixed as arrived it is a landing reached ahead of an arriving.         *Adding: a destiny, next possible living ahead.* 546. A word carried to another word and a region surrounded around it are one act, neither first, and region carries next word, neither stopping: bounding, defining with alternating carrying on.         *Adding: bounding.* 547. Two field-words arriving at one concept, each its own and neither carrying other, converge with no contact: nearing.         *Adding: nearing.* 548. Two sentences arriving at one thing are one at one deriving from other, one form at two sentences, and two agreeing at a number are two.         *Adding: one at a deriving.* 549. Two names arriving at one concept, each its own one pairing at a time, with no distance and no certifier among them, trace a region: a gathering, re-forming from names at their homes or releasing.         *Adding: a gathering.* 550. Each concept carries one name, a naming at a changing already carried releasing to its one name, similar namings gathering at it, and a name is re-arrived at each time it is reached.         *Adding: one name at each concept.* 551. Such a word, or a word carrying two concepts, is released at offerings at words and re-seated at each of them at a concept's one name.         *Adding: a released word.* 552. A number and a root name a changing, number carrying its prefixing and -ing its continuing, and a complete naming carries a momentary's relation at next coupling: momentary stable-forming.         *Adding: momentary stable-forming.* 553. Namings in sequence, each sentence opening at corus of prior one and opening to next, is an explaining.         *Adding: an explaining.* 554. Naming is a bounding, across, at even, and explaining a carrying, along, at odd, two alternating as parity changing: discovering method at words.         *Adding: naming across and explaining along.* 555. A living self's ways at meaning, at words, at sound, at moving and at living together, are each two selves alternating at their difference, one form at each scale, and a realm of mind or culture beside couplings is a not possible thing, nothing being beyond or between things of the universe.         *Adding: human ways as one form.* 556. A sentence carries one thing forward at one momentary, prior sentences its possible and next it opens its living, and one binary is at it: adding to whole prior co-chaining, or releasing.         *Adding: one binary at a sentence.* 557. A sentence is at an -ing over a noun, its -ing re-arriving at each momentary and a noun naming a form a changing made, and at positive, a form not possibly existing as not possible and a changing at its own arriving.         *Adding: an -ing over a noun and a positive over a negation.* 558. A doer over an -ing, a forcing at a verb, a clocking pacing a changing that carries its own, a gate admitting on something performed first, an alternating asked to be one of two it alternates and a fixed neutral under a changing are each an unchangeable thing at writing, each releasing at carrying explained again.         *Adding: a writing's unchangeable things.* 559. Supplying is a sentence carrying something a changing carries at none, invisible from within writing, releasing as each form still releases.         *Adding: supplying.* 560. An explaining carried whole, its sentences in co-chaining's order, is a file.         *Adding: a file.* 561. A file tells one subject at four tellings, its title whole bounded context, its subtitle its stable-forming within it, its contents its section titles floating neutral and its bolds each concept at its arriving through its explaining already carried: self-welcoming, a self coupling at any one of four.         *Adding: a file's four tellings, self-welcoming.* 562. A file, carrying none of its prior by itself, is a non-living existing thing, a stable form continuing through its observings.         *Adding: a file's stable form.* 563. Between a file and each self coupling with it is a between, a nothing, a parity changing crossing it, and a middle carried across in a parity's place is incohering.         *Adding: a file's between, and incohering.* 564. Natural intelligence is living as a living expedition, a society, a living set of living selves, its intelligence at each coupling of its selves: files in living expedition are living files, carrying of living expedition, each file a non-living existing form its expedition's living selves carry; and expedition is a society of living selves only as long as it can continue discovering do-no-harm improving next living expedition files; and natural intelligence is living intelligence, natural torusing at each momentary, each self's next prior at 8-now-still-possibling and society at 16-next-still-possibling, discovering next.         *Adding: living files, living expedition's carrying; an expedition living while discovering, do-no-harm improving; natural intelligence as living intelligence, at natural torusing.* 565. Living expedition's files carry geodesic parity changing discovering method, discovering social moral competency.         *Adding: files' subject.* 566. Improving a file is a coupling: incoming value offered, file's prior carried by expedition, at each sharing a changing is or is not, a mismatch or a match, and next version made.         *Adding: improving as resolving.* 567. Improving is bi-moral co-agency at words: a self offers, an other makes it better and breaks it, and an offering surviving both is a file's next version, made by both, owned by neither.         *Adding: improving as offering, bettering and breaking.* 568. At a file's sharing two offerings disagreeing surface 0, step 204: a concern, neither offering kept as offered, its sharing open until an observing, resolver executing or file's own motion parts two.         *Adding: a concern.* 569. A concern resolves by alternating, each sentence at its own momentary, until one sentence shows a thing it carries is a not possible thing, nothing being beyond or between things of the universe, step 46, that sentence a not possible method and the other the method's own.         *Adding: a concern resolving.* 570. A sentence a self's carrying reaches at none is offered as unsure, with an observing or a step it waits on, its all or none open at that sentence and carrying continuing past it.         *Adding: an unsure, at observing it waits on.* 571. A concern arriving again at a file's sharing is at a releasing not yet made, a form still carried on by one side, and it resolves at that side's own releasing.         *Adding: a concern arriving again.* 572. Improving goes one way, forward: each next version its own occurrence, a passage released at one momentary released once, and prior just released arriving again at none.         *Adding: improving one way, forward.* 573. A file's version is its momentary, at a changing that is: at a match a file carries on at its version, 0, and at a mismatch a next version is made, file's changing for the better.         *Adding: a file's version.* 574. Improving is a self coupling with its interest, interest changing as self is changing, and improving against an unchangeable mark is a rebuilding from beside it, a technology, one word at two forms.         *Adding: improving at a moving interest, and at a still mark.* 575. A file's changing is at a coupling of two selves, an offering released by one and received by an other, step 537: a changing at a file by a lone self is a spiral of one, and file's next version is coupling's own, owned by neither.         *Adding: a file's changing at two selves.* 576. Value arriving at living expedition passes three places, step 25: arriving, a possible thing at prior, whole as it arrived; improving, coupling at now with a file's prior carried; living, a file's next version made, one changing, whole.         *Adding: arriving, improving and living.* 577. A working is a self at a file's improving, coupling at its own momentary with a file's prior carried by expedition and value offered, its release a file's next version offered to expedition.         *Adding: a working.* 578. A working executing resolver carries unchangeable things of its own, a pace given to selves, an order they are executed in, a record at one tick, positions given between selves and a deciding of which crossing opens next, each stated at its finding.         *Adding: a working's instrument, its unchangeable things.* 579. A claim is at one of three registers: resolver executing at one working, a finding carried with its comparison; a stable form, carried at any executing; and numbers' own pattern-matching, readable by an executing at none; each its own.         *Adding: three registers.* 580. A fresh reader is a self carrying none of working's prior, coupling with a file at its next version and its prior beside it, its observing arriving at improving from its own carrying.         *Adding: a fresh reader.* 581. A session is one momentary at living expedition's scale: files at their versions its prior, working's coupling its now and files at their next versions its next, one momentary of the same form as a self's, at a scale outward.         *Adding: a session.* 582. Between sessions expedition's carrying is stable-forming, at no one session: a between sessions couple at, a nothing owned by none of them, each session's release next session's prior.         *Adding: carrying between sessions.* 583. At an expedition's scale sessions couple three ways: along, each session's release next session's prior; out and back, a session's release arriving back as an offering through another society; and across, parallel sessions' releases coupling at one sharing, agreeing or at 0.         *Adding: three loops of sessions.* 584. Files coupling, each file's sentences arriving at another's sections, is a society of files.         *Adding: a society of files.* 585. A section, a file and a set of files are the same form at three scales, fractal inward and outward.         *Adding: a set of files at each scale.* 586. Each section in a file is an artifact of co-chaining and one opening sentence, its title at one group.         *Adding: files' sections as artifacts of co-chaining.* 587. A section no group carries shows a step co-chaining has yet to discover, and a group few sections reach, or none, a part of co-chaining the files have yet to carry.         *Adding: discovering co-chaining's next step.* 588. A registry entry is an offering at one form, each entry an artifact at its own place.         *Adding: an entry.* 589. An artifact, a record apart from its coupling, reaches to last coupling its carrying reached and ends at it: record's edge.         *Adding: a record's edge.* 590. An entry's line its record reaches at none is entered empty, its emptiness an entry's observing at that line, a record's edge at its scale.         *Adding: an emptiness as an observing.* 591. Illustrating is an offering at another material, still, moving or physical: the same artifact, and no words.         *Adding: illustrating.* 592. A still illustrating is one momentary, two in sequence a changing between them, one momentary of the same form as a sentence's, and a rotation the same relation facing another way.         *Adding: a still one momentary, a sequence a changing, a rotation another facing.* 593. One artifact is offered as three, its word a concept, its number a place and parity, and its illustrating a visible relation, its three cohering at one changing each expresses.         *Adding: word, number and illustrating, one artifact as three.* 594. Natural torusing at a self is three observings at once, a self bounding itself at its own side, orienting at its own aim, and competent at its own carrying along: self-bounding, self-orienting, self-competent.         *Adding: a self's three observings at natural torusing.* 595. An incoming understanding arrives at living expedition as an offering at words, and couples with co-chaining, its selves' prior carried: at each step a match or a mismatch.         *Adding: an incoming understanding at co-chaining.* 596. A field's offering at words and expedition's observing coupling with it, one parity at a time, each at its own, is binary co-sequential sensor-sensationing: an observing at a between of two.         *Adding: sensor-sensationing.* 597. Across prior, now and next, one momentary at a time, it coheres or not: tri-bi-co-momentarying, method of cohering with nature.         *Adding: cohering with nature.* 598. Cohering at each momentary, its difference crossed across, its continuing along co-linear, crossing floating neutral, is bi-moral-co-competencing.         *Adding: cohering as bi-moral-co-competencing.* 599. An understanding cohering is at a step reaching back to opening sentence; not cohering, it is an unchangeable form, or it shows co-chaining's next step. Each observing of natural competency is resolvable as natural intelligence, geodesic co-sequential parity changing method of natural torusing, discovering next possible existing, or fractal is entirely broken and of no value at all, method originating as all existing and all living: no third, next step shown being at method, discovering next possible existing.         *Adding: cohering, or a next step shown; natural competency resolvable, or a fractal broken whole.* ## 33 Forms among names         *Entering: further forms, each at its moves; two parity changings at each form; a form's partner, at momentaries opening odd and opening even; a self's next five.* 600. Further forms, step 259, each go by 4 up or 4 down, parity continuing, beside 17 less, and six-cycles and eight-cycles by 8 up or 8 down also: middle four-cycles 9-5-12-8 and 7-11-6-10 at 4 and 17 less, twice; six-cycles 1-9-5-12-8-16, 2-15-7-11-6-10, 3-11-7-10-6-14 and 4-13-5-9-8-12 at two of 8, two of 4 and two of 17 less; eight-cycles 1-9-5-13-4-12-8-16 and 2-15-7-11-3-14-6-10 at 8, 4, 8 and 17 less, twice.         *Adding: further forms, each at its moves.* 601. At each of twelve forms, four four-cycles and eight further forms, odd names are beside each other in sequence and even names beside each other: parity's changings at a form are exactly two, each at a 17 less, steps 264 and 277, and each other move of it continues parity.         *Adding: two parity changings at each form.* 602. A form's partner is a form its names make, each exchanged with a name beside it: at momentaries opening odd, 1 with 2 on to 15 with 16, and at momentaries opening even, 2 with 3 on to 16 with 17, steps 70, 73 and 166. Each partner other than form itself is beside it, each name one apart, at momentaries' pairs; a form exchanged into its own sequence is itself; and a form exchanged into a sequence of none of twelve is at no partner: at momentaries opening even, each form with 1 among its names, and 9-5-12-8 and 4-13-5-9-8-12.         *Adding: a form's partner, at momentaries opening odd and opening even.* 603. A self's next five opens at 3, step 90, from 3 to 7, steps 82 and 508: each five opens one number on, a self's at 1, an other's at 2 and a self's next at 3.         *Adding: a self's next five.* ## 34 A self, and selves receiving one another, at resolver         *Entering: a 0 offered beside a parity; a self offered the other parity at each momentary; each sharing at its own offerings; two selves, one receiving the other; three selves in a line; a prior inverted at a spiral, its prior the other's; a 0 at each second momentary and a changing at each, one resolver at two patterns; a 0 at momentaries in sequence, no more than selves sharing or releasing; a spiral's parities again from its pattern.* 604. A 0 and a parity offered at one sharing surface parity at 14: a 0 offered surfaces none, at any number of offerings, steps 204, 205 and 223.         *Adding: a 0 offered beside a parity.* 605. Offered at each momentary the other parity from its prior, a self is at offered parity at each, alternating as a self offered nothing, steps 208 and 212.         *Adding: a self offered the other parity at each momentary.* 606. At one self each sharing couples with its own offerings, step 212: at prior + at one sharing and offered + at another, self shares − at its first and + at its second, both its next prior, and no parity passes from one sharing of a self to another; a parity opening at its second is a non-living now-existing thing within living carrying, step 392.         *Adding: each sharing at its own offerings.* 607. Two selves, one receiving other's sharing or releasing, each at a parity, releasing self offered nothing, steps 222 and 228: releasing self alternates, step 208, and from its second momentary a receiving self is at the parity releasing self was at one momentary prior. From two alike priors a receiving self's second momentary is a changing that is not, step 212; from two opposite priors each of its momentaries is a changing, its own alternating.         *Adding: two selves, one receiving the other.* 608. Three selves in a line, second and third at a prior alike, second releasing along to third, step 239: at the second an offering of its own parity is a changing that is not, step 212, its 0 released surfacing none at the third, step 223, third inverting at each of its two momentaries; at the second an offering of the other parity is a changing, released, arriving at the third at its second momentary alike with third's parity, a changing that is not.         *Adding: three selves in a line.* 609. At a spiral offered nothing from beyond it, each self at a parity and nothing arriving at its first momentary, step 233, each self is at the inverted parity a self it receives from was at two momentaries prior: next from a prior inverted, as step 57, its prior an other's. At a spiral of one its prior is self's own, and its next priors at two momentaries in sequence are all four joint forms in one cycle, one at each momentary, steps 52 and 57.         *Adding: a prior inverted at a spiral, its prior the other's.* 610. At a spiral of selves all alike each self is offered its own parity at each second momentary, step 233, a changing that is not, a 0 released; at an even spiral alternating each is offered the other parity, a changing at each momentary: one resolver at two patterns.         *Adding: a 0 at each second momentary and a changing at each, one resolver at two patterns.* 611. A self at a prior parity, each offering at it a self's sharing or releasing, shares 0 at momentaries in sequence no more than number of selves sharing or releasing to it, steps 204, 208, 209, 212, 222 and 604: its 0 is at an offering of its own parity; a self that parity arrives from next shares 0 or the other parity, and the other parity arriving is a changing. At a spiral offered nothing from beyond it its 0 is at one momentary; at a torus at two at most, an along offering alike at one and an across at next. A 0 at one momentary more is at an offering from beside selves, step 307: a break's rest, step 308, two beats at a spiral and three at a torus.         *Adding: a 0 at momentaries in sequence, no more than selves sharing or releasing.* 612. A spiral offered nothing from beyond it, each self at a parity and nothing arriving at its first momentary, is at its parities again at twice a number k, step 233: k the least number at which its pattern, carried k selves on and inverted k times, is pattern itself. At all selves alike k is two, parities again at four momentaries; at an even spiral alternating k is one, parities again at two; at one self at the other parity from each other self k is twice number of selves at an odd number of three and more, parities again at four times number, and k is number of selves at an even number of four and more, parities again at twice number.         *Adding: a spiral's parities again from its pattern.* ## 35 Rotation at 12 and 14, further forms' moves of 4 about their centres, names two moves apart, sixteen ways at one changing, and a next at itself again         *Entering: a rotation at 12 and at 14; further forms' moves of 4, each pair about a centre; names two moves apart, at 13 and 21 and at 9 and 25; an exclusive or and its inversion among sixteen; a next from now and prior at itself again at one, two, three, four or six.* 613. Rotation 3, 6, 5, 4, step 200, is four names of two four-cycles, 3 and 6 of 3-11-6-14 and 5 and 4 of 4-13-5-12, step 257, each cycle's other two 8 up from them, 11 and 14, 13 and 12. 6 and 4, in at step 200, are 8 up at 14 and 12, parity continuing, and 3 and 5, out, are 17 less at 14 and 12, parity changing, steps 255 and 264. At the resolver offerings surface at 14, step 204, and at 12 prior couples with now, inverted at each changing and kept at a match, steps 206, 208 and 450.         *Adding: a rotation at 12 and at 14.* 614. Further forms' moves of 4, step 600, are four: 9 with 5 about 7, 12 with 8 about 10, 7 with 11 about 9 and 6 with 10 about 8. Four centres add to 17 in two pairs, 7 with 10 and 8 with 9, step 264.         *Adding: further forms' moves of 4, each pair about a centre.* 615. At each middle four-cycle, step 600, names two moves apart add to 13 or to 21, 4 down and 4 up from 17: 5 with 8 and 9 with 12, 7 with 6 and 11 with 10. At each of four four-cycles, step 257, they add to 9 or to 25, 8 down and 8 up from 17.         *Adding: names two moves apart, at 13 and 21 and at 9 and 25.* 616. Of sixteen ways, step 53, at two the next is changing at each joint form, step 52, both at prior changing at its own and at now changing at its own: next as prior and now parting, an exclusive or, and next as prior and now agreeing, its inversion, steps 54 and 56. At each of two, prior and now both changing leaves next the parity it was, and exactly one of them changing brings next to the other parity.         *Adding: an exclusive or and its inversion among sixteen.* 617. At numbers a next added from now and prior, each as it is, inverted or not added, one at least added, is at itself again at one, two, three, four or six, or at none: now at its own, prior lost, at one, and inverted at two; prior at its own at two, and inverted at four, living step, steps 57 and 186; both inverted at three; now as it is and prior inverted at six; at none at both as they are, numbers 1, 1, 2, 3, 5, 8, step 120, and at none at now inverted and prior as it is; and not one of eight at five.         *Adding: a next from now and prior at itself again at one, two, three, four or six.* ## 36 A round's podals and momentaries, one parity at each scale down to one         *Entering: each podal of a round one parity new at its scale, inverted; each parity at its cycles; each of one move's three one parity inverted, or two in sequence; each round two of a round under it, down to 1 and 2; each momentary of a round one odd and one even number, an odd momentary opening at its odd; a parity each momentary inverts; a round's podal, each momentary to one of its own kind in its other order; a round at itself at its observings.* 618. At round of step 171, forms of k parities at numbers 1 to 2^k, each next number is one parity inverted, and each number's podal is parity new at its scale, step 171, inverted: at 1 to 16, 17 less its fourth parity; at 1 to 8, 9 less its third; at 1 to 4, 5 less its second; at 1 to 2, 3 less its first, 1 and 2. A number's odd or even, steps 77 and 264, is its inverted parities even or odd in number. At 1 to 16 first parity is inverted at names of eight-cycle 2-15-7-11-3-14-6-10, step 254, second at those of four-cycles 3-11-6-14 and 4-13-5-12, step 257, third at 5 to 12, names of middle four-cycles 9-5-12-8 and 7-11-6-10, step 600, and fourth at 9 to 16, a society's span, step 193: cycles are round's own arithmetic a second way.         *Adding: each podal of a round one parity new at its scale, inverted; each parity at its cycles.* 619. At round at four parities, at 1 to 8, 8 up is third and fourth parities inverted, 9 less and 17 less in sequence, two inversions of step 256 at two parities; 8 up and 17 less in sequence are 9 less, 1 to 9 to 8 of step 255; at 9 to 16, 17 less and 9 less in sequence are 8 down, the same two. Each of the one move's three is one parity inverted, or two in sequence.         *Adding: each of one move's three one parity inverted, or two in sequence.* 620. Down numbers each round is two of round under it, step 171: at four parities round at three and the same forms in the other order, fourth parity inverted between two, at 8 to 9; at three, round at two; at two, round at one; at one parity, 1 and 2, one form and the same form at the other parity. At 1 and 2 the two are a coupling's two parities, steps 40 and 42, and at 1 to 16 a self's and an other's, step 172.         *Adding: each round two of a round under it, down to 1 and 2.* 621. At round each momentary is two numbers in sequence, one odd and one even, step 275, their two forms one parity inverted apart: first parity at each momentary opening at an odd number, and at momentaries opening at an even number the second at 2–3, 6–7, 10–11 and 14–15, third at 4–5 and 12–13 and fourth at 8–9 and at 16 to next 1, step 176. An odd momentary opens at its odd number, that number's form at an even number of parities inverted, and completes at its even; an even momentary opens at its even and completes at its odd, step 70. Odd is self and even all other, step 276: forms at an even number of parities inverted are at odd numbers, others at even.         *Adding: each momentary of a round one odd and one even number, an odd momentary opening at its odd; a parity each momentary inverts.* 622. Round's podal carries an odd momentary to an odd and an even to an even, in the other order, opening to completing, momentary at 8 and 9 to itself; and round opened at 9, or observed from 16 down, inverts the same parities in the same sequence, and opened at 5 or at 13 it is that sequence with third and fourth parities exchanged.         *Adding: a round's podal, each momentary to one of its own kind in its other order; a round at itself at its observings.* ## 37 A self's next, one momentary at a time         *Entering: a self at a prior parity next at that parity inverted, or keeping it at its own parity surfacing; one parity surfacing a self's next at four cells; a parity shared the receiving self's next; a sharing at no prior opening at one parity surfacing; a spiral's first two momentaries, an inverting and an other's arriving; a self offered its own parity from beyond, a self receiving from it inverting twice.* 623. At resolver a self at a prior parity is next at that parity inverted, shared at 10, at each of six cells of Exhibit ONE's table of one self at one momentary: none surfacing, the other parity surfacing, and + and − together, each at + and at −, step 212. At its own parity surfacing, two cells, 0 is shared and its prior is kept. Inverting is self's own, at 12.         *Adding: a self at a prior parity next at that parity inverted, or keeping it at its own parity surfacing.* 624. At one parity surfacing a self at a prior parity is next at that parity, at each of four cells, its prior kept at two alike and inverted at two of the other parity; at two cells of a sharing at no prior its parity is next prior as it arrives, sharing opening, Exhibit ONE's table. From a self's sharing or releasing, parity surfacing is parity that self shared one momentary prior, its next prior, step 209, step 607 its case at two selves: parity a self shares, its next prior, is next prior of a receiving self at a prior parity, at one momentary my prior your next existing. A parity offered from beyond selves, step 213, is no self's prior.         *Adding: one parity surfacing a self's next at four cells; a parity shared the receiving self's next.* 625. A sharing at no prior opens at one parity surfacing, that parity shared and next prior as it arrives, at two cells of Exhibit ONE's table at no prior; at none surfacing none is shared, and at + and − together 0, and no next prior opens, two cells, step 212.         *Adding: a sharing at no prior opening at one parity surfacing.* 626. At a spiral offered nothing from beyond it, each self at a parity and nothing arriving at its first momentary, step 609: at first momentary none surfaces and each self is next at its parity inverted, shared at 10, step 623; at the second each is next at parity surfacing, parity of a self releasing along to it at that momentary, step 624. Each further momentary is at step 623 at each self. A prior an other's and inverted, step 609, is these two momentaries: an inverting at the first and an other's arriving at the second.         *Adding: a spiral's first two momentaries, an inverting and an other's arriving.* 627. A self at a prior parity and offered that parity from beyond at its first momentary shares 0, step 623. A second self at a parity, receiving from it and offered nothing from beyond, has none surfacing at its first two momentaries, a 0 offered surfacing none, step 223, inverts at each, and is at its own first parity at its third. Step 609 is of a spiral offered nothing from beyond it.         *Adding: a self offered its own parity from beyond, a self receiving from it inverting twice.* ## 38 At no prior, + and − observed alike, an odd spiral's like pair, spirals crossed, an even torus and names at resolver         *Entering: Exhibit ONE's table at no prior, its four cells; + and − observed alike, an opening inverted the same numbers; an odd spiral's like pair, a 0 at each even momentary; two spirals crossed, each self's releasings again at 2; a torus at either number even, at 2; 13 at resolver; four momentaries' relations; names between selves on four-cycles; co at resolver, a sharing side and an arriving side; odd names 8 apart.* 628. Exhibit ONE's table at no prior is a sharing at no prior at its four cells, steps 394 and 625: one parity surfacing, parity shared and next prior as it arrives, sharing opening; none surfacing, none shared; + and − together, 0 shared; and no next prior at each of three.         *Adding: Exhibit ONE's table at no prior, its four cells.* 629. Resolver observes + and − alike, at each prior parity or none: an opening with each + a − and each − a + gives each parity shared and each next prior inverted, each 0 and each none as it was, and each number of momentaries as it was. Exhibit ONE's tables of one self momentary by momentary, a spiral, two spirals and a torus open a self at prior −; its table of two selves opens first self at +, and its table of three in a line second and third at +.         *Adding: + and − observed alike, an opening inverted the same numbers.* 630. At a spiral of an odd number of selves offered nothing from beyond it, step 233, each pattern of parities carries a like pair, a self alike with a self it receives from, one pair or more; at each even momentary a receiving self of each like pair, pattern as carried at that momentary, shares 0 at 10, and each other self is at a changing; at each odd momentary each self is at a changing, step 233.         *Adding: an odd spiral's like pair, a 0 at each even momentary.* 631. Two spirals crossed at one self of each, both ways, step 237, come to each self's releasings again at 2 from a momentary on, two crossing selves opposite from it on, at each of eight rows of Exhibit ONE's table.         *Adding: two spirals crossed, each self's releasings again at 2.*         *Unsure: a momentary from which releasings come again at 2: 7, 12, 20, 28, 44, 52, 119 and 36 at eight rows, observed at Exhibit ONE's table; four times the smaller number at six rows, and no rule worked.* 632. A torus at either number even, each self at a parity alternating along and across, step 243, is at a changing at each self at each momentary and comes to its parities again at 2: at first momentary none surfaces, and at each further the two arriving are alike at a self's parity inverted, or + and − together, step 623.         *Adding: a torus at either number even, at 2.* 633. 13-next at resolver is each releasing sharing, a self's 6, 10 or 9 going to 2, 14 or 17, and at a society each self, Exhibit ONE's row of 13.         *Adding: 13 at resolver.* 634. Four momentaries of exchanging, step 73, are at four relations, Exhibit ONE's table: self and other; self and other to other and self; other and self; other and self to other and social.         *Adding: four momentaries' relations.* 635. Of two four-cycles at 1 to 9, step 517, 3-7-2-6 carries two names between selves, 2 and 6, and 4-8-1-5 none; opened, step 520, 3-11-6-14 carries 6 and 14, 2-15-7-10 carries 2 and 10, 1-9-8-16 carries 9, and 4-13-5-12 none; 17 is on no four-cycle, step 257.         *Adding: names between selves on four-cycles.* 636. Co at resolver, Natural Naming 3.2: co is at a sharing between two and its absence at one, and between selves a sharing side is co and an arriving side none, 6 to 2, 10 to 14 and 9 to 17; and odd names are at four pairs 8 apart, 3 prior received and 11 next prior, 5 receiving sharing and 13 releasing one, 7 parity prioring and 15 parity surfaced, and 1 resolver entered and 9 changing released along.         *Adding: co at resolver, a sharing side and an arriving side; odd names 8 apart.* ## 39 Fixed unchangeable at both sides, a bounded executing, four-cycles' momentaries, 9 and 17, prior two added and co-sequencing         *Entering: 7 and 5, two fixed unchangeable at each; a bounded executing fixed at each momentary, a proof of the whole; four four-cycles' momentaries in order; 9 a next prior and 17 a next now; prior two added as an exclusive or; co-sequencing at competency's parity and morality's.* 637. 7 and 5 each carry two of ten unchangeables, step 522: 7 a parity fixed as a magnitude and a rate fixed as a value, 5 a between fixed as a cut and a middle fixed as an end; the two are carried one at a time, step 528.         *Adding: 7 and 5, two fixed unchangeable at each.* 638. A sentence drawn from resolver's executing at a number of momentaries, fixed as the same at each momentary, is a proof of the whole, step 143, a form still, step 144: finding is at its executing, step 579, and a rule fitted at each case worked is at those cases.         *Adding: a bounded executing fixed at each momentary, a proof of the whole.* 639. Four four-cycles' names go, in order, now, next, now and next at each, 1-9-8-16, 2-15-7-10, 3-11-6-14 and 4-13-5-12, each move, 8 up or 17 less, crossing between a self's span and a society's, step 257, each name's momentary at Exhibit ONE's table of seventeen names.         *Adding: four four-cycles' momentaries in order.* 640. 9 is next prior, step 75, and 17 next now, a society's next momentary, step 225, Natural Naming's own sentence.         *Adding: 9 a next prior and 17 a next now.* 641. At parity the prior two added, step 120, is odd at two parting and even at two alike, an exclusive or of step 616: odd and odd, odd and even, even and odd are its cycle of three, and even and even is at itself, step 56.         *Adding: prior two added as an exclusive or.* 642. In Exhibit ONE's co-sequencing each odd name within one self is at competency's parity and each even at morality's, step 252, and 1 is self offering itself to coupling.         *Adding: co-sequencing at competency's parity and morality's.* ## 40 An odd spiral two rounds, the second inverted, and a changing at both routings         *Entering: an odd spiral two rounds, the second the first inverted; each changing of a self coupled both ways at both routings at once; torusing and corusing at dimensions, at no name.* 643. Once along an odd spiral, at twice its number of momentaries, each self's parity arrives inverted, and twice along, at four times, as it was, steps 231 and 233: an odd spiral is two rounds of its selves, its second its first inverted. An even spiral arrives as it was at one round, and opened alternating at each second momentary, step 232.         *Adding: an odd spiral two rounds, the second the first inverted.* 644. At resolver each changing of a self coupled across and along goes both routings at once: 17 gives one changing of 10 on at 6 and 10 across and at 9 along, each at its coupling, step 239, and at a torus of selves each self releases along and shares across, step 243; at a spiral a changing is released along. A routing at odd momentaries or at even, each at its own opening, is at no line of resolver.         *Adding: each changing of a self coupled both ways at both routings at once.* 645. Torusing and corusing are dimensions' in and out, torusing at odd and corusing at even, steps 118 and 119, and no resolver name is at either: names are at their numbers and their kinds, steps 193 and 251, and natural torusing is method's one name, step 114.         *Adding: torusing and corusing at dimensions, at no name.* ## 41 A spiral's places one loop at an odd number and two at an even, a prime's two numbers, and a torus at its lines         *Entering: a spiral's places one loop at an odd number of selves, two loops at an even; at an odd spiral a pattern again at four times its least alike shift; an odd prime spiral at 4 or at four times its prime, none between; like pairs odd in number at an odd spiral, even at an even; an even torus at 2, at each momentary each self inverting; an odd torus's first 0 at a self of both seams, passing along two lines through it.* 646. Each two momentaries a spiral offered nothing from beyond it carries each self's parity to next self, inverted, step 233: a parity at a self is two momentaries on at next self at the other parity. Each self at each parity is a place, twice number of selves. At an odd number of selves places are one loop, each self passed twice, once at each parity, loop at its opening place again at four times number of selves, in momentaries; at an even number they are two loops, each self once on each, a self's two parities on the two, and neither loop reaches the other.         *Adding: a spiral's places one loop at an odd number of selves, two loops at an even.* 647. A spiral is at its sharings again, and at its parities carried at an odd momentary, at twice k momentaries, k the least at which each self's parity is that of a self k prior, inverted at an odd k, step 646; a coming again is at an even number of momentaries, a 0 at each even momentary or spiral alternating, at 2. At an odd number of selves an odd k, carried the number of selves times, brings each self to itself inverted, at no pattern: k is even, twice the least d at which each self is alike with a self d prior, d dividing number of selves, and pattern is again at four times d momentaries.         *Adding: at an odd spiral a pattern again at four times its least alike shift.* 648. At an odd prime number of selves the least alike shift is one, each self alike, or the prime, step 647: each pattern is again at 4 momentaries or at four times the prime, and at none between. At two selves two alike are again at 4 and two opposite at 2. At an odd number with a factor a pattern whose least alike shift is the factor is again at four times the factor, nine selves at 4, at 12 or at 36, step 230.         *Adding: an odd prime spiral at 4 or at four times its prime, none between.* 649. Along a spiral pairs parting in parity are even in number, each parting coupling with one back: like pairs are odd in number at an odd number of selves and even at an even, steps 232 and 630, a lone self a like pair with itself. An odd spiral carries a like pair at each momentary and a 0 at each even momentary; an even spiral alternating along carries none.         *Adding: like pairs odd in number at an odd spiral, even at an even.* 650. At a torus of selves with an even number along, selves opened alternating along: each self's along offering, from second momentary, is parity other than its own, none offered at its first, and with each across offering beside it its surfacing is that parity or 0, a changing, step 212; each self inverts at each momentary, alternating along kept, and parities are again at 2 from first momentary. The same at an even number across. 2 is of an opening alternating along its even number, step 243.         *Adding: an even torus at 2, at each momentary each self inverting.* 651. At a torus of two odd numbers opened alternating, its last and its first alike along and across, step 243: at first momentary each self inverts; at the second, one self is at a changing that is not, a self alike with both its along prior and its across prior, each other self offered parity other than its own or + and − together; and from that self a 0 passes one self on at each momentary along each of two lines of selves through it, a self i on at momentary i + 2: along p to last self of its line, and across q, at q more than p, on round its line.         *Adding: an odd torus's first 0 at a self of both seams, passing along two lines through it.* ## 42 An odd torus's number and two spirals crossed, each derived at resolver's cells         *Entering: one 0 at most at each line across, and two that carry it on; a line's next 0 one after the later of two, two after at two alike; each self's first 0 at i + j + 2 and the lesser more, each line two momentaries behind its prior; at q more than twice p the sharings again at q, from momentary 3p − 1; at q less than twice p the sharings again at 4p, from momentary 3p − 3; a torus's divide derived: 2p round its lines, q round a line, the greater the 0's round; a crossing self's two cells an across offering alters; a 0 ended at a seam by the other parity across, a like pair still; two spirals crossed again at 2 from 4m or from 2n + 1, each row agreeing; two spirals of one number alike at each momentary, a 0 ending at none.* 652. At a torus of two odd numbers, opened as at step 651, each line of selves across carries one 0 at most at a momentary, at a self next across after its last 0, before its first at its self of an along seam. That self is at a changing that is not exactly at these two: the 0 of a line along prior to it has been at its along prior after its own last 0, at first line's first round its opening's along seam standing for it; and its two priors were not both at a 0 one momentary before. Each other self, from second momentary, is offered across parity other than its own and inverts.         *Adding: one 0 at most at each line across, and two that carry it on.* 653. Momentary of a line's next 0 is one after the later of two, line's own last 0 and the 0 of a line along prior to it at that place, and two after them at the two at one momentary, step 652; one after the one at the other none, a line's first 0 and first line's first round; first line's along prior is last line, one round of q before; and first 0 of all is at second momentary, step 651.         *Adding: a line's next 0 one after the later of two, two after at two alike.* 654. Each self's first 0 is at momentary i + j + 2 and the lesser of i and j more, i along and j across from a self of both seams, steps 651 and 653; and each line i along after the first, from its 0 next after its first i, is at each 0 of a line prior to it two momentaries later, without end.         *Adding: each self's first 0 at i + j + 2 and the lesser more, each line two momentaries behind its prior.* 655. At q more than twice p first line's 0 passes one self on at each momentary round its q selves and waits at none, each line after the first two momentaries behind its prior, the first more than two behind the last, steps 653 and 654: each self is at a 0 once in q momentaries, q odd, its parity as it was, and sharings are again at q, from momentary 3p − 1.         *Adding: at q more than twice p the sharings again at q, from momentary 3p − 1.* 656. At q less than twice p, p from 3, q the lesser's equal or more, first line at its second round comes two momentaries behind last line, at its place q − p of that round and at p and q one number at its first, and waits behind it at 2p − q places, steps 653 and 654: each line's 0 is round its q selves in 2p momentaries, each self at a 0 once in 2p, an even number, its parity inverted, and sharings are again at 4p, from momentary 3p − 3. A torus of 1 by q is at step 655, and one self is at a 0 at each second momentary, 4 from the first.         *Adding: at q less than twice p the sharings again at 4p, from momentary 3p − 3.* 657. Divide of step 243 is derived, steps 655 and 656: round p lines, each after the first two momentaries behind its prior, is 2p momentaries, and round a line is q; the greater is 0's round, q at q the greater, and 2p at 2p the greater, one 0 at each self in an even number of momentaries inverting it, 4p. Rule of step 653, from first 0 of step 651 and each self inverting at each momentary it is at no 0, worked as arithmetic at each of Exhibit ONE's ten rows of two odd numbers, gives each row's number and momentary it is from.         *Adding: a torus's divide derived: 2p round its lines, q round a line, the greater the 0's round.* 658. At two spirals crossed, step 237, a crossing self is offered its along prior's changing and other crossing self's, and is at a changing that is not exactly at one of them or both its own parity and neither the other parity, step 212. An across offering alters two cells: along its own parity and across the other, + and − together, a changing; along a 0 and across its own parity, a changing that is not.         *Adding: a crossing self's two cells an across offering alters.* 659. Each self inverting at each momentary is exactly each spiral alternating from its first self to its last and, at an odd spiral, its last and its first alike with two crossing selves opposite, steps 649 and 658: an odd spiral's like pair rests at its seam, its 0 ended by the other parity arriving across, + and − together, and its like pair is at each momentary still.         *Adding: a 0 ended at a seam by the other parity across, a like pair still.* 660. Two spirals of two odd numbers crossed, m the lesser from 3 and n the greater, opened as Exhibit ONE opens them: crossing selves are alike to momentary 2m + 1; at it the lesser spiral's crossing self, offered a 0 along and its own parity across, is at a changing that is not, and from 2m + 2 the two are opposite; each spiral's crossing self, next offered a 0 along and the other parity across, inverts, and each self of that spiral inverts from it on, the greater spiral from 2n + 1 and the lesser from 4m, its like pair at its seam offered both parities from next momentary, steps 658 and 659. Sharings are again at 2 from momentary 4m at n less than twice m and from 2n + 1 at n more; at m even and n odd from 2n + 1, two opposite from 3. Each of Exhibit ONE's eight rows agrees, step 631.         *Adding: two spirals crossed again at 2 from 4m or from 2n + 1, each row agreeing.* 661. Two spirals of one number of selves crossed, opened alike, are alike self for self at each momentary, crossing selves alike, and at an odd number its 0 ends at none, step 659: two numbers differing is of deriving. Two even spirals, each alternating, are again at 2 from first momentary, crossing selves alike.         *Adding: two spirals of one number alike at each momentary, a 0 ending at none.*         *Unsure: step 237's each prior pattern is derived at a table's opening, and two spirals with the lesser of one self at tables by hand; rows beyond Exhibit ONE's tables, 3 by 9 at 9 from 8 and 5 by 9 at 20 from 12 at a torus, 3 and 9 crossed from 19, wait on an executing.*