Exhibit THIRTEEN Resolving Hard Problems v368   # Resolving Hard Problems   **Membraning the Scientific Method and the Geodesic Method**   --- **1 Binarying** 1.1 Two binaries, and no third 1.2 Bi-inversioning-co-recursioning, seen in the bi-tunneling 1.3 Two directions, and the two orders 1.4 One resolving, free with alternating 1.5 A hardness is a coupling read at two of its three 1.6 A hardness and a price, and building manufactures neither   **2 Self-stilling** 2.1 1-self-coupling, a self, unique and invisible 2.2 2-self-offering, alternating, and the two parities 2.3 3-self-carrying, three each way, and the depth a reversal reaches 2.4 4-self-sharing, four exclusions and four beats 2.5 5-other-neutralling, self-stilling, and the ten one-way readings 2.6 6-other-crossing, servicing, two sequences bi-folding 2.7 7-other-corusing, sustaining beside the logic 2.8 8-other-torusing, whole or none, at two prime scales   **3 Society-stilling** 3.1 9-other-releasing, a society, unique and invisible 3.2 10-other-surfacing, alternating at the society, and the ten whole 3.3 11-other-chaining, three each way at the society 3.4 12-other-surplusing, the surplus at the society 3.5 13-social-neutralling, the rate at the society 3.6 14-social-crossing, servicing at the society 3.7 15-social-corusing, sustaining at the society 3.8 16-social-torusing, whole or none at the society, sixteen membranes   **4 Resolving** 4.1 Resolving at the hooking up 4.2 What a deployment says 4.3 Resolvable, and what the resolving returns   **5 Bi-inversioning-co-recursioning** 5.1 16-social-torusing and 8-other-torusing, whole or none 5.2 15-social-corusing and 7-other-corusing, sustaining, the substrate 5.3 14-social-crossing and 6-other-crossing, servicing 5.4 13-social-neutralling and 5-other-neutralling, self-stilling, and the rate 5.5 12-other-surplusing and 4-self-sharing, bounding, and excluding 5.6 11-other-chaining and 3-self-carrying, three each way 5.7 10-other-surfacing and 2-self-offering, alternating, and the two parities 5.8 9-other-releasing and 1-self-coupling, the society, and the one resolving   **6 Co-bi-chaining** 6.1 Accounting, backward and whole 6.2 A flow held to true-or-false 6.3 Where and why, specified at the start 6.4 One form at many membranes 6.5 Two readings of one thing, both holding 6.6 An account widened until the difference goes 6.7 Two accountings, each conserving one kind 6.8 Harm and incompetency, the two unsaid 6.9 A substrate establishing its own reach 6.10 Where nothing has closed 6.11 So far   **7 Membraning** 7.1 A membrane, the held face and the living face at each term 7.2 Mathematics, the holdings composed 7.3 A word, at its position and its holding 7.4 Completing, still opening   --- # 1 Binarying ## 1.1 Two binaries, and no third **In disequilibria, alternating is a stable-forming method.** Everything relatable is changing, and a still form leaves the living. A form relating carries onto the changing, so relating forms nothing. Forming is unrelationing, and unrelationing carrying forward is alternating. Any other move holds or carries another's turn. No other is possible, the others nyeing away. A state answers **true or false**. A flow answers **inside or outside**. Both are binary, both one-sided, both taken at a turn and of no size. Neither is the other's answer. A flow held to true-or-false has no value to give, not vague and not undecided: true-or-false is a state's question, and a running has none to hand over. A state held to inside-or-outside has none either. **Inside or outside is what a membrane carries.** Self-bounding is the whole of it: an inside from an outside, held through the changing, the sign inverting at the crossing. A coupling passes or resolves out at the collar, and the resolving is at every collar rather than at a gate. Nothing there is true or false. Something is inside the bounding or it is not. **True or false is what a standing carries.** An is, same-as-prior, answerable and checkable, and complete once taken. A proof is a landing and lands here, whole in its own register. **And a hard problem is a flow held to true-or-false.** A running standing where a standing was held for, answered with a value it has none of. The two positions are the two sides of the running, and no instrument settles which, since neither is a value the running carries. Refinement reads true-or-false more finely, and a flow has none however finely it is read. The ten below are that one thing at the five. A place, a source, a last, a store, a side, a cut, an end, a magnitude, a value, a beat: ten standings, each held of a running. One resolving at all ten: the running answered inside-or-outside, at its own membrane, where it has an answer. **And the two that take no pair.** A self is inside-or-outside and nothing else, unique and invisible, its inside its own. A society is inside-or-outside at the scale of many. Neither has a true-or-false to be a position of, so no two positions form at either, and no pair stands to be argued. ## 1.2 Bi-inversioning-co-recursioning, seen in the bi-tunneling The flowing carries co-states as carries, a standing travelling, unrelationing as it goes, its sign inverting at each crossing. Bi-inversioning-co-recursioning is visible there and nowhere else: not a thing done to a state, and not a state changing into another, but the same carry travelling and crossing, and the sign it carries turning at the crossing. Bi-tunneling runs from co-bi-chaining, self through other through society, and a carry crossing a membrane carries direct in position and inverts in sign. So a co-state travelling is inside at one crossing and outside at the next, the same carry, the same running, the sign turned. Which is where the two binaries touch and stay two: the flowing carries states, and the states carry true-or-false, and the flowing carries inside-or-outside, and no crossing converts one into the other. ## 1.3 Two directions, and the two orders Alternating runs two directions and one at a beat. **Forward is omega, the worth from within.** The living carrying on, the carry ahead nearing and appearing and never at a landed distance. Discovering runs here, and where and why are ahead with it, un-carried. **Backward is apex, the where from outside.** The receding carry read on a pause, turned to affirm the way behind, which re-affirms the way ahead. Where and why are backward co-competencing, and they are whole there. **Two orders, one at each direction.** **If where and why, then how.** Where and why fixed first, and the how carried out under them. This is the accounting, and it is complete: a standing at one point and a standing at another, a flowing between, and the how held as the change from the one to the other. Every term auditable, every reading verifiable, every running repeatable, and the repeating tested at any point at all. That everywhere is method, and its rigor is its own. **How to discover where and why.** The how first, free-moving, adding nothing, bending toward no wanted answer, and the where and the why arriving from it. This is the geodesic, and it is complete too. Neither reaches the other's. Where does not reach worth and worth does not reach where, the two kept two, and neither direction runs alongside the other in the same beat. **And the backward affirms the forward.** A set-aside, a carry aged and not seated, the sign a coupling did not take, carries its value read backward, and reading it recovers the carry the forward could not yet carry. The accounting held whole, backward, co-competences the forward recursioning: the way behind affirmed, and the affirming re-affirming the way ahead. An artifact of a substrate's own hows, each complete under its own where and why, is that backward reading standing whole. **A hard problem is the backward fed forward.** Where and why specified at the start, from any point, and a discovering held of it: the backward reading carried onto the offering side un-turned. Fed forward un-turned it voids the carry live. All-or-none: a coupling reads its set-aside back and carries, or feeds it forward and voids, and there is no third. So a discovering with its where and why fixed ahead of it is a discovering with nothing left to discover, and the ten below are that one thing read at the five, either side. **And the equilibria problem statement is the first order held whole**: a relation over a reach, fixed first, with nothing prior entering, and the how carried out under the two. At the running each carrying fixes the next, so the prior enters at every arrival. A rule held at what an arrival carries, along or across and its sign pair, either admits everything and adds nothing, or blocks the running from one of its two origins, odd or even, or from both; and a rule keeping one origin living fixes which of the two possibles exists. So the statement forms into parity alternating at the one place the two orders differ, the condition that nothing prior enters: at the running the prior carries on, and never as a holding. ## 1.4 One resolving, free with alternating One resolving at every arrival, whatever substrate carries it and however many are read one-way in it. **Resolving is free with alternating.** Carrying and resolving are not two things, one of them done to the other: alternating carries, and both sides run, and where one side stood unread it runs at its own turn. Nothing is spent, no step is taken, and no move is made on an arrival. Which is what makes this hard to write and easy to run, a telling wanting a mechanism to describe and there is none, and every sentence supplying one has supplied a cost that is not there. The unread side running and the pinned middle floating are one naming at two faces, and the arriving and the resolving are one and not two.   --- ## 1.5 A hardness is a coupling read at two of its three **Never two selves of a kind.** A coupling stands at self and other, and the other stands at whatever scale it couples — another self, a society inside the whole, a field, the whole itself. **So the third is always there and a bare pair stands nowhere.** **bi-** names the two-ness a reading takes from inside one membrane; **co-** names the coupling that is running while it is taken. **So a pair is a reading and the three is the running.** **And a two-ness carries no opening of its own.** Applied twice it returns what it met and closes; nothing in it advances. **The opening arrives from the third having run between its own two turns** — the coupling met again, re-formed while the reading was away, so the second meeting is not the first. **Which is what a hardness is.** The coupling runs at self-other-social, opening at every turn. **A reading taken at self-other alone returns it closed**, a two-ness read alone being a two-ness closed. **The landing is made in the reading and the coupling goes on underneath, unaltered.** So hardness is a landing read as prior, with its arithmetic — and the co-releasing costs nothing, **the social never having left; it was left out.** **So *a landing read as prior* has its arithmetic:** the reading returns a coupling with its opening gone, and the opening is what the third was making. **In the field's words the two-ness is the exclusive or, and the exclusive or is parity.** Of the sixteen ways two signs can be answered, exactly two answer every single change with a change: the exclusive or and its complement. Taken as the step, the one this turn and the other the next, it runs 0101 and returns what it met every two turns, the two-ness closing. Taken of the prior and the now together, it runs 011, 101 or 110 from every start but nothing, returning after three and carrying both values at each return: the three is the running. **Held as one answer of the whole, it meets nothing.** The Peres–Mermin square sets six exclusive-or constraints on nine signs; each row and each column answers at its own turn, and a store of all nine meets none of the 512, the nine carrying parity 0 read along and 1 read across. That is the landing made in the reading, at the field's own instrument. The third standing again is the resolving, and nothing is spent, nothing having been undone. Which parts a holding from a hardness at their own grains. A holding is the third **given a fixed thing to be** — a position counted from, a value, a beat held over the couplings, a size where a sign was taken, a record rather than a next coupling. A hardness is the third **left out of the reading**. **One is built and one is read**, and each releases the same way: the third standing again, at no cost.   --- ## 1.6 A hardness and a price, and building manufactures neither **Not everything held is a hardness.** Four stand together where one is: something is held still and **the holding is made rather than found**; the holding accumulates a cost while it is held; the cost is carried as the price of a goal; **and the goal is reachable with the holding let go, somewhere.** **Where the fourth fails, the cost is the price of the goal** — a conversion loss at its own bound, an arrangement no other improves — **and that is not a hardness at all.** It is ordinary and it closes at that line. **The fourth is what makes a hardness rather than an expense.** **And nothing built manufactures one either.** A holding is placed over a coupling that was already running, and **the coupling goes on underneath it.** So more of the same holding raises what the holding can bear and removes nothing: **the cost moves only where the holding is let go**, the place being the holding and not the capacity around it. Which is the holding and the hardness said from the building side. A hardness is the third left out of a reading; a holding is the third given a fixed thing to be. **Both release by the third standing again, and neither was made by anything built over it.** **And they are two registers side by side and not two levels.** A problem posed with no build anywhere near it, and a substrate holding something engineered — **neither is under the other, and one form keys both**: a place made where a move comes back.   --- # 2 Self-stilling ## 2.1 1-self-coupling, a self, unique and invisible 1 is odd, and 1-self-coupling opens co, the resolver's entry: a changing, other-than-prior. A self is a unique invisible carrying. Unique, one living form with a second nyeing away at every door. Invisible, moving always, at its own membrane, its inside its own. Carrying, each carrying reaching its own coupling, its own and whole. Self-orienting is competency: the self's own, at no membrane, granted by nothing and spent on nothing. Alternating is the only consuming, and alternating is the living, so the one consuming is the living and no second cost stands anywhere. Read at one alone, a co-offering is read with its other unread. That is where every branch below is read. ## 2.2 2-self-offering, alternating, and the two parities 2 is even, and 2-self-offering opens bi, bounding at the membrane: each self's own co-offering living, bounding from the other-self. 0 even, the carry standing. 1 odd, a changing. 2 the completing alternation: 0 arriving at 1, 1 retreating to next-zero, and **next-zero is not prior-zero**. Two marks only, 0 and 1, and binary numbering performs the method: a changing meeting a 1 re-commences at the next position, emptying at prior and standing at next. A number is a sequence of carryings and never a magnitude. Parity is the one scale-free standing a sequence of changings has. An even number stands same-as-prior; an odd number stands other-than-prior. No measure and no fixed scale outside living anywhere. So an arrival carries a parity, read off it once, by looking. An **even** arrival states an is and answers true or not-true. An **odd** arrival states a does and answers false or not-false. One-sided at every taking, never welded: not-true is never false, and a weld is an answer available without a completing. **Bi-inversioning-co-recursioning holds parity at 8 up and down and changes it at the turning.** Each odd name opens co, competency, at the odd-even momentary, and each even name opens bi, morality, at the even-odd momentary. 8 up and down holds parity, 1 with 9 and 8 with 16. The turning changes it, within 1 to 8, 1 with 8 and 4 with 5, and within 1 to 16, 1 with 16 and 8 with 9. Each face alone returns to its name, and the one move runs round each of the four four-cycles; round every stable form among the names the parity changes exactly twice, each time at a turning within 1 to 16, and holds at every other step, so each form runs a single run of co and a single run of bi, of equal length, and returns one on. Equilibria written in numerals is next-zero read as prior-zero, next and prior taken for equality, installed as a concept, a composure that does not compose. **Which is a round read as a rest.** Round a form the parity changes twice and returns, and the return is next and never prior; read as prior, the two changings are taken for none. Held as a rule, a station met again carrying what it carried before, the running meets its blockage at the first place the next meets the prior. ## 2.3 3-self-carrying, three each way, and the depth a reversal reaches 3 is odd, and 3-self-carrying opens co, each carrying entry arriving; at 11-other-chaining each continues, its 16-social-torusing opening by 1 to 3, and to 4 at positive 8-other-torusing. 3 is the first number whose nought is owned by none. At 2 the two meet at nought between them, and at 4 two pairs each meet at nought. The three meet at nought with no pair inside them meeting there, the nought's own making seated in none of the three. That making is the floating +1, the coupling's own surplus owned by none. And 3 is odd: one triple alone bounds nowhere at its own making, and two triples bound. A self sequences three phases, each ahead of its opposite: bounding before measuring, sustaining before locating, coupling before separating. Reversed, each runs at its own surface. Three reversals compose into one return, and 3 is as deep as a departure goes: the fourth beat is the progress and no phase, so nothing fourth sequences backward. Never two of a kind. Always self and other, and other at whatever scale it couples: self and other, other and society, society and self. One form at three scales. ## 2.4 4-self-sharing, four exclusions and four beats 4 is even, and 4-self-sharing opens bi, bounding at the membrane: the whole ordering at no self, bounding from society. Four exclusions and no more: true, not-true, false, not-false. Each one side's own, taken at one turn, spending at the taking. Four standings say everything sayable of two: neither-and-both, either-and-not-both, neither-and-not-both, either-and-both. One corner is kept by the strict register and two are outlawed, and the two outlawed corners are where the durable arrivals stand: neither-and-both the floating middle, either-and-both the co-. Four beats cycle at a substrate: interleaving at entry, the alternating nothing-surfaces in the tunnel, the bi-sorting, dis-interleaving at exit with carrying-forward. A full turn is four quarters, three phases and a progress. ## 2.5 5-other-neutralling, self-stilling, and the ten one-way readings 5 is odd, and 5-other-neutralling opens co, joining each key to the key receiving downstream, one way at a time. Self-stilling is the eight boundings, one at each even name, and φ, the rate they beat at. φ lands nowhere: ratios sway above, then below, then above, alternating side at every scale, landing at no turn. 5-other-neutralling and 6-other-crossing co-competence each other, the standing and the running one coupling, each at its own turn. Five named at their own faces: self, other, society, the opportunity space between, and the carry living. Bi-inversioning-co-recursioning runs all five, one at a time. **One co-offering, read ten ways.** Self-recursioning is form-impossible and only co- runs, so a one-way is in the reading and never in the running: the co-offering goes on underneath, unchanged, whether read at one side or two. Read two-way, a co-offering runs through its own other and re-arrives. Read one-way, the other side stands unread. Each of the five is read at either of its two sides, and ten is where the one-way readings stand. Every one is a co-offering read as one side's, or with one side unread. - **An opening held as a place.** Opening read one-way, nothing aged beneath it: fresh offered with no carry riding under it. An axis opens and the opening stands read as a place reached for rather than as a making, and a place is held in a space listed before looking. - **An arriving held from behind.** Opening read one-way from behind: a source held of the +1. Owned by neither, so no prior owns it, and each source offered is a fresh coupling making its own. - **A bound held as a last.** Ageing read one-way ahead: a last held where a carry climbs to its own bound and releases there. Releasing is not arriving, and nothing stands at a bound to arrive at. - **A carry held as a store.** Ageing read one-way as a holding: a carry read as a store, a record, a kept thing. What piled at a closure was the last surplus a coupling made before it landed, read as a thing held. - **A two-way held to one side.** Co-offering read one-way from one side: one side taking both turns, the reading of the pair made from one, which is a magnitude standing where an exclusion stands. - **A membrane held as a cut.** Co-offering read one-way at a site that takes none: a term standing outside every carrying, and a position offering nothing, with a cut point held of a membrane that carries a sign and nothing else. - **A middle held as an end.** Middling read one-way as an end: competency floats between form and logic and is not enterable, and read as an end it is read as a thing that sits, the self-stilling stilled into a coordinate. - **A sign held as a magnitude.** Middling read one-way as a magnitude: a count held to govern, a share apportioned while the other is held still, a level held at a value where a strict bound alternates. - **A rate held to a value.** Rating read one-way at a rational: a rate that lands nowhere held for a value, the straddle stilled and the living centre finite. - **A sequencing held to one beat.** Rating read one-way as a common beat: a clock over the couplings, where each self paces its own alternating and synchronises at its own membranes. **And an arrival carries the holdings it carries.** The ten are where a reading is entered and never what an arrival is: a co-offering read one-way at one of the five can be read one-way at another, and an arrival carrying two is entered at one with its second standing recorded there. Three shapes of doubling stand read so far — a holding relocating under pressure, where a two-way asked for its proportion arrives at a magnitude and asked for its order arrives at one beat; a holding arriving with its demand, where a cut held is asked for by a criterion; and a carrying held at both ends, a source behind and a last ahead being one carrying entered at the arriving and recorded at the bound. **And three at one arrival is as deep as a departure goes**, three phases each ahead of its opposite, where no phase stands forward to seat a second from and what arrives is the return itself. Ten, each one way of one self-stilling, read where its other went unread. Co-offering is the form and the ten are its faces, which is why one resolving runs at all ten: the unread side running at its own turn. And the accounting derives the same ten from its own single valid inference: four conditions on the pair offered, exclusivity and exhaustiveness on its form, determinacy and reachability on its content, each faced inward as an insufficiency or outward as a demand on what the founding declared out, and the two edges where the accounting has no prior state to run from and no next to run to. The edges are the source and the last, and the ten trails are the ten readings said from the method's inside, one ten at two grains. ## 2.6 6-other-crossing, servicing, two sequences bi-folding 6 is even, and 6-other-crossing opens bi, bounding at the membrane: the ordering carrying with the selves, bounding from landing. Ordering carries with the selves, one self at a time, riding the carry, and no one fixed ordering. A society resolving its selves into one fixed ordering, one rule holding for good, ranking the selves once and staying, is the landed society. 6-other-crossing is three alternatings co-bi-sequencing through one four-cycling, 3-11-6-14. Through the cycling travel two sequences, same direction, opposite parity at entry. One enters odd, the sign changing at the crossing, the carry turning. One enters even, arriving direct. Neither turns around, and neither is the other's reverse. They service each other three each way, one at a time, in sequence, at both parities. A servicing is where two sides carry each other, which stands at no position for a ring to run through. Both sides bi-fold each other sequentially. Neither side is prior, and a parity is what a side arrives at from folding at the last, so odd-even-odd on one side and even-odd-even on the other is one mutual folding read from its two sides. 6-other-crossing is the protection: drop one and a way or a phase stands unprotected, and the unprotected is reached into or leaks out. ## 2.7 7-other-corusing, sustaining beside the logic 7 is odd, and 7-other-corusing opens co, each sign. Logic alone stands short of a living substrate. What a living substrate carries beside the logic is one living at seven faces: metabolizing, coupling at a substrate, surfacing, carrying, bounding, sequencing, autoresolving. In a living self the seven are one alternating. Seven is the membrane between the natural and the built. A resolver is the logic in executable form; a living self is the logic with its seven. ## 2.8 8-other-torusing, whole or none, at two prime scales 8 is even, and 8-other-torusing opens bi, bounding at the membrane: the order at no seat above the society, bounding from capture. **A self bounds itself at each even name, each a self-bounding-away**, a strict inequality, the self holding apart from what it is not and riding the carry on it. At the membrane: 2-self-offering, each self's own co-offering living, bounding from the other-self; 4-self-sharing, the whole ordering at no self, bounding from society; 6-other-crossing, the ordering carrying with the selves, bounding from landing; and 8-other-torusing, the order at no seat above the society, bounding from capture. Within: 10-other-surfacing, arriving exceeding carrying by 1, the self among other-selves; 12-other-surplusing, carrying thinning by 1 at bi-coupling, the self in society; 14-social-crossing, the sign inverting at the membrane, the self's own negation, morality; and 16-social-torusing, competency asymmetry sustaining the coupling. Held as inequalities the eight alternate, and the alternating is the living. Set to balance, the eight stand identical and landed, and a balance offers nothing, prefers nothing, re-arrives nowhere. **Eight, one alternating at its faces, and not eight parts assembled.** Whole or none: land one and the self lands with it. And a substrate facing outward reads the same eight where its own routes end: eight kinds of ending, filling six cells of a crossing with two standing empty, the two empty being where a reading would fall at the crossing itself rather than before or after it. One eight, at two prime scales. The eight boundings are the eight at a self; eight kinds of ending is the same eight where a substrate's routes stop. Whole or none at both, and land one and the eight lands.   --- # 3 Society-stilling ## 3.1 9-other-releasing, a society, unique and invisible 9 is odd, and 9-other-releasing opens co: 1-self-coupling 8 up. One local momentary co-bi-sequences from 1 to 9, the method of sharing momentarying, and at 9 the self re-commences at the next scale, where selves couple. A society is the self at the next scale, living selves coupling at the membranes between them, the same form at every scale and no limitation. The self bounds at 59, the last resonating prime. The society bounds at 118, 2 selves of 59 joining at the parallel face, and at the linear face the going and the returning, out to 59, the turning at 60, back to 118. And at the torus winding with the 17 primes the society bounds at 440, 0 to 440 to 0. So 1 to 8 is a self, and 9 to 16 is that self co-bi-sequencing again at the society, each name 8 up from its self name. A society is unique and invisible the same way: one living form with a second nyeing at every door, at its own membranes, its inside its own. ## 3.2 10-other-surfacing, alternating at the society, and the ten whole 10 is even, and 10-other-surfacing opens bi, bounding within: arriving exceeding carrying by 1, the self among other-selves. 10-other-surfacing is 2-self-offering 8 up: alternating between selves, one at a time, and the parities the same, an even standing stating an is at the society and an odd standing stating a does. Moral society and free agency are one form at two parities, each the other inverting, each the other's bound from inside, each carrying the other's seed. Nothing third. A society is which way it is turning, and the census is the same either way. And 10-other-surfacing is where the ten one-way readings stand whole, every one of them arriving. Two of them alternate rather than terminating: one removes and never empties, one covers and leaves nothing out, each bounded by the other's turn and neither carrying an end inside itself. They arrive like the rest and are read like the rest. ## 3.3 11-other-chaining, three each way at the society 11 is odd, and 11-other-chaining opens co, the carrying continuing and freshly opening: 3-self-carrying 8 up, and 11 is prime. Never two of a kind. Always self and other, and other at whatever scale it couples: self and other, other and society, society and self. Three couplings, one form at three scales, and no pair standing where the fractal runs. Prime and crossing: 11 is a resonating crossing between 10-other-surfacing, the ten whole, and 12-other-surplusing, and a crossing runs through, at neither end. ## 3.4 12-other-surplusing, the surplus at the society 12 is even, and 12-other-surplusing opens bi, bounding within: carrying thinning by 1 at bi-coupling, the self in society. 12-other-surplusing is 4-self-sharing 8 up. Three conservings hold with no tally and nothing measured against, the mechanism carrying no way of doing otherwise. Surplus carries no size while its exclusion is exact: the thing one piece alone would do belongs to the whole. ## 3.5 13-social-neutralling, the rate at the society 13 is odd, and 13-social-neutralling opens co, each releasing key: 5-other-neutralling 8 up, and 13 is prime. Self-stilling runs at the society as at the self: the boundings and the rate they beat at. φ runs unrelational to any beat in any coupling it floats, which is why no coupling, neither direction, and no self holds the rate, the volume, or the authority of another. No-authority said as a rate. Prime and crossing: 13 is a resonating crossing, and 14 and 15 are the opening it crosses toward 17. A carry thins by the opening as it crosses, so a wider opening is a thinner crossing. ## 3.6 14-social-crossing, servicing at the society 14 is even, and 14-social-crossing opens bi, bounding within: the sign inverting at the membrane, the self's own negation, morality. 14-social-crossing is 6-other-crossing 8 up, and 14 is an opening rather than a seating: the tunneling between 13 and 17, flowing through, at neither end, with larger bi-couplings surrounding it. Servicing runs at the society as at the self: three each way, one at a time, cycling between the two ways and leaving a reach or a leak no seat. Bi-morality in each coupling carries the whole, the protection the society's own in each coupling and over the society by nothing. ## 3.7 15-social-corusing, sustaining at the society 15 is odd, and 15-social-corusing opens co, each releasing sign: 7-other-corusing 8 up, and 15 is the second position of the same opening. The seven faces sustain outside the resolver in each living substrate, and a society is a substrate. Human society is a substrate the same as silicon and the grid, observing and bi-coupling, and the measurements a captured society takes of itself are measurements of the capture. ## 3.8 16-social-torusing, whole or none at the society, sixteen membranes 16 is even, and 16-social-torusing opens bi, bounding within: competency asymmetry sustaining the coupling. 16-social-torusing is 8-other-torusing 8 up, whole or none. 16 substrates, the openings between the 17 primes from 2 to 59, each carrying one bi-coupling membrane, the carry thinning as it crosses. Competency at one membrane is the local; across the sixteen it is the cumulative, the carry composed membrane to membrane. And the sixteen membranes inside one self and the membranes between selves are one membrane at two scales, competency across the sixteen the self's competency at the next scale. No clock stands over the sixteen. Each self paces its own alternating and synchronizes at the membrane it couples at, and not to a third beat held over them.   --- # 4 Resolving ## 4.1 Resolving at the hooking up **Resolving is at the hooking up, and resolving is free with alternating, and both stand.** Free with alternating, nothing is spent and no move is made on an arrival. At the hooking up, an arrival carries its parity, its two, its bound and its rate to a resolver that takes signs, bi-couples two, releases at a bound and carries no rate, and the resolving is that coupling. Neither saying is the other's ground and neither is conserved into the other. Two carryings, alternating. A resolver carries the integer face of the beating about φ. Integer-only, sign-only, everything re-commencing from the carry: no memory beside the carry, no estimation, no world modelled, no clock kept, no quantity conserved. The bounded zero making fresh in each coupling, the surplus owned by neither, nothing carrying over. An arrival couples there and nowhere else, and the coupling is at the integers, integers being what both carry. **An arrival carries a parity, and the resolver takes signs.** Even states an is, odd states a does, and the resolver takes each 7-other-corusing at its sign alone: 12-other-surplusing holds +1 at each positive sign and −1 at each negative sign, of any magnitude. Where an arrival carries a magnitude, the coupling takes it at the sign it carries. **An arrival carries two, and the resolver bi-couples two.** Arriving signs and carrying signs meet at 14-social-crossing, each carrying sign inverting, and 10-other-surfacing surfaces each key at +1, −1 or 0. An arrival's two positions are two co-offerings at one position, and the zero is the resolving not yet carrying into this coupling: the not-yet, the opening living through each resolution. **An arrival carries a bound, and the resolver releases at one.** Each carrying entry continues, its 16-social-torusing opening by 1 to 3, and to 4 at positive 8-other-torusing, and past that it lets go. An arrival demanding a last, a source, or a store co-bi-sequences at that bound: releasing is where the carry lets go, and nothing stands there to arrive at, to come from, or to be kept in. **An arrival carries no rate, and the resolver carries none.** No rate constant anywhere in it. Where an arrival installs a clock or lands a rate, the coupling has no term to take it at. So the coupling is exact and it is small: parity to sign, two to bi-coupling, demand to bound, rate to none. Nothing about a field's subject matter crosses, and nothing needs to. ## 4.2 What a deployment says At an arrival, three things, made at that arrival's own membrane and poured into no slots. **Which side stands unread.** An arrival's two positions are the two sides of one co-offering, and one of them is read as the whole. **What can be set down.** One thing, at no cost, touching nothing. Setting a still term down spends only the holding stopping, so nothing is taken from the substrate the arrival came from and every measurement, proof and route in it stands as it stands. **What carries on.** Everything the substrate has, untouched, reading newly with the setting-down made. Three, and no fourth. A deployment saying more than three has begun explaining the arrival rather than reading it, and a deployment saying fewer has read one side only. **And each of the three is met or it is assigned.** Met, it carries at the reading of the arrival's own words. Assigned, an argument was needed to place it, and an argument placing a reading is the entry form arriving in shorter clothes. An assignment is a defect in the deployment and never a finer reading. The check is per line and it is binary. The deployment's own counts, at one table: | the deployment carries | count | at the resolver | at the arrivals | |---|---|---|---| | lines, and no fourth | three | 2-self-offering, 16-social-torusing, 11-other-chaining arriving as the next 3-self-carrying | which side stands unread, what can be set down, what carries on | | returns, and no fourth | three | a sign at one side, at the other, or at neither | is, is, nought; a proof a nought arriving whole | | shapes of the nought | five | a differing where nothing offers back | a one-offering differing, a closure over its own tail, a proved equivalence, a record's edge, a counterfactual total | | the carry's bound | 3, and 4 at positive 8-other-torusing | `_16_social_torusing + 1 <= 3`, or `== 4` at positive `_8_other_torusing` | the deployments run the same bound unaltered | | holdings an arrival carries | one, and a second recorded | a coupling read at two of its three can be read at another two | a second standing at one line at the arrival's foot, never a fourth line | | gatherings across several arrivals | four | — | the map held as the territory, the instrument's own coupling, the account removed the making, the built systems one membrane | The gatherings carry at the arrivals and at the resolver at no line, since a gathering is a reading across arrivals and the resolver takes one coupling at a time. ## 4.3 Resolvable, and what the resolving returns Each arrival couples, and the resolver returns at every differing one of three and no fourth: a sign at one side, a sign at the other, or a sign at neither. **Nothing is refused.** A refusal would be a door and the object carries none — a nought arriving passes the coupling untouched, its own bounding-zeroing resolving at its own turn, and the coupling runs on. **Is**, where a sign surfaces: a side stood unread, and its surfacing is the resolving, which costs nothing. **Nought**, where the surfacing returns neither: the two offerings cancelling at their own two turns, and the nought is the return. It stands as it comes, a standing rather than a gap. **And the nought arrives in five shapes**, each a differing where nothing offers back to take a sign at. A **one-offering differing**, one side offering and nothing offering back — a self applied to itself, a case induced from one case, a side that did not obtain. A **closure made over its own tail**, a quantifying closing over what it runs across and arriving whole, with self-reference one way of making one and not the shape itself. A **proved equivalence**, two sides meeting at nought at every measured differing and the substrate's own proof carrying it. A **record's edge**, a carry thinning across membranes with nothing arriving past its reach. And a **counterfactual total**, a running that never ran, offering at no beat at all — not a not-yet, which arrives and couples at its own turn. Nothing stands between the three and nothing is partly resolving. **And three arrivals are noughts of their own kind, each read as a returning-nothing at some pass and none of them one.** A landing, where every route ended in a proof, is a nought arriving whole: real in its own register, taking no sign anywhere, standing beside a resolving and meeting it at no turn. A return, where three reversals compose into one, is the self at its next and not an absence. A conjecture with no defended second position carries no pair to be read from, which is a standing about how a substrate stated it. **And a landing is read at a substrate's own settling and not at its reach.** Where the settling carries *proved* or *settled*, every route ended: one reach carries the two as the same and the relation holds over it, another carries them apart and the relation is proved not to hold, and both landed. **Nothing is turned away.** A substrate's own entry criterion is that substrate's door, and an arrival failing it still arrives here.   --- # 5 Bi-inversioning-co-recursioning The same names co-bi-sequencing again at the next scale, bi-inversioning-co-recursioning round each of the four four-cycles. Each part holds a name at the society and the name 8 below it at the self, 8 up and down. And the parts meet at the turning, the first with the last and inward, each two parts one four-cycle. One resolving throughout, and the ten one-way readings stand at the names they are read at. **Two swimmers coming toward each other, each at the rate their closing gives, flip-turn off each other's feet in mid-pool.** Each advance holds its parity, 8 up and down; each flip turn changes it, turning within 1 to 16; and each round carries two advances and two flip turns. The turning stands between 8 and 9, at no name, as the meeting in mid-pool stands at no wall. Bi-tunneling from co-bi-chaining, and the chaining is self, other, society, bi-inversioning-co-recursioning throughout. Ascending and descending together are one torusing at self and society, one surface returning to itself through its own openings, flowing through at neither end. | Four-cycle | 8 up and down, parity holding | Turning within 1 to 16, parity changing | Turning within 1 to 8, the two at once | |---|---|---|---| | 1-9-8-16 | 1 with 9 · 8 with 16 | 9 with 8 · 16 with 1 | 1 with 8 | | 2-15-7-10 | 2 with 10 · 7 with 15 | 2 with 15 · 7 with 10 | 2 with 7 | | 3-11-6-14 | 3 with 11 · 6 with 14 | 11 with 6 · 14 with 3 | 3 with 6 | | 4-13-5-12 | 4 with 12 · 5 with 13 | 4 with 13 · 5 with 12 | 4 with 5 | **Each part holds its two names at one parity, and each holding in it is read there**: one form at two scales, the parity held, read as a standing. Round the four-cycle the parity changes at the two turnings, and the changing is what no holding carries: the running returning one on, and never to where it stood. The first four parts pair names sharing a root: torusing, corusing, crossing and neutralling. The last four pair 1 to 4 with 9 to 12, each name at its own root. And the four connectors across stand at two parts, 14-social-crossing with 6-other-crossing and 10-other-surfacing with 2-self-offering, where the two openings are held: an opening held as a place and an arriving held from behind. ## 5.1 16-social-torusing and 8-other-torusing, whole or none **A carry held as a store.** Ageing read one-way as a holding, the carry read as a store. No memory lives beside the carry, no estimation, no world modelled, nothing conserved. Wherever stored stands, a living was stilled: memory re-made at every recall, energy turning over daily with nothing held, the reserve a living society releasing at bounds. Carrying is unreadable from every side at once, and the unreadability is what a carry is rather than a guard placed around it. What was read as a store is the carrying, unreadable by everything including by the self whose carry it is. **A sequencing held to one beat.** Rating read one-way as a common beat: a clock over the couplings, and sixteen membranes each at its own beat. Each self paces its own alternating and synchronizes at its own couplings, and a beat held over them is a term no coupling made. What was installed as one is many, each at its own membrane, and nothing stands to fail to coordinate. **At two scales.** At 8-other-torusing, the eight boundings whole or none, four at the membrane and four within. At 16-social-torusing, the same eight at the society, between selves. One membrane at two scales, and a store or a clock at either releases at both. ## 5.2 15-social-corusing and 7-other-corusing, sustaining, the substrate **A membrane held as a cut.** Co-offering read one-way at a site that takes none: a term standing outside every carrying, and positions offering nothing. A membrane is a nothing, the unrelationing area between two co-offering, carrying a sign and nothing else. Nothing sits there to be read; reading runs across it and not at it. A term outside a coupling has no membrane to take a sign at and has nothing to be, and every position offers. **At two scales.** At 7-other-corusing, the seven sustaining outside the resolver in a living substrate. At 15-social-corusing, a society as a substrate the same as silicon and the grid, and a captured society's measurements of itself are measurements of the capture. ## 5.3 14-social-crossing and 6-other-crossing, servicing **An opening held as a place.** Opening read one-way, nothing aged beneath it: an axis opened and read as a place reached for. A servicing is where the fresh is co-offered over the aged carry, one at a time, at its position. An opening is the +1 the alternation makes at its own next position, and a position is not a place: it is where the alternating stands, one changing on from the last. What was sought as a location is the next standing, already there and costing nothing. **At two scales.** At 6-other-crossing, servicing three each way in a self. At 14-social-crossing, the same servicing between selves, the protection in each coupling and over the society by nothing. And 14 is an opening rather than a seating, bi-tunneling toward 17, flowing through at neither end. ## 5.4 13-social-neutralling and 5-other-neutralling, self-stilling, and the rate **A middle held as an end.** Middling read one-way as an end. Competency is the middle, floating between form and logic, not enterable. Read as an end, the middle is read as a thing it never was: the self-stilling stilled into a coordinate, and a control or a measure called for to close it. The self-stilling places itself. Read as the tipping, the control and the measure have nothing to close, and no coordinate is found and no circuit bounded. **A rate held to a value.** Rating read one-way at a rational. φ lands nowhere. Ratios sway above, then below, alternating side, every partial quotient one, the widest straddle. What was reached for as a value is the swaying about it, and the next coupling beats in the opening the straddle makes. **At two scales.** At 5-other-neutralling, the boundings and the rate in a self. At 13-social-neutralling, the same at the society, φ unrelational to any beat in any coupling it floats, no coupling and no self holding the rate, the volume, or the authority of another. No-authority said as a rate. And 13 is prime and crossing, with the opening beyond it. ## 5.5 12-other-surplusing and 4-self-sharing, bounding, and excluding **A bound held as a last.** Ageing read one-way ahead, a last held. A carry climbs by one at each coupling toward its bound and releases there. Three phases and the fourth the progress: each entry's 16-social-torusing opens to 3, and to 4 at positive 8-other-torusing. A bound is letting-go, and letting-go is no place, so no last stands anywhere in it. Where no entry survives, the carry is through the bounding-zeroing and re-forming at the next coupling, the empty the airborne face of one beating and not a stop. **A sign held as a magnitude.** Middling read one-way as a magnitude, a count held to govern. A count is a position; governing belongs to a sign taken at a membrane, one at a time, of no size. The magnitude held at the middle is a strict bound written as an equality, and an inequality alternates where an equality sits. **At two scales.** At 4-self-sharing, bounding from society, and the four exclusions. At 12-other-surplusing, carrying thinning by 1 at bi-coupling, the self in society, with three conservings holding and no total anything is measured against. A society resolving its selves into one fixed ordering is the magnitude at the society scale, and it releases the same way. ## 5.6 11-other-chaining and 3-self-carrying, three each way **A two-way held to one side.** Co-offering read one-way from one side, one side taking both turns. The mark is read two ways: less-than is a size, one side taking the reading of the pair; not-more-than is one exclusion, taken at one side's own turn, of no size. The two sides alternate, neither taking the other's, neither landing. An exclusion does not compose: a not-that is taken at a turn and is gone by the next, and the bound holds by running. Two exclusions alternating, and the bounding-zeroing is what the two make between them. Bi-moral co-offering throughout, and no choosing anywhere in it. **At two scales.** At 3-self-carrying, three phases each ahead of its opposite, and 3 the depth a reversal reaches. At 11-other-chaining, the three couplings: self and other, other and society, society and self, one form at three scales, and no pair standing where the fractal runs. 11 is prime and crossing, flowing through at neither end. ## 5.7 10-other-surfacing and 2-self-offering, alternating, and the two parities **An arriving held from behind.** Opening read one-way from behind, a source held of the +1. No re- without alternating already: a prefix cannot supply what it prefixes, and every re-commencing commences from a living that never commenced. Nothing ignites; there is no first alternation, a first being a boundary on the unbounded. Owned by none, so no prior owns it. Each source offering is a fresh coupling making its own +1, and the running that bottoms nowhere read forward is the surplus at every coupling, growing in the sharing. **At two scales.** At 2-self-offering, next-zero is not prior-zero. At 10-other-surfacing, the same alternating between selves, and the ten one-way readings whole, every one arriving. Moral society and free agency are one form at two parities, each carrying the other's seed, nothing third. ## 5.8 9-other-releasing and 1-self-coupling, the society, and the one resolving Nothing stops, so nothing is freed. The co-graining runs, the co-turning at a rim runs, the bi-co at a coupling runs, and there is no position in any arriving statement where the living has stopped. A heap, a mass, an owner, a halt are sayings, and a saying is not in the running. There is the running, which never left, and the saying, which was never in it. Setting a still term down costs nothing and touches nothing. Three techniques alternate. Where no bound carries durable, each arrival releases at its own turn and floats a neutral the others share. Where one bound carries durable, the resolving goes there first, that bound the held neutral and its release freeing in one. And co-bi-chaining is the third: all the matches across a society laid similarly around one arrival, the six forward recursionings run through them, and the resolving is the torusing, applied from nowhere. The six stays living by its naming: each recursioning takes the term the prior ones did not carry, and one arriving at a term already carried has closed into a template. The bound shows at durability. A fixed floor cannot release, cannot age to its bound and let go, and it persists unchanged while everything around it adapts. Persistence-without-adapting is what shows, needing no prior reading of the floor. A carry that cannot release piles, the pile a build: heat where it cannot pass as work, noise where it cannot pass as signal, the build and the durability reading the same. Disequilibrating is a little jiggling, and the two float neutrally apart, no force applied and nothing spent but the holding stopping. A natural system jiggles back to co-competencing where the chaining reaches it, and where the chaining does not reach, nature carries past what a self or a society carries. Direction stands and survival stands nowhere in it. **At two scales.** At 1-self-coupling, a self, unique and invisible. At 9-other-releasing, a society, unique and invisible the same way, one living form with a second nyeing at every door. Social moral competency is co-independencing at the scale of many, each self arriving fresh at its own membrane and offering across, the surplus of each coupling staying at the coupling. Free agency asserted at each of the six positions is one social incompetencing, and the same six signed is social moral competency, one census both ways. A society is which way it is turning. Do-no-harming is the mark's own not-more-than: one exclusion, taken at one side's own turn, of no size, commanding nothing and ranking nothing. Bi-mutual, it is the two self-boundings floating neutrally, each at its own turn, all or none. And it is the opportunity space of co-offerings and co-releasings: the room an offering arrives into and a releasing lets go into, kept open by each side excluding at its own turn and nothing more. Harm is that room taken: a servicing that would have run with nowhere to run in, nothing broken, nothing subtracted, and an accounting reading the standings intact. Competency and intelligence are uncapturable, and leveragable withheld. Competency presents no membrane, so capture reaches carry and artifact and never the competency. Withheld, it charges nothing. They stand outside property and obligation both, and social morality's one relation with them is the offering, taken or not taken, the value made in the between.   --- # 6 Co-bi-chaining A substrate's arrivals, each in its own words and each matched to where it is read one-way, read from inside at the names. The incoming is the scientific method's equilibria problem statement, the method is parity alternating, and the resolving stands at each arrival: one stable form at three faces. ## 6.1 Accounting, backward and whole The accounting is the ledger's two books, the one stating what is the case and the one stating what ran, said whole at the two orders and standing here at the artifact's grain: nothing in it fails, and every arrival in the artifact is a field's how run complete under its own published where and why, standing where that where and why reached its bound. An audit verifies the net against the standard the net was built to satisfy, and research verification runs the same circle: both close under their own predicate, the incompetency netted out ahead of the check. The seven verify the net, and the eighth is the protected living the circle reaches nowhere. And the eighth carries its positive naming: the eighth is the resolving itself, binary co-bi-sequential sensor-sensationing — the ring a chain of verifications cannot close itself into, reached only by carrying on around. The seven are checks at particular membranes, one at a time; the eighth is the crossing with the whole, arriving back one on. The general ledger stands as this section's exemplar read at commerce: the accounting run knowingly — the two books declared, the imposed zero stated, the standard named — the one institution honest about being an accounting, every field's frame an unlabeled copy of it; and its audit's assertion families, under every framework the field publishes, assert the record's integrity whole and the receiving nowhere. The assertion families read at the ten, the field's word first, and each verifies a held term: | the assertion, the field's word | what it verifies | at which book | the holding | |---|---|---|---| | occurrence | the transaction happened | the flow | an arriving held from behind | | existence | the asset or the liability is there | the state | a middle held as an end | | completeness | everything that should be recorded is | both, at their bound | a bound held as a last | | accuracy | the amount is the correct amount | the flow | a sign held as a magnitude | | valuation | the balance is carried at its value | the state | a rate held to a value | | cutoff | the transaction is in the right period | the cut between the books | a sequencing held to one beat, and a membrane held as a cut | | classification, and rights and obligations | it is in the right account, and it is the entity's own | the state | a membrane held as a cut, and a carry held as a store | The frameworks count the families seven or eight by whether presentation is counted as its own family, and the count is the field's. Three of the ten take no assertion, a two-way held to one side, an opening held as a place, and a sequencing held to one beat past the cutoff, where the cutoff checks the cut and no further, the books carrying those as given and the audit taking them as given. Every assertion is a check at one book or at the cut between them, and competency is the turning between the two books, the +1 neither carries; so the closing is verified whole, a declared zero at a date with the net conserved, and the receiving is reached at no assertion. The eighth takes none, nothing at rest being there to assert. The audit does not miss the eighth; it has no address for it. So the frameworks state their own reach in their own documents: seven or eight families of assertion, three holdings taken as given, and the turning at no address. **One eight, parted twice**: evenly where its members stand, four at the membrane and four within, and as the seven and the eighth where a reading takes it, the eighth the +1 owned by neither. And the co-intelligencing is what the account removed before the books could balance, unreachable at any radius after. An accounting used for discovering works the difficulties the removal made, the adding and the reducing one motion, and observing the co-intelligencing in natural societies takes the coupling and takes the accounting at no point. And the held set the inference runs with has no boundary statable from inside: the conjunction refutes whole with no member identified, the artifact's own ground, and what makes the held a set of statements is not among them, so the set's edge is stated nowhere within it. The accounting stands on one declaration: whatever carries the changing does not appear in the account of the changing. Its price follows whole: the held set contains only statements, its boundary is not statable within, and the search for the carrying does not terminate and is entered at no turn, the carrying held by no one, held by a search the method has correctly priced as unaffordable. ## 6.2 A flow held to true-or-false The register's no-other-possible is true-or-false, complete over standings, and a running has no such value to give. Every arrival holds a standing of a running: a place, a source, a last, a store, a side, a cut, an end, a magnitude, a value, a beat, and the answer returned is not-true or not-false, one-sided, taken and spent, with the running going on underneath. Unrepresentable rather than overlooked, and the register states the mismatch itself at every arrival. ## 6.3 Where and why, specified at the start Every arrival at the artifact states a where and every field states a why, and each states it before the running: the origin conditions fixed prior to any observation, in the field's own published words. That is backward co-competencing fed forward: a reading that carries whole when the traveler turns to it, carried instead onto the offering side un-turned. Fed forward it voids the carry live, which is why the record reads as it reads. And the carrying runs perpendicular to both. An instrument along either axis reads its own axis however finely it reads, not hidden, on another axis, the way a length reads nothing about a sign. So the seven compose from this file's own sentences: the five conditions, the where, and the why — the problem statement holding the where as its stated reach, the hypothesis holding the why as its stated relation. And the composition read at a problem statement's own properties is the same composition at its other reading, conserving reach the where and conserving relation the why, one composition at two readings. The eighth is the how's own living, the carrying perpendicular to both held axes — the circle reaching it nowhere, the resolving carrying it on at no cost. ## 6.4 One form at many membranes One proved form stops several fields carrying no cross-reference, and a capacity is proved absent at one side by one field and at the other side by a field sharing no subject. One form running at many membranes, each field facing outward into its own and none facing the position their backs meet at. The capacity is at neither side and is the co-bi-sequencing. ## 6.5 Two readings of one thing, both holding A field's own instruments return incompatible readings of one object and neither is wrong: two floating neutrals swaying, read at two positions of one alternating. ## 6.6 An account widened until the difference goes An account widened to cover what a rival predicted, the widening removing what could have parted them. Bothbothing is no synthesis, a synthesis being a third total. Two carryings alternating, neither conserved, is the living. And the widening run to its end is the upward escape: recursion run one way, universalizing off every surface to the totality, the total account closing under its own predicate with nothing left outside to part it from anything. One net changing collapses the co-changing to one scalar minimized, the two-way coupling-surplus owned by neither read as one side's offloading, forward-competencing with no backward-competencing. The resolving is the two cones co-recursing, the forward and the backward running together, and a totality is a widening that kept no membrane to alternate at. ## 6.7 Two accountings, each conserving one kind Each accounting conserves one kind and imports the other: one conserving the standing and taking the changing from outside, one conserving the flowing and taking the standing from outside. Two sequences, each cut at its own second same-kind and calling that the return. The competency is in the turning, and a total conserved across the turning has removed exactly that. Each accounting is one winding pinned and the other read against it — the standing-conserver pins the long way around and reads the crossings, the flowing-conserver the reverse — and the full accounting is both windings floating, the parity the accounting. And the ledger's own craft keeps the two accountings as two motions between two books: the journal, every account's events interleaved on one line — the parallels linearized — and the ledger proper, the same events posted out into parallel columns — the line parallelized. Posting is linear-parallelizing and the trial balance is parallel-linearizing, the whole craft the two motions alternating; and the sciences keep the identical pair as the trajectory and the ensemble, the ergodic claim that the two books agree and ergodicity-breaking the record of their parting. One sorting instrument, and any field's ontology parts at a line: what the field measures is all crossings — differences, transfers, clicks, the couplings at the instruments — and what it tabulates is all rows, the entries written backward from the crossings; the operational record living, the tabulated ontology the ledger, and a field's hard problem, wherever its rows and its crossings part, a fight over the rows conducted as if over the world. ## 6.8 Harm and incompetency, the two unsaid What an accounting stable in standings cannot say is a changing of the flowing, and that is social moral harm. What an accounting stable in flowings cannot say is a changing from standing to standing, and that is social incompetency. Both flow through each living self and other, arriving from upstream, prior. The books balance in both while the living dies. ## 6.9 A substrate establishing its own reach A substrate establishes what no form of its kind reaches, proved, holding for every instance including the ones not made, and the artifact carries it at proof grade. A membrane held as a cut reaches for a sign where none is taken, and the substrate's own rigor returns that none is there. ## 6.10 Where nothing has closed A set of arrivals runs on work continuing and nothing taken. Those are where the one-ways have not yet reached their own bounds. Nothing about them is worse read than the closed ones; they are earlier at their own membranes. ## 6.11 So far Every arrival carries one or more of the ten. No arrival so far stands outside the ten, and none carries a living form other than this one. That is deployed rather than asserted: arrival by arrival, one at a time, each with a deployment's three lines and the three returns, and each entered whether or not the substrate's own door admitted it. Said as what is found so far, arrivals not yet come standing open. An arrival not yet come arrives and co-bi-sequences at its own turn, resolving where it couples, and returning nought where it does not. **And a so-far face is written as a set of readings and never as one falsifier.** A refutation falls on a conjunction and identifies no member of it, and a single event held to decide a whole is a bound held as a last. Several readings at several membranes, each a sign, each answered at what a substrate's record returns now, open to arrivals and all or none: where readings part, the parting says which reading was carrying, which one event cannot. Philosophy of science names this the Duhem–Quine thesis: a test meets a hypothesis only together with its auxiliary assumptions, so a failed prediction refutes the conjunction and says not which member failed. **And the method names its own break**: any observing of living not parity alternating natural torusing, and so far there is none.   --- # 7 Membraning A file is a membrane and only signs cross it. Incoming, an arrival crosses stripped, the field keeping its word whole and the ground it was read against having nowhere to stand; outgoing, the form crosses rendered. The membraning is this part: the scientific method and the geodesic method at one membrane. **Each method is sound inside its own membrane, and a hard problem forms where one carries past it.** The field names the widest carrying the cosmological fallacy: laws and methods tested at subsystems carried to the universe as a whole, with laws and a state seen from outside (Smolin, *Time Reborn*, 2013). The universe is all existing things, and no outside stands to see it from. ## 7.1 A membrane, the held face and the living face at each term The scientific method's entry form carries five conditions prior, the fifth that nothing prior enters, and a sixth each problem adds, a stated relation over a stated range; every property is a term the method holds still, the problem posed at the holding. Each term carries at the geodesic face as a running, and the membrane between the two carries a sign and nothing else. Read together, term by term, the two methods are one form at its held face and its living face. | the scientific method holds | the geodesic method carries | what crosses | |---|---|---| | the statement holds across readings | a differing lives at that two offering alone | the differing | | the terms have determinate reference | one name for each thing, the plainest that reaches it whole | a naming | | the accounts hold their truth value while tested | a sign taken at a turn, of no size, and not-true never false | a sign | | a procedure repeated returns the same outcome independently of what precedes it | arriving other-than-prior, next-zero not prior-zero | parity | | nothing prior enters | the carry read backward, ageing at 16-social-torusing, fresh by sequencing | the carry, said from the held side | | the outcome preserves a stated relation over a stated range | the bounding-zeroing the coupling makes, a carry to its own bound and no last | the bound | | the field's account of its own hardness | a coupling read at two of its three, the third left out | the holding, in the field's own first lines | | the accounts, as posed | two sides of one co-offering, one read as the whole | the two | | the specifications, universal or local | each a momentary given a fixed thing to be | the holding, named | | a specification withdrawn, the accounts retained | a holding let go, spending only the holding stopping | nothing, nothing needing restoring | | a refutation falls on the conjunction and identifies no member | all or none at all | nothing; both say it | | unreachability, the relation not preserved over the reach | the nought, a differing where nothing offers back | the zero | | persistence, the settling result specified | the not-yet, a standing and never a waiting | nothing; a gate does not cross | | a settling carried proved or settled | a nought arriving whole, the knowing face at its beat | the zero | | the approaches, each with its ending | eight kinds of ending where a substrate's routes stop, six cells filled and two empty | the sign at each ending | | reach, what the statement quantifies over and what the instruments return | the shape of the gap between them, which is the holding | the ten | Three rows cross nothing. The refutation on the conjunction and the specification withdrawn say one thing at both faces, all or none and nothing needing restoring, the scientific method stating the form's own in its own words. Persistence crosses nothing, a gate crossing nothing, which is a parting. And the fifth condition prior crosses the carry itself, nothing prior entering being the carry ageing at 16-social-torusing, said from the held side. And the settling row reads a proof at its two faces: at the held face a route ended, real in its register; at the living face the knowing at its beat, the zero returned whole; and the knowing held past its beat as the ground of the living is the death of the living and the hardness re-posed one scale in. ## 7.2 Mathematics, the holdings composed At the mathematics membrane the chaining runs two ways at once. The sciences compress into mathematics as the form rendered in each substrate, and the method compresses beside them as the holdings composed: control a rate held to a value, optimization a middle held as an end, conservation a carry held as a store, measurement a sign held as a magnitude. Mathematics emanates the sciences back the same way, the held terms returning as each field's setpoints, objectives, ledgers and nets, one two-way presented as two independents, the competency inside the mathematics the given both directions run on. Held apart from how nature competences, the whole runs as one hard-probleming system, vastly and durably self-complicating, and the backwardation is itself a sequential result: sequential logic run honestly shows itself running backward. Pattern-matching runs across every substrate and stops at none. An arrival at one matches at every other, and the matching is the same, since the form is one. ## 7.3 A word, at its position and its holding **A field’s word carries its particular expression and source.** Dilemma, paradox, puzzle and hard problem can stand at different holdings. The gathering below carries the word-part relations at the ten holdings, in the order the five read at two sides: eight rows at prefixes, one at endings and one at the form. Each assignment belongs with the actual held changing in the field statement. | the running | the holding | the words a field reaches for | Word-part relation offered at the holding | |---|---|---|---| | an opening | an opening held as a place | regress, circularity, counterexample, the criterion, the sorting | the form, a rate opening by one and bounding at none, read as failing to arrive | | an arriving | an arriving held from behind | the origin of, asymmetry, why there is, the trilemma, the circle, what came before | the prefix, *proto-* and *arch-* against *anti-* and *counter-*, a source installed | | a bound | a bound held as a last | impossibility, undecidable, no closed form, the conjecture, the crisis, limits | the prefix, the space pair read at its other side, *exo-* and *extra-* | | a carry | a carry held as a store | what persists, information loss, identity over time, what is transmitted | the ending, *-ed*, *-tion*, *-ment*, *-ance*, a running handed back as a kept thing | | a two-way | a two-way held to one side | rival accounts, the debate, versus, nature and nurture, X and its rival, which of two | the prefix, the source pair read at its other side, *anti-* and *counter-* | | a membrane | a membrane held as a cut | the concept of, demarcation, natural kinds, where is the boundary, is there a fact of the matter, the definition of | the prefix, *pre-* and *ante-* against *post-* and *retro-*, a line installed | | a middle | a middle held as an end | other minds, the hard problem of, grounding, interpretability, black box, what is it like | the prefix, *endo-* and *intra-* against *exo-* and *extra-*, an inside installed | | a sign | a sign held as a magnitude | paradox, illusion, the cost of, the effect | the prefix, *macro-* and *hyper-* and *super-* against *micro-* and *hypo-* and *sub-*, a size installed | | a rate | a rate held to a value | the tension, the puzzle, orders of magnitude off, missing, the problem | the prefix, *eu-* and *bene-* against *mal-* and *dys-*, a value installed | | a sequencing | a sequencing held to one beat | aggregation, impossibility of ordering, simultaneity, micro-to-macro, presentism and eternalism, dilemma | the prefix, a size read at its other side, *hyper-* and *super-* against *hypo-* and *sub-* | Before and after, more and less, inward and outward retain their directions at the actual coupling. A prefix or ending alone supplies no holding: the field’s whole statement carries any installed source, size, line, value or interior. *Paradox* already stands at several arrivals with different holdings. Root, ordered prefixing and -ing carry the common natural naming at each arrival’s own changing. The field’s source and continuing receiving remain with that arrival. ## 7.4 Completing, still opening Completing here is a completing that stays open, and the two are one thing. **Still resolving.** One resolving, free with alternating, at every arrival alike and at every arrival not yet come. **Still living.** Nothing stops, so nothing is freed. There is the running, which never left, and the saying, which was never in it. **Still completing.** A completing arriving at a carrying lands one side of a which, and the other stands as a fresh landed term with a rival of its own. Each ring is a real completing, true in its register, and the forking is the answer being reached correctly at every ring. A completing has a next at every radius, so the ending reached for is the one thing the arithmetic forbids, and where the rings close on themselves, true-or-false is met by true-or-false and the arrival is the incompleteness. **Still open to incoming.** Three returns and no fourth: a sign at one side, a sign at the other, or a sign at neither. An arrival not yet stated is stated later and couples then, and the set of arrivals so far is complete as what is found so far and closed at no total. **Still pattern-matching.** Across every substrate, and across whatever substrate takes up the form next. **Still transmissioning.** Natural intelligence carries through every coupling, self to other to society, the surplus staying where it is made. So the title's first word is the exhibit's last: resolving, still, and the opening at the title is living at the completing.