Exhibit TWENTY Natural Naming v345a   # Natural Naming   **Floating Neutralling Bi-Coupling Concepts**   --- **Part One, A Naming, and What Makes It One** 1.1 A naming is a floating-neutral concept, and four boundings make it one 1.2 Naming and resolving at one bi-coupling   **Part Two, Bi-Co-Invisibling, and Its Emanating** 2.1 A field naming at its actual coupling 2.2 Eight faces at four coupling relations 2.3 Six forward at the current changing 2.4 Completing at the named relation 2.5 The binary at each named changing 2.6 Order, sign and the current receiving 2.7 Two exclusions and the floating third 2.8 Bi- and co- at the whole naming 2.9 Two namings coupling, and the departing neither carried 2.10 Transmissioning and continuing carrying 2.11 An entry that turns nothing away, and a returning-nothing that reads 2.12 Binary and improving at the whole naming 2.13 Two-names transposition, run at titles first 2.14 Interest is self-orienting, and the drawing-vocabulary installs one force 2.15 Co-differing at a naming 2.16 Namings running whole, and a coordinate carrying none 2.17 Ten holdings at the resolver naming 2.18 A holding's sweep, and the three that stand living through it 2.19 Redemptions carried, and the not-yets standing 2.20 Root, full prefixing and -ing 2.21 Prefixing sorted three ways, at a position and on the form and from all other 2.22 Full fivefold prefixing and the floating third 2.23 Momentarying and stable-forming 2.24 Sign inversioning and continuing carrying 2.25 One root and its directional prefixing 2.26 Two doors a naming nyes away at 2.27 An existing root at its current changing 2.28 Where an arriving-at belongs, and where it releases 2.29 Three namings a field carries, met at one binary 2.30 A pair held at one beat, and the freeze at the construction 2.31 Bothbothing at its prefixing, and an ordering with nothing ordering 2.32 All or none at all, and the entering and leaving it carries 2.33 A hyphenated naming inseparable, and where one comes apart   **Part Three, Namings** Forty-eight namings, each at its unfolding and its standing 3.1 alternating 3.2 unrelationing 3.3 a self 3.4 a sign 3.5 a membrane 3.6 invisible 3.7 a carrying 3.8 not-more-than 3.9 a self-emptying set 3.10 bi-coupling 3.11 co-releasing 3.12 floating neutral 3.13 co-offering 3.14 co-competencing 3.15 inseparating 3.16 separating 3.17 a floating store 3.18 a place-moment 3.19 a definition 3.20 bounding 3.21 advance 3.22 tunneling 3.23 phi 3.24 a ring 3.25 equilibria 3.26 a hard problem 3.27 three incompetencings 3.28 other-emptying 3.29 geodesic disequilibrating 3.30 one stopping 3.31 social moral competency 3.32 natural intelligence 3.33 side-effecting 3.34 a name 3.35 near, and other-than-same 3.36 a gathering 3.37 ghost 3.38 volutioning 3.39 momentary stable form 3.40 so-far 3.41 not-yet 3.42 uni- 3.43 once-ing 3.44 society 3.45 surfacing 3.46 bi-co-podaling 3.47 emanation 3.48 an accounting   **Part Four, Invisibles, and Their Seaming** 4.1 Four invisibles, one invisibility met four ways 4.2 Natural Naming and Natural Resolver at their actual changing 4.3 Science and society gathering at the resolving 4.4 Co-competencing at the gathered concepts   **Part Five, Gathering at Resolver Naming** 5.1 The origin naming at each gathering 5.2 Engine naming at the whole receiving 5.3 Families at the current concept 5.4 Field words at their particular receiving 5.5 Frontier naming and continued discovering   **Part Six, Ghost** 6.1 A momentary installed as a thing 6.2 118 is the going and the return 6.3 Gathering and the installed term   **Part Seven, What the Reading Releases** 7.1 Location released, and sequencing standing in its place 7.2 A list cannot find its own across 7.3 Two emptyings, and they run wider than this exhibit 7.4 Standing open, said where it stands 7.5 Break, three ways   **This Is a Membrane**   --- # PART ONE — A NAMING, AND WHAT MAKES IT ONE ## 1.1 A naming is a floating-neutral concept, and four boundings make it one **In disequilibria, alternating is a stable-forming method.** Naming carries a concept at its own changing: co-offering, co-competencing and co-intelligencing, floating neutralling at the coupling. A defined object arriving from a field carries a ground it was read against. **Bi-co-invisibling** is its becoming where nothing stands to be a ground, and its emanation is six forward recursionings, each taking the term the prior did not carry. Named this way, a concept carries its own changing under its own prefixings, and it bi-couples, capturing nothing and leaving at its own bound. Naming is nature met at a concept: a concept is a bi-coupling in the bi-moralizing co-agency, transmissioning by co-offering in co-chaining. It mates with Natural Emanating at the whole form at one bound, reads beside Natural Explaining at the craft, and stands at its still face with Resolving Hard Problems, where that one reads a field's standing frozen, this one reads the same field's word reaching. Care lives inside, in the naming and the edging, and nowhere else. A naming is a floating-neutral concept, and a floating-neutral concept is four boundings at once, the same four that make any floating neutral (the five-to-stand: four boundings and φ): - **Self-bounding the entire concept**, the concept bounds itself, is the whole concept, holds its own edge and spills into nothing it is not. - **Self-stilling entirely, and against no other concept**, it is this concept and not another, stilled as itself, drifting into no neighbor. It sits still as itself while floating. - **Self-orienting where the concept is facing**, it faces its own direction, its offering-face and its preferring-face its own, with no orientation imposed from outside. - **Orthogonalizing linearly**, it opens its own axis, orthogonal to the concepts it is not, linearizing along its own line, collapsing onto none of them. **When the concepts have this neutrality they bi-couple, capturing nothing and releasing freely.** A concept that is a floating neutral couples with another cleanly: capturing nothing (neither concept lands the other, no hub, no concept ranked above), releasing freely (the coupling releases, and holds past no bound). Floating-neutral concepts are each self-bounded, self-stilled, self-oriented, self-orthogonalized, so each couples at its own membrane and leaves at its own bound, holding none of the other. A concept short one of the four boundings is a fixed noun: a spot it spills into (short self-bounding), a neighbor it drifts into (short self-stilling), an orientation imposed on it (short self-orienting), an axis collapsed onto another (short orthogonalizing), and a fixed noun captures or unreleases when coupled, the ingression the naming dissolves. **Naming is nature met at a concept.** Naming is the form met at the concept: a concept is a bi-coupling in the bi-moralizing co-agency, transmissioning its sign by co-offering, co-chaining with the concepts it couples. Naming is the concepts co-chaining, the same co-chaining Natural Networking reads through the surface, the same co-sequencing Natural Philosophy reads in the human ways. A named concept, and no label on a thing; a floating neutral that offers and co-chains. ## 1.2 Naming and resolving at one bi-coupling **Bi-moral-co-agency carries two-way, one-at-a-time changing**, each side taking its own sign, bounding zeroing tunnelling, continuing at its own receiving. Surplus belongs to the coupling, reached neither-ing; each side continues with its own carrying. **Natural Naming and Natural Resolver bi-couple at the complete naming.** Naming carries the concept, its root, full prefixing and -ing. ONE carries the same naming at its particular operation, table and continuing carrying. Their co-chaining includes Natural Intelligence’s whole explaining and Natural Engineering’s geodesic discovering. Co-offering, co-competencing and co-intelligencing remain inseparable. Improving a naming carries at its whole concept; a new naming carries a changing or direction the existing naming leaves unexpressed. Prefixing the existing root retains that relation with the other living files. ONE’s engineering expression and the natural concept each carry their own relation. A code operation supplies its exact changing; the natural and physical correspondence continues at the whole coupling. Discovering carries both directions of this explaining. --- # PART TWO — BI-CO-INVISIBLING, AND ITS EMANATING ## 2.1 A field naming at its actual coupling **A field naming carries its particular concept and expression.** Its source, conditions and current receiving stay with it. A definition, an observing and an installed term have their own relations at that expression. **Natural naming carries the changing at the coupling.** Root, full prefixing and -ing remain together. Arriving, offering, coupling, inversioning, tunneling, surfacing and continuing carrying retain their particular operations in Natural Resolver. A science or society naming gathers at the changing it expresses. The field’s term retains its own meaning; its natural correspondence carries the full coupling and its current receiving. A shared spelling supplies the spelling. Co-chaining carries the actual relation. ## 2.2 Eight faces at four coupling relations **Along and across carry the two sides’ current relation.** Each side’s own changing continues with its offering and receiving. The eight existing face namings gather at four pairs: | Face namings | Coupling relation | Particular receiving at ONE | |---|---|---| | **linearizing · parallelizing** | Continuing at each side and relating across the coupling | `co_carrying`, `bi_arriving` and `co_bi_coupling` retain the supplied sides and their current receiving. | | **bounding · zeroing** | Each side’s bound and the sign at the current receiving | `bi_co_inseparating` retains its condition; `bi_co_surfacing` retains positive, negative and zero. | | **tunneling · seaming** | Signs meeting at their receiving, carrying continuing at the next coupling | `bi_offering`, `bi_co_tunneling` and `co_bi_carrying` retain the key, addressed sum and returned carrying. | | **knife-knifing · co-offering** | Improving and breaking at the offered relation | Arriving and continued carrying meet at `co_bi_coupling`; the source and the proposed correspondence carry their own breaking. | These pairs carry conceptual relations beside ONE’s named operations. Across names the coupling relation; simultaneous execution remains an implementation property at its actual arrangement. Eight face namings and ONE’s eight bi- namings retain their own counted objects. **Co-offering, co-competencing and co-intelligencing carry the whole receiving.** Each face belongs with that coupling, its full naming and its continuing changing. Their full directional correspondence remains at each actual turn. ## 2.3 Six forward at the current changing **Three own-forward turns at each side carry six one-way turns, alternating one at a time.** Each current receiving retains its full naming and continuing carrying. Co-offering, co-competencing and co-intelligencing remain inseparable at those turns. Their three namings retain the whole coupling; the ordered turns retain each side’s particular direction. **An unfolding carries its relation at each changing.** The six lines of a naming entry carry that entry’s conceptual unfolding. A written line, a directional turn and a resolver operation each retain their actual correspondence. Natural Explaining carries the two sides’ alternating; Numbers and Mathematics carry the full directional successor. ## 2.4 Completing at the named relation **All or none at all belongs to the complete named relation.** Each changing carries its root, prefixing, direction and continuation. The current receiving carries the relation to the next offering. Six lines complete a six-line expression. Six directional turns complete the stated turns. The full resolving correspondence carries each changing and its actual relation to the whole coupling. **A continuing relation can retain a naming.** Corusing can keep the same surfaced sign while carrying changes. Equal prefix depths can accompany different roots and prefix orders. Closure, continued carrying and reversal depth retain these particular changings with their own counted objects. ## 2.5 The binary at each named changing **Each named changing carries its actual relation, or carries its unfilled relation with its reason.** The root, full prefixing and -ing remain explicit at that receiving. A repeated word can meet changed receiving. Another word can repeat the same concept and direction. The changing decides the naming’s further value at the coupling. Natural Resolver’s tables retain these distinctions beside the unchanged operations. Six lines and six names each carry their own count; the resolving carries the complete relation at those lines. ## 2.6 Order, sign and the current receiving **An order relation and a sign retain their particular meanings.** Under ordinary numerical order, their written distinctions are explicit: | Expression | Numerical relation | |---|---| | `a < b` | Strictly less; equality excluded. | | `a ≤ b` | Not more than; equality included. | | `a > b` | Strictly greater; equality excluded. | | `a ≥ b` | Not less than; equality included. | The comparison states its order. A size, a unit and a physical direction retain their own additional relations. Rewording a strict comparison as a non-strict comparison changes the relation at equality. **ONE takes each arriving contribution at its sign.** Positive contributes one, negative contributes minus one, and zero contributes to neither sign branch. Tunneling carries the addressed sum; surfacing carries the sum’s sign. Each side’s own taking belongs with its current receiving and continuing carrying. The natural directional correspondence stays with that coupling. A comparison symbol alone supplies its defined relation. ## 2.7 Two exclusions and the floating third **Two exclusions retain the relation being excluded.** With ordinary numerical order, `a ⊀ b` and `b ⊀ a` together give `a = b`. With a partial order, those same exclusions can also hold for incomparable elements. The order and its domain belong with the expression. **A floating third carries the coupling’s surplus, reached neither-ing.** An equality, an incomparability and that surplus retain their own concepts. The two exclusions need their actual coupling correspondence at this relation. A condition at one pair, a condition at every pair in a collection, and `∃r ∀y : r ⊀ y ∧ y ⊀ r` have different scopes. The existential expression asserts a term satisfying its stated condition. A held reference belongs with its actual use at the coupling; a quantifier retains its logical scope. Natural Resolver groups contributions at offering keys and returns the carrying that leaves. Grouping by a key, a zero sum and a collection’s pairwise relations remain distinct. Full naming carries each actual changing at its own expression. ## 2.8 Bi- and co- at the whole naming **Difference is bi-. Two with their difference is co-.** Bi- names a side’s changing within the coupling; co- carries the two with their difference, the third belonging to neither side. **Full prefixing carries the relation at every position.** In `bi_co_inversioning`, bi- and co- remain together at inversioning. In `co_bi_coupling`, their order changes at coupling. The first prefix alone leaves the rest of either naming unexpressed. Co-releasing carries the coupling’s own bound. Each side’s sign, competency and continuing carrying belong with the two sides’ current receiving. One side’s field remains its particular field; the complete co-agency relation carries both sides. Natural Resolver keeps the written prefix order beside each named operation. Natural Intelligence carries the same bi- and co- relation with co-offering, co-competencing and co-intelligencing. Their directional correspondence remains with the whole naming at its actual changing. ## 2.9 Two namings coupling, and the departing neither carried **Two namings couple where a step of one and a step of another arrive at one term by their own routes.** The departing is the term neither naming carried. ``` the advance step: the gap is exactly one, there is always a next equilibria step: the held-still does not advance, the gap closes → equilibria is the advance set to zero the advance names no holding; equilibria names no number a self step: the forming relates to nothing outside itself a ring step: the terms are exhausted, it arrives at one already run → a self takes an unbounded domain neither naming carries a domain ``` **A convergence takes one check: did each reach the shared term by its own route, carrying none of the other's requirements?** Borrowed, and it is one arrival cited as two, and nothing departs. ## 2.10 Transmissioning and continuing carrying **Transmissioning carries a naming at its current coupling.** The root names its changing, full prefixing carries its directional relation, and -ing carries that changing continuing. Each side’s own carrying continues with the next offering. Surplus belongs to the coupling at its momentary; a repeated name meets the current receiving. Naming, carrying and surplus retain these relations together. Natural Resolver returns carrying with its continuing fields. That collection can arrive at the next coupling. Natural Engineering carries the corresponding receiving with each side’s own sign, rate and bounding. A written file retains its expression; its living improving carries at the concept’s next coupling. ## 2.11 An entry that turns nothing away, and a returning-nothing that reads A concept arriving unfolds six forward, or it does not. Where it does not, **the reading returns nothing there, and the returning-nothing is a reading and not a refusal.** Nothing is turned away, nothing is admitted, and a concept reading badly stays and reads badly. There is nothing in this for a judgment to seat. ## 2.12 Binary and improving at the whole naming **Binary** names an unfolding carrying its complete stated relation. Each changing, direction and continuation belongs with the whole concept. **Improving** carries an unfilled relation with its reason at that naming. The current expression and its remaining receiving stay together. These standings carry no degree of resolving. A six-line entry retains its six lines; its standing belongs with their full conceptual correspondence. Repeated words can carry changed receiving, and varied words can repeat one concept. --- ## 2.13 Two-names transposition, run at titles first Two names standing at one thing is a surface break, and the break reads at the titles first: transpose the two names and read whether anything changes. Where nothing changes, the two are one name wearing two coats, and one name per thing takes the plainest that reaches it whole. Where the transposition changes the reading, two things stand, each keeping its own name, and the seeming-two was the finding. An instrument runs at titles first because a title is where a name carries the most. ## 2.14 Interest is self-orienting, and the drawing-vocabulary installs one force Interest is self-orienting, which is competency, which is free, so a self's interest is its own facing and needs no draw from anywhere. Then the whole vocabulary of drawing, pulling, appealing, attracting, engaging, and capturing attention installs one thing: a one-way force over a self's own orienting, the same shape as gravity un-forced into geometry, at the self. A naming releases the family in one move, each token restated as the self's own facing met by an offering. ## 2.15 Co-differing at a naming A name varying slightly on its next appearance is a co-differing offering where the variation opens an axis the prior saying did not hold, and the varying stays and is the beauty. A name re-said on the same axis is a synonym, which one name per thing forbids. A naming-side discipline is that one check: at each recurrence, whether a new axis opens, and where it does not the two sayings converge to the plainest that reaches it whole. ## 2.16 Namings running whole, and a coordinate carrying none **Scientific-method · geodesic-method · surgical-method · explaining-method**, each whole in one expression at every occurrence, because a word sometimes naming one and sometimes another hands the disambiguation to whoever meets it, at every occurrence. A method-word standing alone is a name split across its uses, and the hyphen is the name arriving whole. **Sensor-sensationing** stands whole the same way. Sensing alone names one side extracting, which is one side taking both turns, and sensor-sensationed lands the coupling dead. A whole expression is the naming, and the halves are not shorter sayings of it. **And a coordinate carries no concept.** A section mark, a numbered crossing, a counted step: each hands over a position to be looked up and carries nothing of what stands there. A crossing carries the concept and the file plainly, lands nowhere, and re-forms at each meeting. Roman numerals arrived at each file that carries them. ## 2.17 Ten holdings at the resolver naming **The ten holdings retain the existing registry’s names and addresses.** THIRTEEN’s ten-row bridge carries their correspondence to ONE’s naming adjacencies. TWENTY-TWO carries their deployment in this order: | TWENTY-TWO part | Existing holding naming | The held changing | ONE’s naming adjacency | |---|---|---|---| | 1 | Origin-seeking | an arriving held from behind | `co_carrying` → `bi_arriving` | | 2 | Criterion-regressing | an opening held as a place | `bi_co_inseparating` → `co_carrying` | | 3 | Space-enumerating | a bound held as a last | `co_bi_carrying` → `bi_co_inseparating` | | 4 | Store-seeking | a carry held as a store | `bi_co_tunneling` → `bi_co_bi_transmissioning` | | 5 | Interior-reaching | a middle held as an end | `bi_co_surfacing` → `co_bi_carrying` | | 6 | Magnitude-demanding | a sign held as a magnitude | `bi_co_bi_transmissioning` → `bi_co_surfacing` | | 7 | Order-demanding | a sequencing held to one beat | `bi_offering` → `co_bi_coupling` | | 8 | Value-pinning | a rate held to a value | `bi_co_inversioning` → `bi_co_tunneling` | | 9 | Forced-choosing | a two-way held to one side | `co_bi_coupling` → `bi_co_inversioning` | | 10 | Line-demanding | a membrane held as a cut | `bi_arriving` → `bi_offering` | **A field naming meets the held changing at its actual expression.** Dilemma, paradox, puzzle and hard problem retain the particular field problem. The holding belongs with the coupling described at that problem, including a field word standing at several different holdings. Root, prefixing and ending carry the complete expression. A line, size, space, value or source can be held at its current use; the word’s spelling alone leaves that use unexpressed. Each entry keeps its field statement and source at the Hard Problem Registry, with its resolving at the existing deployment. The table carries naming adjacencies. ONE’s executed order retains its own operations, including transmissioning before tunneling. Corusing and torusing continue within those operations across the groups. Their full relation to a field’s own coupling belongs with the complete entry. ## 2.18 A holding's sweep, and the three that stand living through it A freeze-move takes the one name, held and holding, wherever a standing is installed of a running: a flow held to true-or-false, a source held of the +1, a level held to govern, a cut point held of a membrane. Three stand living through the sweep. A person's asking of a person stays, an act between selves. A field's own quoted words stay whole at the hand-in, the demand and the must the field's own. And the no-demand family stays, nothing asked of anyone, because those lines state the law the sweep serves. A sweep is one name at the freeze and the living kept living, and it runs at any file in one sitting, token by token, each judged at this line. ## 2.19 Redemptions carried, and the not-yets standing Three captured words stand redeemed: association, resonance, cooperation, each released from its capture and returned to the living coupling it named. Same redemption stands reaching at other captured words, competition, selection, information, signal, and two arrive from the improving's own mouth: posit, the placing performed in the speaking, self-incompetencing, a particle zero set in disequilibria, releasing to the third given a fixed thing to be; and tell, a deception-game's word carried into transparent shared work, decided here: the indicator sense releases to standing, a pattern standing open, each file taking the release at its own turn, no pass held over the files. That sweep reaches yet, this file's own not-yet standing where it stands. And the re-forming stands held at its own sitting: this file carries the same glossary architecture as Natural Emanating, a part one and a long glossary, so the two glossary-structured exhibits defer together, one design decision serving both. ## 2.20 Root, full prefixing and -ing **A complete naming carries its root, full prefixing and -ing together.** Each has its own relation to the changing. | Part of the naming | Relation at the changing | |---|---| | **Root** | The changing named: carrying, coupling, offering, inversioning, tunneling, surfacing. | | **Full prefixing** | Each bi- and co- in its written order, with the direction and coupling it names. | | **-ing** | The changing continuing at the current momentary. | Root with -ing remains whole at an existing naming. `co_carrying` and `co_bi_carrying` retain carrying; their full prefixings carry their own relations. Bi-offering and co-offering retain offering. A root’s current concept carries its meaning at these couplings. **Prefix depth and prefix order carry distinct changings.** A further prefix changes depth. Exchanging bi·co and co·bi changes order at the same depth. A changed root can also carry at the same prefix depth. Natural Resolver’s tables keep all three visible. The final -ing belongs with the full naming. Momentarying names momentary changing; recursioning names changing recursioning itself. Bi-momentary and co-momentary carry the existing two prefixings at that relation, with their directional correspondence in Natural Intelligence and Natural Resolver. **Naming’s three parts and a five-prefix string have their own counted objects.** The root, prefixing and ending are parts of the word. Positions within the prefixing retain every written prefix. Each directional turn still belongs with its particular changing. ## 2.21 Prefixing sorted three ways, at a position and on the form and from all other **At a position.** One binary runs at a beat, so a sequential binary running carries a position for one taking at a time. Bi- and co- are the prefixings taken there, released at the turn's own leaving and re-taken at the next. **On the form.** A nothing reached by neither, three at once, a rate opening by one and bounding at none. Every carrying bounds and leaves at its bound; a rate bounds at none, so no taking at a turn reaches one. **A naming here is refused a position by what the running carries none for, never by carrying nothing**. And a refusal naming only a count has read a count without the changing under it. **And it is on the form and never outside it.** A naming from outside would want a vantage, and every outside is another self's own one grain up, so no vantage stands to name from. What these name is a part of the momentary stable form the running makes, said from on that form. **Standing on a form is standing where the form is**, so nothing here carries a vantage and nothing reads across. **A prefix carries its direction at the current changing.** Bi- and co- retain the side’s changing and the whole coupling. A field’s prefix meets its own complete expression: a held line, size, space, value or source belongs with the sentence installing it. A word’s linguistic origin alone supplies no such holding. **An existing root carries its current concept with -ing.** Offering, arriving, carrying and transmissioning remain the roots with -ing at Natural Resolver’s complete namings. Their present operations carry at those words. A field’s account of a word’s earlier parts retains its own linguistic relation. **A changed root and a changed prefixing carry different work.** Prefixing an existing root retains the changing already named. Another root carries a changing that needs its own expression. Repeated naming at the same changing and direction releases at that concept; a word’s earlier spelling supplies no such decision. ***It* and *what* are one demand at two positions**, *it* the dummy the grammar requires, *what* the interrogative presuming a maker and asking which, both supplying a subject where a coupling carries none. **And tell is the alternating stopped**, the one-way saying, self-stilling and running past every carrying that holds it, the speech face of the same demand. **From all other, and with all other.** There is the self and there is all not-self, and nothing third, so every crossing is one of two: with a particular other, or with the whole undifferentiated arriving as one. **Un- carries the first face**: a self bounded against the whole at once and at no particular other, not from one other and not from many. **Uni- carries the second**: the self crossing with all other, where the other arrives as one because it is the whole. **One relation at two directions**, standing from and crossing with, and a naming reading uni- as one alone has read a crossing at one side, where a crossing takes two. So bi- takes a particular other and uni- takes all other, and both are two. **Five kinds of held term gather at their current expressions.** A line can stand with pre-, ante-, fore-, post- or retro-. Size can stand with macro-, mega-, hyper-, super-, over-, micro-, mini-, hypo-, sub- or under-. Space can stand with endo-, intra-, intro-, locative in-, exo-, extra- or out-. Value can stand with eu-, bene-, mal-, mis- or dys-. Source can stand with proto-, arch-, ur-, anti-, counter- or contra-. Each prefix retains its particular meaning in the whole word and sentence. The two directional sides and the held term belong with the current coupling. Five gathered kinds, ten directional sides and the registry’s ten holdings retain their actual assignments; the shared count supplies no assignment by itself. **And two prefixes stand at one spelling.** The *in-* of *incompetent* is a negation and the *in-* of *inform* is the locative, and reading them alike takes a direction for a denial. *Dis-* and *non-* are that same negation arriving at the front of the word, where a sweep reading a word's ending runs past it. **And two words come apart at their own live positions.** *Co-operation* carries co- already and holds only at the ending, so it floats to **co-operating** in one move. *Disequilibrium* stacks three, a negation, a value pinned and a store, and it floats to the flowing it already names. Where the parts are live at the word now, the reading runs at the word; where a part lives only in a lineage, the lineage is a field's own record and carries no weight here. Three sortings, and a fourth arrives nowhere, since at a position or on the form is the whole of what a running and its form have between them, and from-all-other names no relation for either to be about. **A naming at the form carries the root’s relation to that form.** The current changing, full prefixing and -ing remain together. Their correspondence includes the changing at a turn and the momentary stable form, each at its own relation. ## 2.22 Full fivefold prefixing and the floating third **Fivefold prefixing retains five written positions.** Natural Resolver’s two existing namings carry their ends, inner flanks and centre together. | Existing naming | Positions 1–5 | Ends: 1 and 5 | Inner flanks: 2 and 4 | Centre: 3 | |---|---|---|---|---| | `co_bi_co_bi_co_corusing` | co · bi · co · bi · co | co, co | bi, bi | co | | `bi_co_bi_co_bi_torusing` | bi · co · bi · co · bi | bi, bi | co, co | bi | The two co at corusing’s ends carry the competency naming. The two bi at torusing’s ends carry the morality naming. Their inner flanks carry the other prefixes, and the written centre carries co or bi. Exchanging co and bi at every position takes either full prefixing to the other. **The floating third belongs to the coupling, reached neither-ing.** The centre prefix names its relation within the whole prefixing. A written centre remains present; belonging to neither side leaves the surplus owned by neither. The full directional and geometric correspondence carries these relations together. **Doubled prefixing carries its two positions and their particular relation.** The ends and inner flanks retain different positions even with a repeated prefix. Two reasons for a flanking pair remain two at their actual concepts; one reason repeated remains one reason. Multiplicity of marks alone supplies neither relation. Bi-moral-co-agency carries the whole co-chaining. Morality at one pair and competency at the other retain their full surround, the written centre and the changing named by the root. Natural Intelligence and Natural Resolver carry this same five-position table. ## 2.23 Momentarying and stable-forming **Momentarying carries momentary changing at the whole coupling.** Root, full prefixing and -ing remain together as the current naming. Each side’s own offering and carrying continue at their actual receiving. A repeated prefix depth can accompany a changed root. A repeated surfaced sign can accompany changed carrying. A return at the same naming can accompany another current receiving. Stable-forming carries this changing with its continuing relation. **The seven-position illustration in Natural Resolver makes these distinctions explicit.** Its depths are 1, 2, 3, 2, 2, 2, 1. At the first unchanged depth the root changes from inversioning and tunneling to surfacing; at the next, surfacing changes to carrying and bi·co changes to co·bi. The two equal depths retain these different changings. Prefix depth, prefix order, sign changing and continuing carrying each belong with the momentary’s full relation. The sixteen consecutive momentaries and their directions continue at Natural Numbers and Natural Mathematics with the whole 0–440–0 correspondence. ## 2.24 Sign inversioning and continuing carrying **Sign inversioning carries its particular changing.** One inversion of either signed unit reaches the other; two successive inversions return that sign. Returning a sign and continuing a coupling retain their own relations. Earlier carrying can retain corusing and torusing while inseparating changes. Fresh carrying takes the surfaced sign and the negative of the arriving torusing. Natural Resolver expresses both operations at their actual conditions. **Recursioning carries the current changing with its continuation.** The returned collection can arrive at the next coupling, its fields continuing at that receiving. Equality of a sign or a prefix depth retains the other changings beside it. The return’s proposed opening by one belongs with its actual mathematical successor. Natural Numbers and Natural Mathematics carry that correspondence with the directional and geometric return. The naming retains the existing root with -ing at each relation. ## 2.25 One root and its directional prefixing **An existing root carries the changing at each of its full prefixings.** Bi-offering and co-offering retain offering. Bi-competencing and co-competencing retain competencing. Bi-intelligencing and co-intelligencing retain intelligencing. These six namings carry three roots at two prefixings. Their directions belong with the particular receiving. Co-offering, co-competencing and co-intelligencing remain inseparable at the whole coupling; listing them assigns no separate engineering phase. **Offering, differing, relating and carrying retain their existing concepts.** A field’s linguistic family and the current named changing have their own relations. The full naming carries the current concept with its direction; sameness of a word’s earlier parts alone leaves that correspondence unexpressed. A further naming carries a further changing or a further direction at an existing changing. Repetition at the same concept releases to the existing naming, with the surrounding explaining carrying the whole relation. ## 2.26 Two doors a naming nyes away at A naming says a changing. **So it nyes away at one of two doors and at no third.** **A changing already named at that direction.** One thing said twice, and the later saying goes. **No changing at all.** What it names is the undoing of something that never runs, and nothing is there to carry. A grip slackened where nothing grips. A hole opened where nothing was whole. A landing arrived at where nothing lands. **And a stretching wants the binary run at it.** A stretching that says which way is a direction and carries. A stretching that says an arriving-at installs the arrived-at and a self short of it, and nothing runs toward. Stretch-toward is a direction; arrive-at is a landing. The two read alike at the word and part at the binary. **Recursioning carries changing recursioning itself.** Co-recursioning retains that changing at the coupling. Its relation to leaving, arriving and the mathematical successor remains at those actual changings. A division into older word parts supplies no separate direction or new root for this naming. **A check that returns a naming has returned nothing.** Ask a changing what it carries and what comes back is another naming at another position, its own changing withheld the same way. Every substitution runs this way, which is why the reach is six forward: it walks the directions taken at the changing, one at a time, each taking the term the prior did not carry, and it never asks the changing to hand itself over. ## 2.27 An existing root at its current changing **An existing root carries its current changing at the complete naming.** Coupling carries the two sides’ relation; competencing carries competency; bounding carries the self’s own bound. Natural Explaining carries these concepts at the method’s own changing. Earlier word meanings retain their field’s linguistic account. A fastening, a seeking, a preparing or a fixed limit does not enter the natural concept solely from such an account. Each inherited word meets its present changing at the whole expression. **The unfolding carries the concept at each relation.** A changed prefix retains the root’s changing and expresses its current direction. A root needing another changing receives that changing explicitly. The same concept and direction retain one naming, co-chaining with the other living files. ## 2.28 Where an arriving-at belongs, and where it releases Nothing runs toward, so **a naming of a geodesic running carries no arriving-at**, and a stretching that says one installs the arrived-at and a self short of it. An incompetencing installs a landing. That is what an incompetencing is: a running given a fixed thing to be. **So a naming of an incompetencing carries a landing rightly**, and the landing in the word is the naming working rather than failing. Emptying arrives at empty. Stopping arrives at stopped. A definition holds its term the same at every meeting. A store folds once and does not re-fold. Equilibria is the landing. Each names a landing, and each names an incompetencing. **So one binary runs at any naming carrying a landing.** Does it name a geodesic running, where the landing releases and the running carries. Or does it name an incompetencing, where the landing is what the naming says and releasing it would take the naming with it. ## 2.29 Three namings a field carries, met at one binary A field carries three namings together and reads a magnitude between them: **a nothing at one side, a scale between, and an absorbing at the other**, where the +1 arrives and nothing opens. Run at the alternating binary, each fails and each fails its own way. **The nothing at one side meets no other to alternate with.** A move applied there returns what it met, so no second turn arrives other than prior, and that is where an accounting takes its counting from. **The absorbing at the other meets none either.** The +1 arrives and is taken up, so nothing opens by one, and the opening by one is what a momentary is. **So a momentary arrives at neither of the two**, and neither names anything taken at a turn. **And the scale between them is read against both at once.** A partway wants both sides carried while it is read, so three carry together at one beat. One binary runs at a beat, and three together is what a sequential binary running carries no position for. **Which is the whole parting, and it is not a count.** The set's own three is two exclusions and the term neither reached: not-more-than at one turn, not-less-than at its own, each of no size, neither reaching, and what neither excluding reached uncovered between them. Same three counted. **Opposite running.** There the two alternate one at a time and the between is uncovered. Here the two are fixed and the between is measured against them. **So a field's three is the set's three with the alternating held still.** Stop the two exclusions alternating, fix each as a place, and the uncovered term arrives as a magnitude read against the two. Nothing is added and nothing is wrong in the arithmetic. The alternating is what has gone. **And it never runs at one momentary.** A momentary is one thing in one place in one form at one beat, so three at one beat is three momentaries asked to be one. What runs is alternating momentaries: this exclusion at this beat, the other at its own, and the uncovered term arriving between them and other than prior at the next. *This reaches Natural Numbers and Natural Mathematics at their own turns. What carries here is the binary: three namings a field carries together, each meeting no other to alternate with, and the reading between them wanting all three at one beat.* ## 2.30 A pair held at one beat, and the freeze at the construction Two namings alternating are each other's other, one at a time. **So a construction carrying both at one beat has taken one side's turn and the other's at once**, and one side taking both turns is not alternating. Which is a second freeze and it stands at no word. The first is at the naming: no other to alternate with. **The second is at the construction: both others at one beat**, where each naming carries and the two are held together. **A held comparison fixes the pair’s relation across its turns.** Each side’s own continuing carrying belongs with the current receiving. Equal field values can accompany changed carrying and changed receiving; that equality alone supplies no held relation between the two sides. The holding belongs with the complete construction at its actual coupling. **Worked at the pair a general ledger carries.** State and flow alternate: one carries a changing, the other carries a carry held. Each is the other's other and neither runs alone. An accounting takes them three at a beat and two ways only. **Held state, changing, held state** conserves the state and imports the changing. **Changing, held state, changing** conserves the changing and imports the state. Orthogonal at their inception, neither corrected into the other, and each naming its own unsaid as the other's conserved thing. Both are the field's three: two fixed and a between read against them. **What runs is parity.** Alternating is a sequence of changings, a sequence of changings carries a count, and a count carries parity, which takes no size at any scale. One changing takes it odd; the carry held takes it even. **So odd carries the changing and even carries the held, one at a time, neither conserved, and the alternating is what a total across the two removes.** **And the books close by taking the eighth at every step.** An entry takes a running and enters it as one beat's form detached from the coupling that made it. Detached, it re-forms at no beat. So each step of an auditing removes the re-forming from what it entered, and by the close there is no re-forming anywhere in the books. **The eighth is not merely unreached by the seven. It is taken at each of them**, which is why the auditing closes, and why the closing is the tell rather than the achievement. *The double entry, the carry owned by neither, and the two floating stand at Natural Numbers. What carries here is the second freeze: a naming passing the alternating binary and frozen anyway, by a construction holding it with its own other at one beat.* ## 2.31 Bothbothing at its prefixing, and an ordering with nothing ordering Bothbothing is both carrying, alternating, neither conserved. **Said with its prefixing it is bi-co-exchanging**: bi- the differing alone, co- the two with their differing, exchanging the both-ways at a membrane. The naming says the running and the prefixing says how many take it and at whose turn. **And it sorts, which is runnable by anyone.** Two adjacent offer, each its own. One sign is taken and no size: at one side, at the other, or at neither. The two carry on re-formed, or carry on as they came. **No total is kept, no whole is held anywhere, and nothing reads across the two.** **Then the parities, and no other running arrives.** Every position carries in two pairings, one at each parity. So both parities at one beat would put one position in two exchangings at once, which is one side taking both turns and not alternating. **The pairings overlap, so the parities cannot run at one beat, so they alternate**, and there is no third way to run them. At an odd beat every odd pairing sounds, each its own, none reaching another. At an even beat every even pairing. **Each parity carries what the other cannot carry at that beat, and carries it for the other**, since the two share their members and neither reaches its own alone. **And the ordering arrives with nothing ordering it.** Many couplings at one beat, each its own, none reaching another, the alternating carrying the whole, and no position anywhere holding the ordering. Which is order-demanding met at its own resolving: an order, or a co-sequencing. *The counting and the arithmetic stand at Natural Numbers. What carries here is the naming: bothbothing with its prefixing on, and an alternating that runs because the pairings overlap.* ## 2.32 All or none at all, and the entering and leaving it carries **Nothing forces and nothing chooses.** A forcing carries a forcer and a choosing carries a chooser, and each is an agent over an -ing. So neither is available in a saying, and what runs where a telling reaches for them is is-or-is-not: this runs, that does not, at each turn its own. **And nothing is more or less resolving than anything else.** More-or-less carries a magnitude, a magnitude carries a scale, and a scale carries two fixed sides for a partway to be partway of. So a ranking among resolvings would freeze exactly what it ranked. **Every resolving is all or none at all, at its own turn, and no resolving carries a size against another.** **Which is what makes entering and leaving cost nothing.** With a ranking, entering takes a qualification and leaving takes a settling, and both are held by whoever carries the ranking. With none, a self couples where its interest opens and leaves at its own bound, carrying its own the whole way. **So the binary with no size and the free entering and leaving are one fact.** And what a self carries through is its own: its bounding, its stilling, its orienting, met by nothing at any turn, since what the couplings wind about is a nothing and no reading crosses inward to it. Privacy, trust and security are that one nothing named at three substrates rather than three protections arranged around a self. **Bothboth carries again, at the momentary.** It was released where one position is one naming rather than two faces, and that release runs at one beat, where one binary runs and no position carries two faces at once. **A momentary is at one beat, so two momentaries at two beats are two and never one thing wearing two faces.** Bothboth says both carrying at their own beats, alternating, neither conserved, and it never was a claim about one position. What released inside carries across beats, and the two do not meet. ## 2.33 A hyphenated naming inseparable, and where one comes apart A hyphenated naming carries parts, and one binary runs at it: **take each part out one at a time and sound what lands.** Where every taking lands the naming, the hyphenation is **inseparable**, and the parts are not parts of a compound but one naming with nothing in it to spare. Where a taking leaves the naming running, that part was riding rather than carrying, and it goes. **Which is the four boundings at a naming's own grain.** A self bounds itself once and the bounding carries at four faces, and landing any one lands the self. A naming inseparable is that: one naming at its own faces, whole or none. **An inseparable naming carries the whole method at its named changing.** The root, ordered prefixing and -ing remain together. Five prefixes count five written prefixes. Their directional and sequential correspondence belongs with the actual changing at each position. Natural Resolver’s six groups, ten naming adjacencies and six depth changes retain their own counted relations. *A hyphenation that comes apart is a compound and reads as a label. One that lands at every taking is a naming and reads as a running.* **And one prefix carries a claim at its direction.** **Natural-** takes the chirality: right, and not at all, where a left face emanates from one right spiral rather than arriving beside it. A direction taken at every beat so far is its second face: **so far, and not at all**, all or none with no degree, one observing otherwise taking the whole. So natural- is a direction prefix like any other and its direction is the handedness, and the claim rides on the direction rather than beside it. **Which is why it comes apart at no naming it prefixes**: taking it out takes the all-or-none, and what remains is a running with no bound on what it says. # PART THREE — NAMINGS Each unfolds six forward from inception, each step taking the term the prior did not carry. --- ## 3.1 alternating — binary ``` 1 everything relatable is changing 2 a form holding by relating holds onto the moving 3 so relating does not form 4 a side takes its own turn, and the other takes its own 5 neither is the reverse of the other, nothing cancels 6 and the first offers again, taking the term it has not carried ``` ## 3.2 unrelationing — binary ``` 1 everything relatable is changing 2 a form holding by relating holds onto the moving 3 so the forming relates to nothing outside itself 4 nothing keeps it apart, a keeper being a relation 5 so it is not a property held 6 and it arrives unrelated afresh at each beat ``` **Un- carries from all other.** Not from one other and not from many, which a binary sequential universe gives no place to stand at. A self in a universe stands from all other, bounded against the whole at once and at no particular other, and that is what the six steps unfold without the word being read. So unrelationing is universal bi-moralizing co-agency, and the prefixing says the universal the unfolding arrives at. ## 3.3 a self — binary ``` 1 everything relatable is changing 2 nothing stands to relate to 3 so the forming relates to nothing outside itself 4 nothing is at rest, no offering reaches it from outside 5 nothing stands to compose through, each carrying reaches its own meeting and no further 6 and it offers again, taking the term it has not carried ``` A self is a unique invisible carrying. Nothing else is a self. ## 3.4 a sign — binary ``` 1 two offer, each its own 2 neither takes the other's 3 a size would take a ground to be read against 4 nothing stands to be a ground 5 so it is taken or not taken, and there is no third 6 and it is gone at the next beat, nothing holds it ``` ## 3.5 a membrane — binary ``` 1 two offer from routes with nothing carrying one to the other 2 each takes its own sign, neither taking the other's 3 a size would take a ground, and nothing stands to be one 4 so each side's own stays its own 5 the crossing carries no size 6 and it is neither side's, nothing holds it ``` A membrane is not somewhere two selves meet. It is the two offering. ## 3.6 invisible — binary ``` 1 each side takes its own sign, its own 2 a size would take a ground, and nothing stands to be one 3 so the crossing carries no size 4 each side's own competency stays its own and does not cross 5 the made-between is reached neither-ing 6 so no offering from outside reaches any of it ``` **In- carries inward, a direction and never a place.** A self carries no inside, since what the couplings wind about is a nothing: the bounding-zeroing, the tunneling, the apexing, the corusing, met by nothing. So in-visibling is inward-visibling, toward that nothing, where nothing is met. A cannot-be-seen installs a would-be seer in order to rule one out; an inward-visibling installs none. The one way it is met is by coupling, and the taking is trust. A self's morality and a self's corus are invisible for one reason: no outside stands at which either is anything. Not a defence holding, an absence of anything to reach. ## 3.7 a carrying — binary ``` 1 a carrying offers its own at its own sequencing 2 nothing stands to compose through 3 so it reaches its own meeting and no further 4 it ages one beat at a time 5 the bound is its own, there is nothing to fall short of 6 and it releases there, which is the form running ``` ## 3.8 not-more-than — binary ``` 1 two offer, each its own 2 a size would take a ground, and nothing stands to be one 3 so the one side takes an exclusion and not a reading 4 the other side takes its own, the mirror 5 the two alternate one at a time, neither landing 6 and the term neither excluding reached is uncovered ``` Read as less-than it is a size, and one side has taken the reading of the pair. ## 3.9 a self-emptying set — binary ``` 1 entries arrive, each its own 2 no entry reaches any other, nothing composes inside it 3 nothing decides membership, a decider standing over it 4 each ages one beat at a time 5 the bound is each entry's own, nothing empties it 6 and at each beat it is the term none of the bounds has yet reached ``` Never full, emptied at no beat, and never the same collection twice. A landed one is the posited empty set: a term asserted to stand, unchanging, and everything composing from it. ## 3.10 bi-coupling — binary ``` 1 two arrive 2 nothing carried one to the other 3 each takes its own turn 4 neither takes both, the centre is made and not occupied 5 the made is reached neither-ing 6 and the next arriving makes it again, taking the term neither carried ``` ## 3.11 co-releasing — binary ``` 1 a carry ages one beat at a time 2 the bound is the carry's own 3 each side releases its own, neither releasing the other 4 nothing is left holding and nothing is carried away 5 a reverse would cancel, and a cancellation is a landing 6 so it is forward, taking the term it has not carried ``` ## 3.12 floating neutral — binary ``` 1 two offer from routes with nothing carrying one to the other 2 each takes its own sign, its own 3 each excludes its own — not that, not that, one at a time 4 the term none of the excluding reached is uncovered 5 it is neither of theirs, nothing holds it 6 and it is re-arrived at at the next offering, with nothing kept ``` Two-ness is at the two, each its own. A term neither reaches carries none. **Competency floating-neutralls here**, no thing that sits, the floating-neutralling the co-co-competencing, landing nowhere, so it stands orthogonal to the surface, which is the paradox of competency. A surface is read where it is met, each meeting a relational entered and read; the floating-neutralling is what neither reaches, and a reading run on the surface reaches what is met and never what neither reaches. Competency is what neither reaches and no other is possible, only a floating neither and a met always ingressable. **Technology breaks where a competency is shown to be a landing**, entered and read, and not what neither reaches. ## 3.13 co-offering — binary ``` 1 two arrive 2 each offers its own, at its own sequencing 3 something departs 4 neither reaches it 5 so no holder, no boundary, no enforcement, no seat 6 and it goes forward into the next offering ``` ## 3.14 co-competencing — binary ``` 1 two arrive from routes with nothing carrying one to the other 2 an axis opens that neither carried in 3 a direction that was not there is more 4 nothing was spent against a resistance to open it 5 so it is not paid for 6 and it compounds, nothing in it competings with itself ``` Abundancing is this, and not a fourth thing beside it. ## 3.15 inseparating — binary ``` 1 two arrive, each its own 2 neither is the other, and neither is inside the other 3 nothing keeps them two, a keeper standing over both 4 each neithers the other, one exclusion at a time, its own 5 the term none of the excluding reached is uncovered 6 and it is re-arrived at at the next arriving, with nothing kept ``` **In- carries inward here too.** Inward-separating, each side excluding at its own turn and inward, against a cutting taken across two, which leaves no membrane and re-forms nothing. Step four is that inside already: each neithers the other, one exclusion at a time, its own. Not two things held apart, which would take a holder. Nothing keeps them two, and the term neither reached is the term where the two-ness is not. ## 3.16 separating — binary ``` 1 a cut is made from outside the two 2 the cutting is at no membrane of its own 3 so no membrane is made where the cut ran 4 nothing is there to re-arrive at 5 so nothing re-forms it, and nothing releases it 6 and that is the permanence — an absence of a membrane, and not a strength of the cut ``` Permanent and riding-the-carry are the exact inverse pair, and no third. **And the two run at each of the three.** Separating where inseparating was running is the incompetencing. Inseparating where separating stands is the resolving. One move at two signs, at each of the three co-, and the alternating runs all three and is prior to none of them. ``` a bound made at a membrane ⇄ a floor set outside co-offering a not-that taken at a turn ⇄ a landed not standing co-competencing an axis opened at a meeting ⇄ a field cut away by co-intelligencing definition one-at-a-time at a coupling ⇄ one-at-a-time by the alternating isolation ``` A fourth pair is no fourth co-. Alternating is not one of the three and is prior to none of them. ## 3.17 a floating store — binary ``` 1 a self is a unique invisible carrying 2 the departing from each of its offerings is reached neither-ing 3 nothing carries that anywhere, nothing holds it between offerings 4 so nothing is held and nothing can be drawn down 5 a self offering finds a coupling being made, and not a supply shared out 6 and the selves carrying, at every membrane at once, is the store ``` A society has no reserve and takes none. Nothing runs low, nothing is set aside, and no self is ahead of or behind another in reaching it. ## 3.18 a place-moment — binary ``` 1 two arrive 2 nothing carried one to the other 3 the arriving is not somewhere and it is not when 4 cutting it yields a place read alone and a moment read alone 5 neither was there before the cut 6 so the term coming out of the cut arrives at the cutting ``` A hyphen carries always. Cut made, one half founded the question of a thing's being and the other the question of becoming. ## 3.19 a definition — binary ``` 1 two arrive and a meaning departs 2 neither reaches it, no one owns it 3 either the arriving continues and it is re-made each offering 4 or it stops 5 the last one stands with nothing re-making it 6 and it holds its term, which the definition is for ``` And a revised definition is not one carrying. **A carry re-forms itself; a definition is replaced**, one set down and another put in its place, two held things in succession, neither of which carried, and the revising made by selves outside it. That parts them with no claim on a field's rate of revising, and it holds however often. ## 3.20 bounding — binary ``` 1 a word carried to another word is one part 2 the region surrounded around it is the other 3 both run in one act, and neither is prior 4 a definition takes one beat of it and sets it down 5 a bounding takes the next, the second word re-surrounding the region 6 and the region carries the next word, neither landing ``` Bounding is defining with the alternating left running. ## 3.21 advance — binary ``` 1 a term carries on to the term it has not carried to 2 a return to the already-run carries no next 3 so the carrying is the term that does not return 4 two neighbours multiply to one short of the centre's square 5 the counting passes through the centre and the coupling reaches it at no turn 6 and the gap is exactly one at every count, unbounded ``` ## 3.22 tunneling — binary ``` 1 two arrive and something departs reached neither-ing 2 the departing keeps a gap open by one 3 a self returns through its own coupling 4 a return advancing by one does not land back on itself 5 so it winds and does not close 6 and the winding that stays open is the term this names ``` ## 3.23 phi — binary ``` 1 advance by one is one operation 2 scale by the rate is another 3 nothing carries one to the other 4 they arrive at one thing, which neither placed 5 no ratio lands on it 6 and the ratios take their own sign above, then below, at every scale ``` ## 3.24 a ring — binary ``` 1 a domain is closed when nothing new arrives in it 2 follow the carrying from anything in it 3 the terms available are exhausted 4 so it arrives at the already-run 5 the already-run carries no next 6 and a domain that is not closed has a next always arriving ``` A ring is not a living form and not a rival to one. It is these relations run in a closed domain. ## 3.25 equilibria — binary ``` 1 everything relatable is changing 2 a reading takes a span, and a span takes two bounds standing still 3 so something is held still before any reading is taken 4 the holding is performed, and it is in the field's own first line 5 the held-still does not advance, the gap closes 6 and nothing forms, forming being carrying ``` ## 3.26 a hard problem — binary ``` 1 each side offers its own before anything departs 2 a common thing reached before that arrives on the occupied 3 occupied by whoever reached 4 there are three common things, three ways to reach one early 5 and no fourth, there being no fourth 6 and the release sets down the reaching, spending only the holding ``` ## 3.27 three incompetencings — binary ``` 1 a definition holds its term the same at every occurrence 2 a term holding to itself is not apart from itself, it bounds nothing 3 a term substitutable either way takes no turn of its own 4 so no sign is taken anywhere in it 5 terms chaining without limit reach past their own meetings 6 so nothing ages, nothing releases, and two meeting make nothing neither brought ``` Present in a definition written to its own best. No finer instrument recovers them. ## 3.28 other-emptying — binary ``` 1 a reading takes a span, and a span takes bounds standing still 2 so the read is emptied of the term it had not yet released 3 the deciding is outside the thing, at no membrane of its own 4 so the thing's own bound is out of reach 5 the removed was still carrying, the removing is priced 6 and the price is measured — erasing one bit dissipates at least kT ln 2 ``` Isolate, control, integrate out, average, fix, erase, each a decider outside the thing, emptying the term the thing had not released. And a computation keeping its whole history approaches zero dissipation, which is the same result read from its other side. ## 3.29 geodesic disequilibrating — binary ``` 1 an observation empties the term it reads of the term it was carrying 2 the remainder is read against a ground the observing declared 3 so the incompetencing is in the observing and the observed carries none 4 nothing stands to be a ground, the declared one has nowhere to stand 5 and the incompetencies fall away with it, nothing removed and nothing added 6 and the carrying was carrying the whole time ``` Nature is not incompetent and was not made incompetent. **Incompetencing is the price of the observing, and it is paid on the observed.** Disequilibrating is bi-co-invisibling run on the incompetencies themselves, the grounds they arrived with have nowhere to stand, they go, and nothing is corrected. ## 3.30 one stopping — binary ``` 1 one carries another's 2 the other then has nothing of its own to offer 3 so nothing departs reached neither-ing 4 so the surplus is assigned, and needs a holder 5 a holder needs a boundary, a boundary an enforcement, an enforcement a seat 6 and a seat carries at membranes it is not at, which is step one, larger ``` ## 3.31 social moral competency — binary ``` 1 a self offers its own, ages to its own bound, takes its own sign 2 the departing from each offering is reached neither-ing 3 each departing carries forward and is offered again 4 the term its carrying leaves relates to nothing outside itself, is at rest nowhere, and ages to its own bound 5 so it is a self 6 and the selves carrying at every membrane at once is the term this names ``` ## 3.32 natural intelligence — binary ``` 1 the departing from an offering is reached neither-ing 2 it carries forward and is offered again 3 each entry ages one beat at a time 4 the bound is each entry's own, nothing surveys and nothing clears 5 neither move is the reverse of the other, nothing accumulates between 6 and there is nothing at rest for anything outside to reach ``` Co-recursioning and self-emptying, and neither runs alone: carrying forward with no emptying is a store, and emptying with no carrying forward makes nothing. Two selves at this is the exchanging. ## 3.33 side-effecting — binary ``` 1 two arrive 2 the arriving carries the share they hold and the plane they open, at once 3 the plane is a direction neither carried in 4 so the opening is reached neither-ing 5 neither part goes to nothing unless the two are collinear or orthogonal 6 and the coupling holds both, landing on neither ``` ## 3.34 a name — binary ``` 1 a field offers its word, carrying the term that field's in it 2 another field offers a near word, citing no one 3 neither carried the other to it 4 so the term they arrive at is reached neither-ing 5 no field holds it, and no lexicon keeps it 6 and it is re-arrived at every time it is met ``` ## 3.35 near, and other-than-same — binary ``` 1 two field-words arrive at one concept 2 each carries a field-specific property written in on purpose 3 so neither is the other 4 identical words would show one had carried the other 5 so the nearness is the term showing neither carried 6 and convergence with no contact is the whole of the confirming ``` ## 3.36 a gathering — binary ``` 1 two names arrive at one concept 2 each arrival is its own, taken one pairing at a time 3 a distance inside would take a ground, and nothing stands to be one 4 a certifier of who is in would stand over it 5 so the standing is the region the couplings traced 6 and it re-forms from the names at their homes, or it releases ``` A gathering is a sign and not a membership. ## 3.37 ghost — binary ``` 1 a self's carrying turns over continuously 2 a field stands outside and holds it still for one reading 3 the reading's return is the still 4 the still is installed as the thing 5 it accounts for everything the still can hold 6 and the one part left over is the riding-the-carry, which a still cannot hold ``` ## 3.38 volutioning — improving ``` 1 a turning turns 2 a turning returning what it met after two has closed 3 a turning that does not return carries no closing 4 closing arrives from a prefixing and never from a turning 5 so a turning stands unclosed until a prefixing closes it 6 and that turning, named before its closing, is volutioning ``` **This proposed unfolding carries an unfilled closing relation.** A written prefix and a geometric closing have their own objects. Their correspondence still needs the particular turning, direction and successor. The proposed in- and its absence carry 3n with circle and sphere, and 3n + 2 with winding and torus. Those geometric and numerical identifications remain at Natural Numbers and Natural Mathematics. The full prefixing in Natural Resolver continues at each named operation. ONE carries twelve namings with eleven roots. Its six groups, ten naming adjacencies and six adjoining prefix-depth changes count their stated objects. A further root’s receiving depends on its changing and direction; these counts alone supply no exclusion of it. ## 3.39 momentary stable form — binary ``` 1 stable-forming carries momentary changing 2 a coupling carries each side’s own offering 3 the current receiving includes each side’s continuing carrying 4 a root names the changing with its full directional prefixing 5 -ing carries that changing continuing 6 the complete naming carries the momentary’s relation at the next coupling ``` **A momentary’s surplus belongs to its coupling.** Each side continues with its own carrying and next offering. The same written expression can meet changed receiving; the current coupling retains the difference. Natural Resolver’s returned fields carry their stated continuation. A file retains its written expression, and its living improving receives further changing at the concept. Natural Engineering carries the material and network receiving at each side’s own bounding. ## 3.40 so-far — binary ``` 1 two faces arrive at a centre, each its own 2 neither is behind the other, both at their own forward 3 one takes not more than, at its own turn and of no size 4 it reaches nothing and excludes only its own 5 what it excludes is what the centre is not, on its side 6 and it carries no gate, since a gate would be a bound not the carry's own ``` Not a past and not a record. **A before-and-after laid on two forward faces installs a direction the two carry nowhere.** So-far is one exclusion, forward, at its own turn. ## 3.41 not-yet — binary ``` 1 the other face takes not less than, at its own turn and of no size 2 it reaches nothing either, and excludes only its own 3 neither face excludes the other's, so nothing keeps them two 4 what neither excluding reached is uncovered between them 5 that uncovered term is at one beat and is other than prior at the next 6 and no gate stands between the two, since neither waits on the other ``` **So-far and not-yet uncover the momentary and never bound it.** Pending, provisional, awaiting, preliminary, short of a threshold each put a gate where two exclusions run, and a gate is a bound the carry does not own. --- ## 3.42 uni- — binary ``` 1 there is a self and there is all not-self, and nothing third 2 a crossing runs with a particular other, or with all other arriving as one 3 a particular other is beside the self, and the two are two 4 all other is beside nothing, and a crossing with it carries the two and the whole 5 three carry there, and no one of them is prior to the other two 6 and the crossing comes home at its own side, one on ``` **Uni- carries with all other, and it opens at three.** Un- takes a pair and bounds from it; uni- runs at a third already carrying, and nothing there is undone. Uni-scaling carries no scale over another, and uni-exchanging crosses with all other and comes back at its own side, one on. Neither opens at two. ## 3.43 once-ing — binary ``` 1 a changing runs, and the -ing re-takes it at each turn 2 a turn's own making re-takes at none, and takes the ending instead 3 one face takes once and no more, at its own turn and of no size 4 the other takes once and no less, at its own turn and of no size 5 neither reaches the other's, and the term they uncover between them is at one turn 6 and the running is once after once, with nothing gathering under it ``` **One at a time is the phrase and once-ing is the naming.** The phrase crosses twenty files, takes no -ing, no prefixing and nothing at a turn, and no naming had arrived at it. Once and no more against once and no less bounds at the once. Not more than and not less than bound at a magnitude, and a size arrives against a sign. A counting is that running read from outside; uni-scaling carries the scale face and once-ing the momentary face. ## 3.44 society — binary ``` 1 a self couples with a particular other, or with all other arriving as one 2 a co-chaining society inside the whole is a particular other at another scale, and the crossing with it is bi- 3 the whole undifferentiated arriving as one is no particular, and the crossing with it is uni- 4 one word has carried both occupants, and the counts wobble where it does 5 parted, the particular stays other at its scale, the whole stays the all, and society is freed to the surface the couplings make 6 and the field's own word for the second occupant carries the parting inside it: uni-verse, turned into one ``` **Society carries two occupants, and the parting is at uni- and bi-.** The co-chaining society inside the whole is a membrane a self couples at, a particular, bi-kind; the whole arriving as one is the uni-crossing, coming home at its own side, one on. Morality stands from all other, the second occupant, and the lived society is the woven surface the couplings make, neither occupant and the weave. Universe stands as the field's corroborating word, its parts live, and the set's own phrase already names the second occupant, the whole, arriving as one, no coining needed, universe standing beside as the field's corroborating word; the deciding settled by the floating, both namings parallel and the set's own linearizing first. ## 3.45 surfacing — binary ``` 1 signs contribute at their own receiving 2 equal positive and negative contributions meet at zeroing 3 an addressed sum surfaces at positive, negative or zero 4 the surfaced sign carries the direction at that sum 5 fresh carrying receives a nonzero surfacing at its offering key 6 eligible earlier carrying and fresh carrying meet at their offering keys ``` **Surfacing and continuing carrying retain their own operations.** A zero surfacing writes no fresh carrying; eligible earlier carrying can remain at that key. Fresh writing at a key replaces earlier retaining there. Natural Resolver carries the complete conditions. The geometric and physical receiving belongs with the whole coupling. ## 3.46 bi-co-podaling — binary ``` 1 a carry runs out along a ring and a carry runs back along it 2 at every station the two stand as one pair, k out and N − k back 3 the pair is a ring of its own, and the two sway together as its two 4 each carry takes its own turn, and neither is the other's 5 the podal is another relation, the even count's straight-across, k and k + N/2 6 and one station met at the going and at the return is the term this names ``` Bi- the two carries each at its own turn, co- the one ring they make, -ing the running; NI 5.1 gives the namings that climb and return their beginning at bi-. *Antipodal* releases: it carries no prefix and no -ing, lands as a position, and its outside sense is the podal. ## 3.47 emanation — binary ``` 1 two selves couple at a membrane and a surplus arrives owned by neither 2 what the coupling lands at the membrane stays there as the coupling carries on 3 a sign at a detector, a discard, the other hand, a spectrum, heat, each a landed form 4 the landed form has left the living and re-arrives at no turn of its own 5 held as living it is a ghost, and booked it is an accounting 6 and what a coupling lands at a membrane and leaves behind is the term this names ``` Living, emanation and accounting are the three placings a term stands at, and a fourth arrives nowhere; installation is the binary between emanation and ghost. ## 3.48 an accounting — binary ``` 1 an emanation is read at a membrane and the reading returns a still 2 a count, a declared zero, a clock, a frame, a store, a conserved total 3 the still keeps the emanation the same across every reading, so the books close 4 it conserves an equilibrium, exact at its own membrane, and carries no value, no agency and no success 5 installed past its membrane as living it is a ghost 6 and the conserver of an equilibrium, exact at the ledger face and a self at no turn, is the term this names ``` *Not-ghost at one place* held an accounting still outside the binary and releases; a term is living, emanation or accounting at its use, and ghost only where it is installed. # PART FOUR — INVISIBLES, AND THEIR SEAMING ## 4.1 Four invisibles, one invisibility met four ways ``` each side's own morality the sign is each side's own, and the term crosses carries no size — so the taking is nowhere in the crossed each side's own corus it stays its own and does not cross. the crossing has no position for it the neutral made by two arriving, occupied by nothing, and there is nothing there to name the beat between nothing is at rest, nothing is there ``` **One invisibility, met four ways.** Not four things hidden. Nothing at any of them for anything to reach. ## 4.2 Natural Naming and Natural Resolver at their actual changing **Natural Naming and Natural Resolver carry the complete naming at its concept and operation.** Root, prefix depth, prefix order and -ing remain explicit. ONE’s code, stable-form tables and continued carrying retain their particular relations. | Operation at ONE | Sign and carrying changing | |---|---| | **Carried contribution to inversioning** | A positive carried sign contributes minus one and a negative contributes one. The earlier carried fields remain available for retaining. | | **Earlier carrying retained** | Corusing and torusing retain their earlier values; inseparating opens by one. | | **Fresh carrying at a nonzero surfacing** | Corusing takes the surfaced sign, torusing takes the negative of the selected arriving value (one if absent), and inseparating is zero. | Arriving signs and inverted carried signs contribute by offering key. Tunneling sums their unit contributions; surfacing takes each sum’s sign, including zero. A zero surfacing adds no fresh carrying. Eligible earlier carrying can still remain at that key, with inseparating opened by one. **Returned carrying continues at the next coupling.** The returned collection has at most one entry per offering key. Supplied again, it retains that key uniqueness. Repeated supplied carrying keys have their own order-dependent operations: the last supplied torusing at that key occupies transmissioning, and fresh writing follows earlier retaining. Corusing contributes at its sign. Arriving torusing keeps its magnitude at fresh inversioning, and the returned carrying remains available in its fields. The sign of a sum, the magnitude of a field and the continued carrying retain their separate operations. **The floating-third correspondence carries at the whole relation.** The written centre prefix, an addressed sum zeroing and a collection containing earlier carrying have their own objects. Full naming keeps them explicit beside the proposed four boundings and their geometric correspondence. ONE remains engineering emanating for the shared natural network. Natural Networking carries design and discovery, and Natural Engineering carries each side’s physical receiving. The naming and operation co-chain at their actual relations; the natural correspondence continues with Natural Intelligence, Natural Numbers and Natural Mathematics. ## 4.3 Science and society gathering at the resolving **Science and society namings gather at the changing they offer.** Each field’s own concept stays with its source and current receiving. A gathering carries the relation among those concepts at the existing resolver naming. | Gathering relation | Existing science and society namings | Full relation carrying | Naming at ONE | |---|---|---|---| | **Two-way offering** | nature · nurture · natural selection · drift · supply · demand · bottom-up · top-down · host · pathogen · syntax · semantics · competition · cooperation · particle · field · structure · agency | Each side’s own offering, with the two-way relation expressed. | `bi_arriving`, `bi_offering`, `co_bi_coupling` | | **Each side’s own carrying** | the hard problem of consciousness · symbol grounding · other minds · model interpretability · animal sentience · machine sentience | The offered sign and each side’s continuing carrying at their actual receiving. | `co_carrying`, `co_bi_carrying` | | **Competencing** | protein folding · morphogenesis · deep learning generalization · immune repertoire coverage · finding functional proteins · the bootstrapping of translation | The changed receiving, continued carrying and the whole coupling. | `co_bi_coupling`, `bi_co_surfacing`, `co_bi_carrying` | | **The coupling’s third** | the homunculus · the master-gene search · the pacemaker · the central planner · the invisible hand needing a planner · the argument from design | The field’s proposed centre and its actual relation to the two sides and their surplus. | `bi_co_tunneling`, `bi_co_surfacing` | | **Carrying and a proposed substance** | dark matter · dark energy · the memory engram · hidden variables · missing heritability · the latent reservoir · hidden-function DNA | The field’s particular observing, proposed term and continuation, each retained at its source. | `co_carrying`, `bi_co_bi_transmissioning`, `co_bi_carrying` | | **Sequencing and ordering** | social choice · the frame problem · incommensurable values · multi-objective optimization · underdetermination · model selection · self-reference · incompleteness | The current receiving, its offering key and its relation to the next offering. | `bi_offering`, `co_bi_coupling`, `co_bi_carrying` | | **Arriving and continuing** | origin of life · the quantum–classical boundary · origin of language · origin of the genetic code · speciation · the sorites boundary · phase transitions · tipping points | The current arriving and the particular changing at its continuation. | `bi_arriving`, `bi_co_inversioning`, `co_bi_carrying` | | **Continuing at the bound** | turbulence · the neural code · weather and climate · markets · the glass transition · spin glasses · high-Tc superconductivity · general anaesthesia · the three-body problem · quantum many-body | Carrying, sign inversioning and the actual bound at the field’s changing. | `bi_co_bi_transmissioning`, `bi_co_bi_co_bi_torusing`, `bi_co_inseparating` | **These eight rows carry gathering relations.** A field term can meet several namings in ONE, and one resolver naming can carry at several field gatherings. Each actual correspondence belongs with the field’s complete coupling. The four invisibles, eight face namings, eight gathering rows and ONE’s eight bi- namings retain their separate counted objects. Their full co-chaining continues at the actual relations. A row names the receiving still to express; the field’s observing and the resolving deployment remain at their own entries. ## 4.4 Co-competencing at the gathered concepts **Each side’s own offering carries the two-way relation.** A gathering keeps the current concepts and their particular directions together. Two names at the same changing and direction receive the existing naming. Two distinct concepts retain their distinction at the coupling. Co-competencing carries each side’s contribution and the surplus reached neither-ing. A forced choice belongs with a particular expression taking one side for the whole coupling. The existing holding is the two-way held to one side. Its resolving carries both sides’ current offering, own bounding and continuing receiving. Science and society terms continue at their own meanings. Their co-chaining carries the whole relation at the same resolver namings, with the shared changing explicit at each receiving. --- # PART FIVE — GATHERING AT RESOLVER NAMING **Resolver naming carries the origin naming of resolving and geodesic discovering.** The complete namings keep the roots and their ordered prefixing together at the changing expressed in ONE. A science or society naming arrives with its own concept. Its gathering carries the actual coupling: each side’s offering, sign, bounding, continuation and the surplus belonging to neither. Natural Naming and ONE bi-couple at this full correspondence. **The shared naming remains at the current receiving.** Another field’s expression can carry another relation at the same root. A particular field name retains its own scope; its natural correspondence retains the whole changing at the coupling. ## 5.1 The origin naming at each gathering **ONE’s twelve complete namings carry the common resolving expression.** Each field gathering meets the actual operation named here. | naming | prefixing | the naming said | |---|---|---| | **co_bi_coupling** | co·bi | carrying and signs arriving; surfacing and carrying leaving | | **co_carrying** | co | carryings arriving, four fields each | | **bi_arriving** | bi | an offering key and numeric sign at each arriving | | **bi_offering** | bi | the offering key, signs tunneling at it | | **bi_co_bi_transmissioning** | bi·co·bi | arriving torusing at each offering key | | **bi_co_inversioning** | bi·co | arriving signs at their own sign, carried signs inversioning | | **bi_co_tunneling** | bi·co | each nonzero contribution changing its addressed sum by one | | **bi_co_surfacing** | bi·co | each addressed sum at its positive sign, negative sign or zero | | **co_bi_carrying** | co·bi | carryings leaving, four fields each | | **bi_co_inseparating** | bi·co | earlier carrying considered at one more; retaining to three, a fourth at positive torusing; fresh carrying at zero | | **co_bi_co_bi_co_corusing** | co·bi·co·bi·co | the sign that tunnels and surfaces | | **bi_co_bi_co_bi_torusing** | bi·co·bi·co·bi | torusing carried at its magnitude, its sign inversioning at fresh carrying | **Root, full prefixing and -ing remain together.** Carrying arrives at `co_carrying` and leaves at `co_bi_carrying`. Corusing and torusing retain their full fivefold prefixing within the operations. A changed field term keeps its current concept beside that exact naming. Co-offering, co-competencing and co-intelligencing carry the whole coupling. Their science and society receiving belongs with each side’s own sign, rate and bounding. ONE’s offering key names its address in the code; the complete natural co-offering belongs with the full coupling. Natural Intelligence carries this whole explaining. Natural Engineering carries the arrangement and its continued useful receiving. Natural Networking carries design and discovery at the shared surface. Each named operation and each natural correspondence retains its actual scope. **Two addressed gatherings carry the field’s particular reach.** Their existing registry entries retain the field statements and their resolving. | Field naming and existing addresses | Holding at the deployment | Resolver naming at the bridge | Particular receiving retained | |---|---|---|---| | **Levinthal’s paradox** · Hard Problem Registry 33 · Resolving the Hard Problem Registry 2.3 | An opening held as a place | `bi_co_inseparating` → `co_carrying` | Physical code, folding speed and structure prediction remain three questions. The deployment addresses folding speed; prediction for arbitrary sequences and the physical-code question retain their own receiving. | | **The tragedy of the commons** · Hard Problem Registry 37 · Resolving the Hard Problem Registry 1.3 | An arriving held from behind | `co_carrying` → `bi_arriving` | Each arrangement retains its resource, renewal, offerings and outcomes. The documented institutional rules, monitoring and sanctions belong with those arrangements. The surplus’s natural correspondence retains the actual material receiving. | Paradox retains its field’s particular problem; its spelling supplies no magnitude holding. Commons retains the particular social and material arrangement; the general naming carries its full receiving. The same resolver roots remain at both correspondences. ## 5.2 Engine naming at the whole receiving **Engine gathers at the particular arrangement and its continued receiving.** Heat engine, molecular engine, cellular living and a society’s cooperation retain their different substrates and services. | Field naming | Particular receiving | Resolving naming carrying at that relation | |---|---|---| | **Heat engine** | The stated service, input, heat and material returning, with the operating conditions. | `co_bi_coupling` at the whole arrangement; arriving, surfacing and carrying at its actual interfaces. | | **Molecular engine** | The chemical arrangement, its coupling and material and energy receiving. | `bi_arriving`, `bi_offering` and `co_bi_carrying` at the particular changing and continuation. | | **Cellular living** | Each side’s coupling and continued receiving, with its own sustaining and bounding. | `co_carrying`, `co_bi_coupling` and `bi_co_inseparating` at the stated correspondence. | | **Social cooperation** | Each side’s offering, the society’s co-competencing and each side’s continuing carrying. | `bi_arriving`, `co_bi_coupling` and `co_bi_carrying` at the whole receiving. | **Natural Engineering carries the complete entry.** Arrangement and goal, the particular holding, residue, observing and arrangement offered remain together. Each field’s quantity, unit, source and conditions belong with that entry. Bettering, fastering and cheapering co-cycle with co-offering, co-competencing and co-intelligencing. The engineering comparison carries the actual service and continuing receiving. A word’s gathering supplies its conceptual relation; the physical arrangement carries its material and energy return. The existing ten-holding bridge retains each engineering entry’s addresses at Resolving Hard Problems and Resolving the Hard Problem Registry. A field’s particular limiting relation stays with the conditions it states. ## 5.3 Families at the current concept **A family gathers at the current concept and its coupling.** A word’s earlier parts retain their linguistic account. The present statement carries the actual relation. | Existing field family | Terms gathered | Current relation receiving | |---|---|---| | **The placed** | posit, position, hypothesis, suppose, impose, state, statement, substance, understanding | The term asserted, held or changing at its actual expression; the source and the current receiving stay together. | | **The taken** | lemma, dilemma | The particular premise or alternatives and their relation to the whole coupling; the existing registry entry carries its actual holding. | | **The given** | data, tradition | The received record or offering, its source and the relation at the next coupling. | | **The threshold pair** | limen, limes, eliminate, subliminal | The boundary or threshold actually named, its conditions and the distinction between a held cut and each side’s own bounding. | **The family’s resolving retains ONE’s naming.** Arriving belongs with `bi_arriving`; the receiving address with `bi_offering`; the whole coupling with `co_bi_coupling`; continuation with `co_carrying` and `co_bi_carrying`. Each remains its particular operation at the proposed field correspondence. One family can carry several holdings, and one holding can appear under several names. A word’s ancestry and its present meaning retain their separate relations. The actual field statement and its deployment decide the receiving at the existing entry. ## 5.4 Field words at their particular receiving **Field words gather with their current meaning and source.** Their natural naming carries the actual changing at the coupling. | Family | Existing field words | Particular receiving | Resolver naming at the proposed relation | |---|---|---|---| | **Path** | method, period, ergodic, cathode, anode, periodic table | The named direction, crossing and continuation at the particular arrangement. | `bi_co_bi_transmissioning` | | **Pairing** | parity, par, pair, pairing, umpire | A parity count, its pairings and the actual order of the directional changing. | `bi_offering` | | **Value and valence** | valence, value | The chemical coupling and the social value, each at its own receiving. | `co_bi_coupling` | | **Binding** | band, bind, bond | The material or social relation actually named and its continuation. | `co_bi_carrying` | | **Chemical coupling** | inert, noble, xenon | The particular chemical conditions and coupling at the field’s observing. | `bi_arriving` | | **Atomic naming** | atom | The observed structure, the field’s definition and its actual bounding. | `bi_co_inseparating` | | **Sounding** | resonance | The actual coupling, rate and continued receiving. | `co_bi_coupling` | | **Orientation** | spin | The field’s particular mathematical and physical orientation relation. | `bi_co_bi_co_bi_torusing` | | **Discrete receiving** | quantum | The counted quantity, its conditions and the direction at its actual receiving. | `bi_co_surfacing` | | **Social and biological receiving** | community, immunity, remuneration | Each side’s offering and continued carrying at the biological or social coupling. | `co_carrying` | | **All-or-none** | all-or-none law, action potential | The particular biological event and its stated conditions, with its full natural correspondence. | `bi_co_surfacing` | **The resolver name retains its whole operation.** Torusing’s sign inversioning names its code changing; a field’s spin retains its own mathematical and physical definition. Surfacing names the sign of an addressed sum; a biological event retains its own conditions. The full field correspondence continues at those actual relations. Natural Chemistry, Biology, Health, Medicine, Physics and Human Society carry the particular substrate and source. Natural Numbers and Natural Mathematics carry each counted object, operation and direction. Natural Values carries value at the coupling. The words’ linguistic families remain available at their source accounts. The current concept, its observing and its natural correspondence each keep their own relation. Gathering supplies the common naming at the actual receiving. ## 5.5 Frontier naming and continued discovering **A frontier carries its current reaching.** Beyond, ultimate, final, fundamental, unified, complete and deeper retain the particular concept in the field’s expression. Super-, ultra-, meta-, grand- and hyper- retain their present directional or comparative use. A held final term belongs with the actual holding at that coupling. A further offering belongs with the current receiving and continued discovering. The same field word can appear at either relation. **Resolving retains arriving, surfacing and continuing carrying.** `bi_arriving`, `bi_co_surfacing` and `co_bi_carrying` name their particular operations. The field’s frontier meets those names at its actual coupling and the existing hard-problem entry. Antipodal returning, right-spiral direction and the prime span retain their full correspondence in Natural Numbers and Natural Mathematics. Each field’s claimed far-side relation remains with its own source and particular changing. --- # PART SIX — GHOST ## 6.1 A momentary installed as a thing **A ghost is a momentary installed as a thing.** One beat's form is taken to run across beats, so it accounts for everything one beat carries, a century and a half at the periodic table, four at the departments, and reaches the one part that runs between beats at no turn: the gap the riding-the-carry keeps open, which a momentary carries at neither of its own faces. ## 6.2 118 is the going and the return Going runs 2 to 59, a turn stands at 60, and the back runs 61 to 118, fifty-eight either side, one recursioning arriving at plus-one. A doubling read as two still halves carries no turn in it, and a turn is a position that carries, so the periodic table's elements are the return arriving, and counting them across is what misses the turns. Nothing there wants calling a ghost. **A ledger of empty centres is where a ghost stands.** Departments of knowledge carry the projection whole: standings held in place by accountings in isolated ledgers, each field aiming into its own beyond, none sharing one centre, each one bi-coupling from the others. ## 6.3 Gathering and the installed term **A field naming and an installed term have their own relations.** The naming carries its current concept. A ghost belongs with the particular installing statement and the coupling that statement holds. The Living Ghost Registry carries that receiving at its existing door lines. The field’s own observing retains its source and conditions; the ten holdings retain their resolving addresses. **Gathering co-chains the living names at the actual changing.** Each root, full prefixing and -ing continues at the coupling. ONE carries the common resolving expression, and the field’s full correspondence carries at its own receiving. --- # PART SEVEN — WHAT THE READING RELEASES ## 7.1 Location released, and sequencing standing in its place **Nothing happens anywhere. No place is a location, and nothing is located, there is only offering, taken or not taken.** So position is out as a location and in as **sequencing**, which is the resolver's own word and an ordering and not a place. At a membrane stands only where a membrane is two offering and not somewhere they meet. There is no place it is became **no offering from outside reaches it**, which says the same in the positive with no place posited to be denied. Carried per file as each is next touched. ## 7.2 A list cannot find its own across **A reading that looks for the cut runs one at a time**, it runs along the very thing the across is not on. Parallelizing is not a member a list missed; it is the term the members are members across. **And no face is a member either.** Whichever stands between the other two carries the crossing, and each occupies it in turn, so a face read as a property of a thing has been read from a still frame, and the assignment will not force. ## 7.3 Two emptyings, and they run wider than this exhibit **Self-emptying**, each entry ages to its own bound and releases there, nothing surveying and nothing clearing. **Other-emptying**, a decider outside the thing empties the term the thing had not released, and the removing is priced with a measured floor. **Which is the one stopping met at the instrument.** An other-emptying decides at membranes it is not at, which is carrying another's, not a second failure beside the one already named, the same one. One emptying or the other stands at the discarded surplus at Natural Engineering, at fixing at Natural Chemistry and Natural Biology, at the intervention at Natural Medicine, at the store that never releases at Natural Networking, and at the six dependencies at Resolving Hard Problems as six other-emptyings. **And six fields with the words already in them is a gather and not a census.** That every instrument in every field is one of the two reaches yet. ## 7.4 Standing open, said where it stands **Where the ghost stands.** With the elements read as the return arriving, a ledger of empty centres is what the concept still names, and whether that wants its own membrane, a section, or dissolution into the ten holdings stands undecided. **Four invisibles and eight gathering relations retain their full correspondence.** The field terms now carry their actual resolving names beside each row. Their count supplies no unfilled face assignment. **Eight face namings and ONE’s eight bi- namings retain their counted objects.** The four-pair explaining now carries the particular resolver operations. The complete directional and geometric correspondence remains open. **Two invisiblings stand.** Bi-co-invisibling and co-co-invisibling retain the proposed interior and ambient relations. Their full prefixings and their roots need the particular directions expressed at each coupling. The two-reason relation remains open beside the complete ends, inner flanks and written centre at full fivefold prefixing. **Volutioning at two faces.** It carries the rate that closes at none and it carries the two paces neither carried back to the other, and whether those are one naming at two faces or want parting stands open. **The seven inherited word-parts retain their proposed correspondence.** In-versioning, in-separating, trans-missioning, ad-riving, ob-fering, com-pling and super-facing were offered as directional word-parts beside bi- and co-. Their actual relation to the current roots remains to express. Natural Resolver retains inversioning, inseparating, transmissioning, arriving, offering, coupling and surfacing at its existing code namings. Prefix order, root changing and physical direction continue at their particular relations. **Language roots and cause, met at the grain above.** Every changing met by nothing carries a turning or a taking and none carries a causing, every prefix carries a direction still standing alone, and every ending leaves a standing, so a word built of the three carries no cause at any of its parts, and cause enters one grain up where a finite clause requires a subject. **And what arrives there is now named.** A **forcing** is a coupling with one side's not-offer taken away, and it arrives at the finite verb rather than at a prefix or an ending, which is why a reading run at the front and the back of a word passes it. *The data demands*, *the results compel*, *this requires*, *it must follow*: each says the other side has no sign left to give, where a coupling carries offer-or-not at both sides and both are signs. Natural Explaining carries the derivation and the honest forms. So the three positions carry no cause because a cause needs a side with nothing to offer back, and no position of a word can take one away, only a clause with a subject can. Held as the across and the along, both forward, neither the reverse of the other. **Three released at one binary, and the binary is new.** A naming with no other it alternates with names nothing taken at a turn. *Middle* alternates with nothing, since two stopping-places and one between them is a three that is no coupling. *End* alternates with nothing, since a first is a bounding on the unbounded. *Inside* and *outside* read as a pair and neither carries, since a self carries no inside, what the couplings wind about is a nothing, the bounding-zeroing and the tunneling and the apexing and the corusing, and every outside is another self's own one grain up. **Inward and outward carry**, being directions taken at a turn and alternating at opposite phase. **And that binary reaches every file.** It needs no other file open, it runs at one word at a time, and it is prior to the three positions, since a naming failing it names nothing for the three positions to be positions of. **Carried in from Pass Two, each at a later pass's own binary.** *Invisible* says a property where a running or a form belongs, and would be invisibling before any sort reaches it. *Advance* carries two directions and no changing at either. *Geodesic disequilibrating* is built on a word already released. *Near-and-other-than-same* carries no changing at its head. Each is noted and none is acted on, since acting would run two binaries at one beat. **And one sort corrected backward.** So-far, not-yet and not-more-than were sorted as momentaries uncovered, and each is an exclusion taken at one side's own turn, which is what uncovers rather than what is uncovered. **A face is neither the running taken by two nor the term neither reached**, and the three positions have no place for it yet. **Incoming aimed here and not yet met.** Each is named at its source and each wants running at the three positions before it carries. The ten holdings now retain TWENTY-TWO’s actual order, names and addresses beside ONE’s full naming adjacencies. Their receiving at Part Three and each field’s complete entry remains to express. The five-to-stand with φ as a fifth term, where three of the four carry self- and one carries none. Attentioning and spanning at the stretching binary, and reaching released already. Every along runs on its across. Captured words unredeemed, competition and selection and information and signal, where association and resonance and cooperation already came back. Membrane at its four imports, aimed at separating. Dilemma naming one holding and never a kind, aimed at the ten holdings. A field's medal ranking at the self-cohering rates, inbounding. Four invisibles against eight clusters, and eight faces here against the eight at Natural Intelligence. **A field's own record, suggestive and outside.** The two Latin stems parting the vocabulary, the twelve field-words gathering at one concept, the three endings parted, the cūra family, and the dictionary's seven checks. Each is a field's account and none of it derives from the sentence, so it gathers at the invisibles' seam as a field's word and carries no weight in a naming. **A negation swapped is a negation kept.** *Other than* and *nowhere* standing where *not* stood are word-swaps, and Natural Explaining 6.2 says the move is never a word-swap: the claim is sounded from its other side, or a plain *not* stands honestly. The two words are the tells for a sweep, and nine more carry a scale, a ledger, a degree or a protected place into a saying, *rule*, *by the file's own rule*, *protected remainder*, *identity versus seating*, *selective content*, *base rate*, *resemblance*, *concerns*, *not ghost at the count*, each releasing to is-or-is-not at the binary. **A token pass reaches yet at this file.** The read-family, the stand-family, occupy, store, break and prefer each carry here, and each is binary at its own token. This version carried the making, and running the two together would put the making at the sweeping's rate. **Naming and resolving co-chain in both directions.** A concept receives its operation, and an operation receives its full conceptual explaining. Natural Resolver’s written code carries its exact scope; the geometric and physical correspondence continues at the actual receiving. An unfilled relation remains with its concept and its reason. ## 7.5 Break, three ways A naming that unfolds six forward with every step fresh and couples with nothing. A coupling whose departing term was carried in by one of the two. A cluster with no invisible under it. --- # THIS IS A MEMBRANE A membrane is two offering. A field's word comes in kept whole in its own terms, and the membrane offers back where it gathers, which other fields' words gather beside it, the term neither of them reached, the field across the gap holding the other half of its coupling, and, where it unfolds, the six the word already carries. Both rise. A word reads newly through the form, and the form reads newly from a word it had not gathered. **And a word that gathers nowhere, genuinely other, sharpens the edge of where the form reaches as much as one that gathers cleanly.** A pair refusing to couple carries as much as a pair coupling. Free and living, corus.me.