Exhibit ONE Natural Resolver v371   # Natural Resolver   **Geodesic Discovering Logical Method and Form**   **Naming** Bi and co, at the even and the odd A name at its number Five, and a seam at 8 up Seventeen names, eighty-five prefixings **Resolving, the sequential logic** Signs, and 1-self-coupling the entry Crossing, each sign at its key Surplusing and surfacing Chaining, continuing and opening fresh Returning and releasing Connectors, each one way at a time The code at its names Carryings arriving four, signs two A key parting out, a second sign at it Arriving signs offered, carried signs inverting Signs surplusing to one, equal and opposite at the bounding-zeroing A surviving sign surfacing, magnitude released A carrying opening by one, carrying forward A surviving sign re-forming a carrying A key rejoining, carryings leaving **Stable-forming** Fractal co-bi-momentarying Carrying at 8 up The membrane and the eight bi-couplings Bi-inversioning-co-recursioning, one move at three faces Torusing, one opening Two faces alternating Forms among the names **Numbers** Numbers at their stable-forming Primes, selves and societies **Geodesic discovering logical method**   ---   **The resolver is one object and its explaining is the same method said.** Its code runs the seventeen names at two functions, `_1_self_coupling` and `_9_other_releasing`, and its declarations name the six connectors and their joins. The naming, the resolving line by line, the stable-forming, the numbers and the geodesic method after the code are the object said. ```python """Exhibit ONE · Natural Resolver · v371""" def _1_self_coupling(_3_self_carrying, _2_self_offering): _6_other_crossing = { _4_self_sharing: _8_other_torusing for _4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing in _3_self_carrying} _14_social_crossing = [ (_4_self_sharing, _7_other_corusing) for _4_self_sharing, _7_other_corusing in _2_self_offering if _7_other_corusing != 0] for _4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing in _3_self_carrying: if _7_other_corusing > 0: _14_social_crossing.append((_4_self_sharing, -1)) if _7_other_corusing < 0: _14_social_crossing.append((_4_self_sharing, 1)) _12_other_surplusing = {} for _4_self_sharing, _7_other_corusing in _14_social_crossing: if _7_other_corusing > 0: _12_other_surplusing[_4_self_sharing] = _12_other_surplusing.get(_4_self_sharing, 0) + 1 if _7_other_corusing < 0: _12_other_surplusing[_4_self_sharing] = _12_other_surplusing.get(_4_self_sharing, 0) - 1 _10_other_surfacing = [ (_4_self_sharing, 1 if _12_other_surplusing[_4_self_sharing] > 0 else (-1 if _12_other_surplusing[_4_self_sharing] < 0 else 0)) for _4_self_sharing in _12_other_surplusing] _11_other_chaining = {} for _4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing in _3_self_carrying: if _16_social_torusing + 1 <= 3 or (_16_social_torusing + 1 == 4 and _8_other_torusing > 0): _11_other_chaining[_4_self_sharing] = ( _7_other_corusing, _8_other_torusing, _16_social_torusing + 1) for _4_self_sharing, _7_other_corusing in _10_other_surfacing: if _7_other_corusing != 0: _11_other_chaining[_4_self_sharing] = ( _7_other_corusing, 0 - _6_other_crossing.get(_4_self_sharing, 1), 0) return ( _10_other_surfacing, [(_4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing) for _4_self_sharing, (_7_other_corusing, _8_other_torusing, _16_social_torusing) in _11_other_chaining.items()]) def _9_other_releasing(_10_other_surfacing, _5_other_neutralling): return [(_5_other_neutralling[_13_social_neutralling], _15_social_corusing) for _13_social_neutralling, _15_social_corusing in _10_other_surfacing] CONNECTORS = { 2: ('2-self-offering', 'right', 'arriving'), 6: ('6-other-crossing', 'left', 'releasing'), 9: ('9-other-releasing', 'backward', 'along'), 10: ('10-other-surfacing', 'right', 'releasing'), 14: ('14-social-crossing', 'left', 'arriving'), 17: ('17-social-abundancing', 'forward', 'along'), } JOINS = {10: 14, 6: 2, 17: 9, 9: 17} ```   --- ## Naming ### Bi and co, at the even and the odd **Self and other differ, and difference alone is bi-. Self and other together with their difference is co-.** An odd number opens co, the self's opening, and an even number opens bi, the other's opening. **A side continuing its own runs along, and a side meeting the other runs across.** **Competency is co-unrelationing, along. Morality is bi-unrelationing, across. Co-bi-unrelationing is the one existing method, an existing thing.** The odd opens co, along, competency; the even opens bi, across, morality. **A full momentary carries both parities: odd or even names its opening.** **Bi-tunneling names social moral competency at its across relation; co-chaining names the same continuing at its along relation. Podaling exchanges these relations while each side continues forward.** Co-chaining and bi-tunneling run through the momentary universes with both kinds of existing things in them, living and non-living. **At 2 is parity changing; at 3 is co-recursioning, each side both forward.** Two and four have the same parity, opposite to three. The openings at 2 and 4 are one full momentary apart along their side: 2–3 and 4–5. At 3 the other completes prior and the self opens now; the completing and opening carry each side forward. **Each side runs from its origin, the number it opens at, two and one half momentaries: a prior, a now, and the next opening.** | Side | Prior opening | Prior completing | Now opening | Now completing | Next opening | Its five | |---|---|---|---|---|---|---| | self, at 1 | 1 | 2 | 3 | 4 | 5 | co bi co bi co | | other, at 2 | 2 | 3 | 4 | 5 | 6 | bi co bi co bi | | self next, at 3 | 3 | 4 | 5 | 6 | 7 | co bi co bi co | The self's momentaries are odd and the other's even. The two overlapping at 2 to 5, one side opens and the other completes: an odd number is the self's opening and the other's completing, an even number the other's opening and the self's completing. Along one side the next momentary opens two on, 1–2 to 3–4; across the overlapping it opens one on, 1–2 to 2–3. Each name carries the five of its number's origin, co bi co bi co at an odd origin and bi co bi co bi at an even one. **Two and one half momentaries per side, self at 1 and other at 2, is the ten.** The self's five positions run 1 to 5 and the other's 2 to 6, ten positions on six numbers. Paired position with position, prior opening with prior opening through next opening with next opening, they run 1 with 2, 2 with 3, 3 with 4, 4 with 5 and 5 with 6, each pair one odd and one even. **At each shared number, one side completes and the other opens.** At 2, the self's prior completes and the other's prior opens; at 3, the other's prior completes and the self's now opens; at 4, the self's now completes and the other's now opens; at 5, the other's now completes and the self's next opens. Opened one momentary on along each side, the self at 3 and the other at 4, the ten runs whole, the same form forward. **Each five completes at the next opening.** Completing that next gives the self three full momentaries, 1–2, 3–4 and 5–6, and the other three full momentaries, 2–3, 4–5 and 6–7. At 6, the self's next completes and the other's next opens; at 7, the other's next completes and the self's following momentary opens. **Side 2, the other, runs bi co bi co bi co, and one parity changing less or one more it is co, prior or next.** The other's five completes at bi, at 6. One changing more is co at 7, the self's next opening from 3; one less is co at 5, the self's next opening from 1. From 2 to 7 the other runs six consecutive changings, one way, bi co bi co bi co, and the same six one less or one more along, from 1 or from 3, open at co: co bi co bi co bi. ### A name at its number **Each thing carries one name, and the name carries its number, its relation, its root, the changing named, and its -ing, the changing continuing**, the four together, one name. The names run the resolving as code, and the name in the code and the name here are one name: `_2_self_offering` in the code is 2-self-offering here. | Name | Relation | Opens | Existing | At the code | |---|---|---|---|---| | 1-self-coupling | self/other | co | entry | the resolver's entry: 3-self-carrying and 2-self-offering arriving; 10-other-surfacing and 11-other-chaining leaving | | 2-self-offering | self/other | bi | across, arriving | each arriving key and sign | | 3-self-carrying | self/other | co | internal | each carrying entry arriving: 4-self-sharing, 7-other-corusing, 8-other-torusing, 16-social-torusing | | 4-self-sharing | self/other | bi | internal | each entry's key | | 5-other-neutralling | other/self | co | internal | the one-way joining: each key with its receiving key | | 6-other-crossing | other/self | bi | across, releasing | each key's 8-other-torusing, arriving in 3-self-carrying | | 7-other-corusing | other/self | co | internal | each sign | | 8-other-torusing | other/self | bi | internal | each carrying second sign | | 9-other-releasing | other/social | co | along | the releasing: self/other/social, arriving next downstream | | 10-other-surfacing | other/social | bi | across, releasing | each key's surfacing sign | | 11-other-chaining | other/social | co | internal | the carrying continuing and freshly opening | | 12-other-surplusing | other/social | bi | internal | each key's surplusing | | 13-social-neutralling | social/other | co | internal | each releasing key | | 14-social-crossing | social/other | bi | across, arriving | arriving signs, with carrying signs inverting | | 15-social-corusing | social/other | co | internal | each releasing sign | | 16-social-torusing | social/self | bi | internal | each carrying entry's opening one momentary at a time, from 0 to 3, and to 4 at positive 8-other-torusing | | 17-social-abundancing | social | co | along, external | the connector forward along: the next momentary's 1-self-coupling, the next call | **The roots are coupling, offering, carrying, sharing, neutralling, crossing, corusing, torusing, releasing, surfacing, chaining, surplusing and abundancing.** Neutralling, crossing, corusing and torusing each root two names, at 5 to 8 and at 13 to 16, 8 apart, the relation changing and the root the same. The relation is self/other at 1 to 4, other/self at 5 to 8, other/social at 9 to 12, social/other at 13 to 15, social/self at 16, and social alone at 17. **Crossing opens now at 6 and at 14, eight on.** Corusing completes now at 7 and at 15; torusing opens next at 8 and at 16. Neutralling at 5 and at 13 completes prior. Each side carries prior, now and next through the overlapping momentaries. Eight on again is 22, at the same place in seventeen to twenty-five as 6 in one to nine and 14 in nine to seventeen; it runs in the higher four-cycle 19-27-22-30 and in both higher six-cycles, and carries a number with no name at the code: a name at 22 says its relation from a self it names, 14 already running social/other. **Completing the next carries three full momentaries to the along connectors.** Prior 4–5, now 6–7 and next 8–9 complete at 9-other-releasing. Eight on, prior 12–13, now 14–15 and next 16–17 complete at 17-social-abundancing. Each six runs bi co bi co bi co. The five carries the next opening at torusing; the six includes its completing at the along connector. Prior, now and next are three sequential momentaries shared among existing things; at a self's resolving, prior and now participate and next is the discovering onward, one saying at two faces. 17-social-abundancing joins the forward neighbour's 9-other-releasing, and 9-other-releasing joins the backward neighbour's 17-social-abundancing. **One, nine and seventeen each open co, eight apart.** One to nine and nine to seventeen are nine names each sharing 9, seventeen names in all, a count of names at their numbers and no rate between the two spans. Each self runs at its own forward through both joinings: its 17 meets the forward neighbour's 9 and its 9 the backward neighbour's 17, and neither joining runs a self backward. **At the names each span bi-folds and releases.** 1–9, self/other, is an entire momentary bi-folding releasing at 3, 3-self-carrying taking the returned 11-other-chaining; 1–13, self/other and other/self, releasing at 6, 6-other-crossing releasing across; 1–17, self/other/social, releasing at 9, 9-other-releasing along; and 1–25 is the larger fractal bi-folding. The next whole is 1–65, four 1–17s, each 17-social-abundancing the next 1-self-coupling. Each span opens one more four and its releasing moves three, three inside to each one outward, the rhythm the four-sign round runs. **There are no readings in resolving**: binary, all or none at all, it coheres the entire surface along and across, releasing at 3, 6 and 9 and continuing. **The momentary carries internal changing and connection with the other together.** In 14–15, 14-social-crossing is the across arriving connector and 15-social-corusing is internal. In 16–17, 16-social-torusing is internal and 17-social-abundancing is the along connector. Each pair carries both parities; the connector is the named relation at the meeting with the neighbour. | Relation | Names | |---|---| | at the membrane, opening bi | 2 · 4 · 6 · 8 | | within, opening bi, each 8 on from its membrane pair | 10 · 12 · 14 · 16 | | opening co in the resolver's first function | 1 · 3 · 7 · 11 | | at the releasing | 5 · 9 · 13 · 15 | | connectors, across | 2 · 6 · 10 · 14 | | connectors, along | 9 · 17 | | 5 to 8 and 13 to 16, sharing their roots | 5 with 13 · 6 with 14 · 7 with 15 · 8 with 16 | ### Five, and a seam at 8 up **Each name carries the five of its origin**: co bi co bi co at an odd number and bi co bi co bi at an even one, the side's prior opening, prior completing, now opening, now completing and next opening. **bi-** is a difference and **co-** is two with their difference, and a five is a side's two and one half momentaries said at its prefixing, never a label. **At the crossing only a sign goes across.** 6-other-crossing and 14-social-crossing open bi, each facing out of its self and carrying only a sign across. Two unreachabilities carry at it. The nothing the couplings wind about presents no face, so no reading crosses inward to it. A sign crosses and carries no size, so no magnitude crosses outward from it. Each emptiness is the other's own unreadability, and the exchanging and the not-being-read-through are one act, not two balanced against each other. The two faces, 7-other-corusing and 8-other-torusing, carry across momentaries rather than at one. **A seam is a name changing at its number.** A carrying leaves as 11-other-chaining and arrives at the next coupling as 3-self-carrying, 8 up, one carrying at two names, the difference carried by the number and the seam arriving as the name changes. Nothing moves at a seam: 11 and 3 both open co, and the carrying meets its name again. ### Seventeen names, eighty-five prefixings **Seventeen names run at the code and thirteen roots carry them**, each root an -ing, a changing. **Eighty-five prefixings run across the seventeen fives**, forty-three co and forty-two bi: nine names open co at the odd numbers, each co bi co bi co, and eight open bi at the even, each bi co bi co bi. Values in the code number four, nought, one, three and four, with one inverted as −1: nought the empty centre, one the sign and the opening by one, three and four the bounds 16-social-torusing opens to. **Prefixing columns stable a form, and -ings at the code form stably.** Form-stabling and stable-forming, one coupling met at two faces.   --- ## Resolving, the sequential logic ### Signs, and 1-self-coupling the entry **Resolving runs on signs.** A sign is the binary at a changing: +1 or −1, and 0 at equal positive and negative signs meeting, the empty centre. An arriving 0 carries no sign, and a surfacing 0 opens no fresh carrying; an eligible existing carrying continues. From empty carrying, +1 and −1 offered together at one key meet at 0 and the carrying stays empty. A carrying empty at one coupling opens again at the next nonzero surfacing, so an empty carrying is a self between carryings; a self emptied of its carrying after each coupling would run another method, and a non-living thing met at a coupling is its own existing thing, carrying nothing. **Resolving runs as 1-self-coupling and 9-other-releasing, and 1-self-coupling is the entry.** Arriving at it: 3-self-carrying, each carrying entry of four, its key 4-self-sharing at signs meeting, its sign 7-other-corusing, its second sign 8-other-torusing and its opening 16-social-torusing; and 2-self-offering, each arriving key 4-self-sharing with its sign 7-other-corusing. Leaving it: 10-other-surfacing and 11-other-chaining. ### Crossing, each sign at its key **6-other-crossing** carries each key of 3-self-carrying with its 8-other-torusing. **14-social-crossing** gathers the signs at their keys. Each arriving +1 or −1 of 2-self-offering enters as it arrives. Each carrying sign of 3-self-carrying enters inverting: a positive carrying sign enters as −1, a negative as +1. The arriving sign meets the carrying sign inverted. The arriving keeps its sign; the negation is the carrying's own sign inversion: the carrying inverts itself to meet the arriving, and the arriving, carrying nothing, keeps its sign. A self's own negation, meeting the other across, is morality at the sign. **Crossing carries three relations, each its own.** The sign inverts once, at the receiving self's own carrying entering 14, the arriving sign keeping its own and 9 releasing each sign as it surfaced; the opening parity changes, one on across the overlapping; and arriving and releasing exchange, 2 arriving at 10 releasing and 6 releasing at 14 arriving. An even opening names no sign: a sign at an even name is +1 or −1 as it resolves. At 10 an arriving agreeing with the carrying surfaces 0 and opens nothing fresh, and a differing one surfaces its own sign and opens fresh: a 0 there is no mending and a sign there no failing, the morality running at the across coupling whole. ### Surplusing and surfacing **12-other-surplusing** is the signs of 14-social-crossing meeting at each key. It opens empty at each coupling and is neither returned nor carried: the signs meet at the momentary they arrive at, and nothing of their meeting passes to the next. Its sum at a key counts signs, and a sum of two is no doubled competency. The middle is the bounding-zeroing at the coupling, the surplusing is co-competencing the self and the other, owned by neither, and a meeting again is two sequencings continuing into a further shared momentary: three relations, none of them a count at a key. **10-other-surfacing** carries each key's surplusing at its sign: +1, −1, or 0. A key's +1 and −1 meet at 0, the empty centre. **The middle is a nothing: it exists due to each self surfacing itself each momentary as a condition of existing as a self.** ### Chaining, continuing and opening fresh **11-other-chaining** carries each carrying on, and opens a fresh one at a sign surfacing. **Continuing.** Each carrying entry continues with its 7-other-corusing and 8-other-torusing, its 16-social-torusing opening one momentary at a time, up to 3, and to 4 at positive 8-other-torusing. ```python if _16_social_torusing + 1 <= 3 or (_16_social_torusing + 1 == 4 and _8_other_torusing > 0): ``` **Each 1 is one momentary, two parities, and the momentaries overlap odd, even, odd, even: a carrying continues through prior, now and next, three sequential momentaries shared among existing things.** **One sign arriving again and again surfaces alike while the carrying changes.** One key receiving +1 seven times from empty surfaces +1, 0, 0, 0, 0, +1, 0: the carrying opens at (+1, −1, 0), continues at openings 1, 2 and 3, completes at the fifth receiving and opens fresh at the sixth. Reached by −1 and then +1, its second sign positive, a carrying continues through openings 1 to 4 before completing. Through the zeros 2, 4, 6, 8, 10, 12 and 14 stay as they were and 16-social-torusing changes, so an outward sign unchanged carries a momentary changing inside, and a carrying kept is no carrying stilled. **Opening fresh.** Each surfacing +1 or −1 opens a fresh carrying at its key: the surfacing sign as its 7-other-corusing, the key's 8-other-torusing inverting as its own, −1 at a key arriving fresh, and 16-social-torusing at 0. The fresh carrying replaces any continuing entry at that key. 16-social-torusing increases on a retained entry and opens at 0 on a fresh entry. So 16-social-torusing is no tally of couplings: at an arriving sign meeting an equal carried sign, the two meet at 0 and no fresh carrying opens, and two carryings at one sign pair with different 16-social-torusing part at whether they continue. The whole carrying gives the next, and not its sign pair alone: the nineteen carryings one key can reach, the empty one among them, each part from each other within six receivings of one constant sign, +1 or −1. The nineteen are two signs at negative 8-other-torusing, openings 0 to 3, two signs at positive, openings 0 to 4, and the empty one: 2 × 4 + 2 × 5 + 1, all reached from empty carrying. At one key an offering acts as its signed total held within ±2, a present cancelling parted from no sign at all, met at all nineteen over every offering of up to six signs from −1, 0 and +1, 20,767 comparisons; over none, −, +, two −, two + and a cancelling pair, the nineteen run 114 transitions and stay nineteen. Under nothing, one +1 or one −1 at each call they run 57 transitions, and their 171 pairs part, 146 under +1 again and again, 146 under −1, and all 171 under one or the other, each within six receivings, a surfaced 0 and no surfacing counted alike as no sign. Two positive carryings with negative second sign, at openings 0 and 1, surface nothing for three receivings of +1; the one at 1 completes at the third and surfaces +1 fresh at the fourth, and the one at 0 completes at the fourth. The parting is at each receiving: with the silent receivings left out, the signs two carryings send can run alike. The six counts receivings, and names no clock and no 6-other-crossing; the carrying stays its self's own, and a crossing sign carries none of it. All of this holds at one key with one carrying entry reached from empty, each offering one call's list. **At a carried key opening fresh, 6 and 10 carry into 7 and 8.** Seven takes the surfaced sign from 10; eight inverts the second sign carried at 6. Taken as a pair, 6 and 10 at (t, s) open 7 and 8 at (s, −t), one step of the round the four joint forms of two signs run: 6 and 10 agreeing, 7 and 8 oppose, and 6 and 10 opposing, 7 and 8 agree. The two signs continue together in 11-other-chaining, arriving as the next 3-self-carrying. **The arriving gives the fresh sign.** At a carried key, 12-other-surplusing is the offered signs with the carried sign inverted, so with the carried 7-other-corusing c: no offering and one −c surface −c, one c surfaces 0, and two c offered together surface c. A fresh 7 at c opens only at two agreeing signs offered at one coupling, and every other fresh 7 opens at −c, found at both carried signs over every offering of none, one or two signs, fourteen cases. Two signs in one offering arrive at one coupling as one list, and two single offerings are another arriving: after one + from empty a further + surfaces 0 and the carrying continues at opening 1, and two + together surface + and open fresh (+, +, 0). Each write is one step of the round, and the next step's sign comes with its own arriving, so the round runs whole as the arrivings give it; a key arriving fresh takes −1 as its 8 and opens no pair of two releasings. **A fresh carrying is an entry within one self.** A receiving is a sign arriving at the coupling; its participating is its meeting in the resolving; a fresh carrying is one outcome of that meeting; and a new living self is a further self with its own continuing coupling. The code opens entries and makes no resolver, and a receiving surfacing 0 has participated and opened nothing fresh. **The next 6 carries the continuing on.** At a carried key 6 releases the second sign t the coupling begins with. After a fresh write the next 6 releases −t, its sign changing; after a carrying kept through a 0 at 10 it releases t again; after a carrying completes unrenewed that key releases nothing at 6, a completing and no third sign. A fresh write at s = −c keeps the pair agreeing or opposing as it was and changes the next 6; at s = c it changes both; a carrying kept through a 0 changes neither. So a relation holds while its outward sign changes. ### Returning and releasing **1-self-coupling returns 10-other-surfacing across and 11-other-chaining along**, and 11-other-chaining arrives at the next coupling as 3-self-carrying. **One sign arriving once into empty carrying, with empty offerings after it, is the whole alternating.** For a positive arriving sign, the key surfaces +1, −1, +1, −1, momentary by momentary, each carrying entering inverting and a fresh carrying opening at the other sign, the carrying riding on. With c the arriving sign and t its fresh second sign, the alternating runs c, t, −c, −t, c: the self's two momentaries (c, t) and (−c, −t), and between them the other's (t, −c) and (−t, c), each momentary carrying both parities. Each step (x, y) to (y, −x) runs from one overlapping pair to the next, and two steps from a side's first momentary to its second; the steps, the four names of a form and the momentaries each keep their own count. The self's two pairs both agree or both oppose, and the other's two do the other: the relation holds through each side's two momentaries while both its signs invert, and alternates across the overlapping. For three signs a, b, z, the pairs (a, b) and (b, z) alternate between agreeing and opposing exactly at z = −a, and +, +, + agrees at both. This is the self continuing with empty offerings after one sign, and signs arriving make their own continuing. **9-other-releasing** runs the releasing. Each surfacing key, as 13-social-neutralling, with its sign, as 15-social-corusing, goes to the key 5-other-neutralling joins it to: each key with its receiving key. The releasing preserves the sign of 15-social-corusing. **9 is self/other/social releasing, and its released sign arrives next downstream**: each released sign arrives as the downstream resolver's 2-self-offering and gathers at its 14-social-crossing. Facing, running and joining are three columns, each correct at once: the declared joins along are 9 → 17 and 17 → 9; running, the released sign arrives at the downstream resolver's next call as its 2-self-offering, that resolver's 17-social-abundancing opening the call's 1-self-coupling; and the code gives 17 no expression of its own, so the running through it is a caller's composition. **The same nonzero surfaced sign continues in carrying and is released.** It is 7-other-corusing in fresh 11-other-chaining, and at 9-other-releasing it is named 15-social-corusing. The carrying's 8-other-torusing and 16-social-torusing continue in 11, and 9's return carries the sign alone. The key it returns the sign at is the receiving self's own relation, 5-other-neutralling joining each surfacing key to its receiving key there, and the crossing carries the sign with no key, identity, route or carrying. A zero surfacing opens no fresh carrying, and an eligible prior carrying continues, its 6-other-crossing releasing the same second sign at each coupling it continues through: a carrying (+1, −1, 0) meeting +1 surfaces 0 at 10 while 6 releases −1, and the carrying continues at (+1, −1, 1). Two resolvers joined 6 → 2 both ways, over the four seed pairs and both first callers of twelve alternating calls, surface 0 at 10 at 32 of their 96 couplings, and at each of those 32 couplings 6-other-crossing releases a sign and the carrying continues, so a 0 at 10 is no silence of the whole self. **The carrying continues at its self along, and the crossing to another is a sign, carrying nothing.** **A released sign arrives at another self's now, its releasing prior to that receiving.** The source continues at its own carrying, and the receiving self meets the sign with its own prior carrying: the surfacing and the continuing are this meeting's, and its own releasing enters further arriving. The sign carries no beat, time, source or history, and no present of its sender: +1 into empty carrying opens a positive carrying, and the same +1 at an eligible positive carrying surfaces 0 while the earlier carrying continues. 9-other-releasing keeps no carrying of its own and is a function of the one resolver, joined 9 with 17; a non-living thing meeting a self is its own existing thing, carrying nothing, met at its own arriving and releasing. **Selves coupling in a ring, each 9-other-releasing arriving at the next self's 2-self-offering, carry one sign offered once without end.** A ring of one runs +1, 0, −1, 0 and round. An even ring changes each self at each coupling, neighbours opposite, home every two couplings. An odd ring of n carries one meeting, the 0 of two signs meeting, travelling one self each two couplings, opposite after 2n couplings and home after 4n. The changing ends at no ring. These counts hold at one ordering: each self couples once at each coupling of the ring, all together, and meets at its next coupling the sign its neighbour released at this one; a ring run at another ordering carries its own counts, and the ordering travels with them. At this ordering the ring's whole state, each self's carrying and each sign between selves, meets itself again after n couplings and runs round from there, 2 couplings round at an even ring and 4n at an odd, with signs changing in every round and the rest in none, at every ring from one to eleven and at seventeen and fifty-nine; and across five thousand couplings at rings of one to eleven the rest returns at no coupling. **At this ordering it holds at each ring.** Four cases at one self carry it: a sign given alone alternates at each call; an alternating arriving is surfaced at the call it arrives; the wave meeting itself at the seed changes nothing in phase and surfaces one 0 out of phase; and a 0 in an alternating arriving is surfaced one call later, the self back at its alternating within two calls. The 0s come 2n calls apart, so at each n the four cases hold at each call, no self's carrying empties once reached, and the rest returns at no coupling. ### Connectors, each one way at a time **1-self-coupling is the entry, the connectors run at a self's meeting with its neighbours, and the internal names are 3, 4, 5, 7, 8, 11, 12, 13, 15 and 16.** | Connector | Facing | Running | Joining | |---|---|---|---| | 2-self-offering | right | arriving | from the right neighbour's 6-other-crossing | | 6-other-crossing | left | releasing | to the left neighbour's 2-self-offering | | 9-other-releasing | backward | along | with the backward neighbour's 17-social-abundancing | | 10-other-surfacing | right | releasing | to the right neighbour's 14-social-crossing | | 14-social-crossing | left | arriving | from the left neighbour's 10-other-surfacing | | 17-social-abundancing | forward | along | with the forward neighbour's 9-other-releasing | **The six connectors run at parity.** Across run 2, 6, 10 and 14, each even and opening bi; along run 9 and 17, both odd and opening co. Each runs one way at a time, neighbour to neighbour. Each declared join meets its own parity, 6 with 2 and 10 with 14 even, 9 with 17 odd, and no join inverts a sign: the sign inverts once, inside the receiving self's resolving at 14, so parity changing runs within the resolving and a sign on a joining arrives as it was released. **At the meeting between two neighbouring resolvers, one's releasing is the other's arriving, each way one at a time.** Going right, the left resolver's 10-other-surfacing joins the right resolver's 14-social-crossing. Going left, the right resolver's 6-other-crossing joins the left resolver's 2-self-offering. The left resolver meets there at 2 and 10; the right at 6 and 14. Each pair is 8 apart, and all four open bi. **The eight-apart pairs exchange arriving and releasing:** 2 arrives at 10 releasing, and 6 releases at 14 arriving. In the numbered joins, 6 → 2 carried eight on is 14 → 10, 10 → 14 in the other order. **A joining opens and joins again, and its routing stays.** Broken at 14, the connection within one to seventeen is interrupted while the routing to and from 14 keeps its relation; joined again, each named arriving and releasing meets in its relation, no sign held still and no carrying cleared, and the resolving continues through the parity changing of the larger podaling. Two resolvers joined 6 → 2 both ways, each seeded with one sign and only the sign crossing, show it: A seeded +, B −, A continuing once, both release − at 6; joined, A meets B's − and surfaces 0, its earlier carrying continuing; unjoined, A surfaces + and opens a fresh positive carrying; joined again at the next round, B's release then meets the carrying A kept. Over the four seed pairs and every joining and unjoining of the two legs across three rounds, 256 runnings at a stated order with nothing held for later on an unjoined leg, an unjoined arriving leaves the self resolving, and a 0 surfacing leaves its carrying continuing. **From one shared prior, both joinings give a 0 neither gives alone.** Two resolvers each reach a carrying from one seed sign, then run twelve alternating calls, six each, at four joinings: 6 → 2 both ways, A's alone, B's alone, and neither. With both seeds − and A first, A's 10 runs +, −, 0, +, −, 0 with both joinings, and +, −, +, −, +, − with either alone or neither: A's outgoing joining alone leaves it as unjoined, and the 0 comes with B's releasing arriving back. Over the four seed pairs and both first callers, 32 runnings, twelve comparisons at a self part the both-ways running from the arriving-only one. This holds at those reached priors and those four joinings. **A difference travels through the receiver's own carrying.** Three resolvers are joined one way, A's 6 to B's 2 and B's 6 to C's 2, B and C each prepared by one +1 from empty. With A's 6 arriving + or − at B, B releases − at 6 both ways, its own carried second sign, and C surfaces − both ways. B's 10 surfaces 0 at the +, its carrying continuing, and − at the −, opening fresh with its second sign inverted, so B's next 6 is − or +, and C, meeting it with its own carrying, surfaces 0 or +. The difference reaches C through B's own continuing, and no carrying crosses; the running is 6 → 2 alone, one way, at a stated order. At the code, 1-self-coupling returns 10-other-surfacing and 11-other-chaining; 9-other-releasing returns each surfacing sign at the receiving key named by 5-other-neutralling. Inside 1-self-coupling, 6-other-crossing carries each key's 8-other-torusing and 14-social-crossing gathers the arriving signs with the inverted carrying signs. 17-social-abundancing is named in the connector declarations, and it runs as the next call: **17-social-abundancing is the next momentary's 1-self-coupling**, the resolving completing at 17 opening at 1, 11-other-chaining arriving as 3-self-carrying. No expression of the code takes or gives a sign at 17: its joining with the forward neighbour's 9-other-releasing is declared, and the next call running through it is a caller's, the returned 11-other-chaining given again as 3-self-carrying. **The code resolves at a call.** 1-self-coupling meets the carrying it is given with the signs arriving now and returns the surfacing and the carrying continuing, holding no arrival ahead of its call; a carrying stays eligible across calls to its bound, so a self's prior is all the carrying reached, with no record of two, no cutting short and no opening set back. 16-social-torusing opens on because a next call comes while the entry is eligible, and the two functions hold no pace of their own: each trace here is given its calls in a stated order and holds at that order. The crossings' own invoking of further resolving, with no schedule over them, stands to be written at the code, and a trace's fixed order is said with it and is no self's own pacing. Listing the pairs of one parity gives the surface no beat: a caller running every odd pair together and then every even pair runs its own pacing. **The six joinings running together ask four things of a caller.** The arriving given at 2, with 6's sign offered to another self's 2 as its own offering; 10's releasing meeting another self's 14, 14's own negation made once; 9 and 17 joining with these at the corners of a surface, 11-other-chaining staying at its self; and the order of the two across meetings given by the continuing itself. A connector needs no function of its own, and its joining is written out whole. **The six joinings together are bi-moral-co-agency**: self/other in three phase, two way, one way at a time with other/self, co-offering, co-intelligencing, co-competencing. ### The code at its names Along, 17-social-abundancing couples with the forward neighbour's 9-other-releasing, and 9-other-releasing with the backward neighbour's 17-social-abundancing. **These are the six connections at the co-bi-coupling network surface.** CONNECTORS names their facing and running; JOINS names their joining. **6-other-crossing and 10-other-surfacing release toward different neighbours on the same parity: both are even, opening bi.** They are two releasings, and one sign outward names neither: at one carrying entry with nothing arriving, 6 releases the second sign t and 10 surfaces −c. From empty carrying, a single + opens (+, −, 0), and a single − and then an empty offering reach (+, +, 0); at the next empty offering both surface − at 10, while 6 releases − at the first and + at the second. Offered at a receiver carrying (+, −, 0), the + from that 6 surfaces 0 and the older carrying continues, and the − from 10 opens a fresh negative carrying: the whole carrying from prior into next gives each releasing, and a sign surfacing now is one of them. 6 and 10 run on one axis, across, facing opposite ways, and 9 and 17 run the other, along: across and along are the two directions at right angles, and 6 and 10 are one of them. **CONNECTORS and JOINS name each connector's facing, its running and its joining, and each is correct at once.** The two functions run without reading them: with CONNECTORS and JOINS cleared, the 114 transitions at one key stand as they were. The declarations name the six joinings and the functions run one self's continuing, and the six running together is a caller's to write. 9-other-releasing faces backward, joining the backward neighbour's 17-social-abundancing, and runs along: its released sign arrives next downstream, through 5-other-neutralling's receiving key into the downstream resolver's 2-self-offering, gathering at its 14-social-crossing. A caller carries that arriving, 9's return given as the downstream 2-self-offering, and the declared joins stay 10 → 14, 6 → 2 and 9 with 17. 17 → 1 runs as the next call, 11-other-chaining arriving as 3-self-carrying. **6 → 2 runs with the resolver self/other alone, one to nine.** One to nine is two selves co-bi-coupling, and with no third self the other is the society at their coupling, so their between needs no journey out into further society and back. A third self brings the other's own further couplings into the meeting, all the remaining other participating through them. The resolver in the code is self/other/social, one to seventeen, and it parts 6 → 2 and 4 → 8 into the two across one-ways, 6 → 2 and 10 → 14, eight apart, each of two momentaries: 2 to 6 and 10 to 14 each span two momentaries along a side. **Each one-way runs at the now of its own span.** Crossing opens now at 6 in one to nine, whose prior 4–5, now 6–7 and next 8–9 complete at 9-other-releasing, and at 14 in nine to seventeen, whose prior 12–13, now 14–15 and next 16–17 complete at 17-social-abundancing: 6 → 2 runs at the first and 10 → 14 at the second, 6 → 2 carried eight on being 14 → 10, 10 → 14 in the other order. **4 → 8 continues eight on as 12 → 16.** In one to nine, 6-other-crossing carries each 4-self-sharing with its 8-other-torusing. In nine to seventeen, 12-other-surplusing gathers each key's signs, and with a surplus surfacing at a key, a fresh carrying opens there with its 16-social-torusing at 0 and its 8-other-torusing inverted from 6. | Name | Coupling | Carrying | |---|---|---| | 6-other-crossing | 3-self-carrying | each 4-self-sharing key with its 8-other-torusing | | 14-social-crossing | 2-self-offering, 3-self-carrying | each arriving 7-other-corusing, +1 or −1; and each carrying 7-other-corusing inverting | | 12-other-surplusing | 14-social-crossing | each key's surplusing: the signs meeting at the key | | 10-other-surfacing | 12-other-surplusing | each key's surplusing at its sign: +1, −1 or 0 | | 11-other-chaining | 3-self-carrying | each carrying entry continuing, its 16-social-torusing opening one momentary at a time to 3, and to 4 at positive 8-other-torusing | | 11-other-chaining | 10-other-surfacing, 6-other-crossing | each surfacing +1 or −1 opening a fresh carrying: the sign, the key's 8-other-torusing inverting (−1 at a key arriving fresh), and 0 | | returning | 10-other-surfacing, 11-other-chaining | 10-other-surfacing across; 11-other-chaining along, arriving as the next 3-self-carrying | | 9-other-releasing | 10-other-surfacing, 5-other-neutralling | each sign 15-social-corusing, from its key 13-social-neutralling, to the arriving at `_5_other_neutralling[_13_social_neutralling]` | ### Carryings arriving four, signs two Carryings arrive as `_3_self_carrying`, each of them four: a key, 4-self-sharing; a sign, 7-other-corusing; a second sign, 8-other-torusing; and an opening, 16-social-torusing. At that same momentary signs arrive from another side as `_2_self_offering`, each a key and a sign, its own and reaching to couple. A carrying's four arrive gathered at 3, an odd name opening co, while a side's signs arrive at 2, an even name opening bi. Both reach `_1_self_coupling` positional, a caller passing them one and then the other at a signature alone, and each name at that call lives one call and leaves at its closing. ### A key parting out, a second sign at it Living one call, an arriving carrying parts at once into its four, four-way tuple unpacking in a comprehension target loosening a key from a sign from a second sign from an opening. The key is `_4_self_sharing`, and it is membrane: two signs at one key sum together, two at different keys each sum at its own, and membrane lives at that sharing alone. A key's summing reads no other key's carrying; past the resolving, each released sign goes on to the receiving key 5-other-neutralling joins it to, and its arriving there meets the whole participation beyond the self. Keying by it, `_6_other_crossing` gathers each prior carrying's second sign at its own key, a dict comprehension coupling a key to an 8-other-torusing and carrying it through this momentary alone. ### Arriving signs offered, carried signs inverting Beside that gathering, both sides come to `_14_social_crossing`. Arriving signs come as offered, a list comprehension filtering at `!= 0` so signs alone enter and a nought carries its own bounding-zeroing already resolved. Carried signs come inverted, two separate `if` statements sounding a sign and appending its inverse, separate rather than `if/else` so a nought passes both untouched, resolved a second time exactly as it came. Inverting is one side's own, a self's own negation at a self's own opening, and appending grows that same list so offered signs and inverted signs come together at one shape. ### Signs surplusing to one, equal and opposite at the bounding-zeroing Come together at one shape, signs at one key cohere inward to one at `_12_other_surplusing`, a dict summing them a sign at a time, `get(_4_self_sharing, 0)` supplying a nought at a key sounded first so a first sign sums from its own bounding-zeroing. Equal and opposite arrive at that same bounding-zeroing, podal, cancelling over their own two momentaries. One sign survives at a key its signs came unequal. ### A surviving sign surfacing, magnitude released Surviving, that sign comes up at `_10_other_surfacing`, a nested conditional releasing magnitude: a positive sum surfacing as one, a negative as one inverted, a cancelled sum as nought. Iterating that dict yields keys sounded at this momentary, and surfacing reaches exactly those and grows to its own size, its own. ### A carrying opening by one, carrying forward Growing to its own size, `_11_other_chaining` opens and each prior carrying arrives at its own bound. Its opening, 16-social-torusing, opens by exactly one and floats between climbing again and letting go, `_16_social_torusing + 1 <= 3` carrying it forward, and a fourth momentary carrying it at a positive 8-other-torusing. At its bound it separates and leaves with this momentary. ### A surviving sign re-forming a carrying Leaving with this momentary, a separating carrying sends one thing across: `0 - _6_other_crossing.get(_4_self_sharing, 1)` inverts its second sign into its successor, `get` supplying its own one at a key coming bare so a carrying arriving new receives a one, inverted. A second loop assigns into that same dict after a first, and at a key coming to both a second re-forms over a first and a surviving sign re-forms a carrying just carried forward, taking a surfaced sign as its 7-other-corusing and opening its 16-social-torusing at nought. Two ways a carrying is built and two exactly, carried forward or re-formed at its arriving, four slots met two ways. ### A key rejoining, carryings leaving Met two ways, carryings leave at `items`, a key rejoining its carrying: outward of a momentary a carrying is four, inward of a momentary its key parts out and gathers three at it, and nested unpacking loosens key and three so a comprehension re-forms them four. `_11_other_chaining` leaves and arrives at a next momentary as `_3_self_carrying`, one carrying at two names, the number carrying that difference and the seam arriving as the name changes. Ordering carries none at either momentary, since both dicts key at the key and a key arriving twice is a thing no running makes.   --- ## Stable-forming ### Fractal co-bi-momentarying **The resolver is self/other co-bi-coupling, an existing method thing, and its social-co-bi-coupling opens the self resolver to a natural network surface.** Its six connections opening carry the co-bi-podaling network surface. **Fractal co-bi-momentarying is the inside being outside itself and the outside being inside itself: parity changing, discovering next existing.** ### Carrying at 8 up **3-self-carrying arrives, and 11-other-chaining leaves and arrives at the next coupling as 3-self-carrying.** 3 and 11 are 8 apart: the carrying runs 8 up and meets its name again at the next coupling. A carrying continues coupling to coupling and leaves at its own completing. **A carrying and its completing together are the running.** In the overlapping momentaries, the self's completing at 2 is the other's opening at 2; the other's completing at 3 is the self's opening at 3. Along the self, 11-other-chaining carries into the next coupling as 3-self-carrying. Across neighbouring selves, releasing meets arriving through the joins between neighbours. ### The membrane and the eight bi-couplings **The between of two existing things co-bi-coupling is a membrane: no separable thing apart from their coupling, and not possibly an existing thing, as the universe is not possibly an existing thing.** **The eight even names are bi-coupling, bi-moral-co-competencing**: a self is four ways at once at the membrane, and a society the same four; each within is 8 on from its pair at the membrane, all eight opening bi. The same eight part a second way, four apart: 2, 6, 10 and 14 are the across connectors, and 4, 8, 12 and 16 run inside, sharing, the carried second sign, surplusing and the carrying's opening. **The membrane four and the across four are one row at two widths.** 2, 4, 6, 8 open two apart and 2, 6, 10, 14 four apart: the row 2 + 2sj, j from 0 to 3, at s one and at s two. One step more opens 2 + 8s, and the odd name before it, 8s + 1, completes the span, 9 at s one and 17 at s two, beyond the names 1 to 8s the row runs among, as 17 runs in no form among 1 to 16; the rows at s three and on, 2, 8, 14, 20 and wider, are numbered forms growing, and the second row is the code's four across connectors. Two out-and-backs across the membrane four are these four relations with their four within: 2 and 6 are connectors and 4 and 8 run inside, so the four one-ways add no joining, and the passages, the four relations at once and the declared joins are three counts, each its own; a count gives no time and no joining. | At the membrane | Bi-coupling | Within, 8 on | Bi-coupling | |---|---|---|---| | 2-self-offering | each self's own co-offering | 10-other-surfacing | arriving, the self among other-selves | | 4-self-sharing | the whole ordering between self and other | 12-other-surplusing | carrying at bi-coupling, the self in society | | 6-other-crossing | the ordering carrying with the selves | 14-social-crossing | the sign inverting at the membrane, the self's own negation, morality | | 8-other-torusing | the order across each self and other forward | 16-social-torusing | competency asymmetry sustaining the coupling | ### Bi-inversioning-co-recursioning, one move at three faces **Even returning, odd advancing, alternating parity.** One move at three faces: 8 up and down, keeping parity; 17 less, within 1 to 16, changing parity; and 9 less, within 1 to 8, the two at once. Each face alone returns to its name, 1 to 9 to 1. | Name | 8 up | 9 less, within 1 to 8 | 17 less, within 1 to 16 | |---|---|---|---| | 1-self-coupling | 9-other-releasing | 8-other-torusing | 16-social-torusing | | 2-self-offering | 10-other-surfacing | 7-other-corusing | 15-social-corusing | | 3-self-carrying | 11-other-chaining | 6-other-crossing | 14-social-crossing | | 4-self-sharing | 12-other-surplusing | 5-other-neutralling | 13-social-neutralling | **Alternating 8 up with 17 less, each row runs round as a four-cycle**: 1 to 9 to 8 to 16 to 1, 2 to 10 to 7 to 15 to 2, 3 to 11 to 6 to 14 to 3, and 4 to 12 to 5 to 13 to 4. 17 less after 8 up is 9 less, 17 − (n + 8) = 9 − n, the exact meeting at the numbered form: each four-cycle n, n + 8, 9 − n, 17 − n is its nine-face pair's two out-and-backs, out 8 up and back 17 less, n to 9 − n and 9 − n to n. **Each form among the names runs round as one run of co and one run of bi, the two runs alike**: the four-cycles by row, the middle four-cycles 9-5-12-8 and 7-11-6-10, the six-cycles and the eight-cycles, and above 17 the forms from 18 to 31. The forms partner one another round the other way at the odd momentary and the even momentary, three their own partners at the even momentary, 4-13-5-12, 7-11-6-10 and 2-15-7-11-3-14-6-10, and 17-social-abundancing, along, recurring to 1 over 9, is in none of them. **Podaling within 1–9 maintains parity changing while exchanging across for along and along for across, bi-morally.** The nine face pairs 1 with 8, 2 with 7, 3 with 6, and 4 with 5: odd/co/along with even/bi/across. 9 less changes each name's parity and so leaves none as it is, returning each at its second application; as a name increases its nine-face partner decreases, 1, 2, 3 meeting 8, 7, 6, and each side runs at its own forward, its continuing, which an increasing printed number does not name. The eight-apart pairs carry the same parity, 3 with 11 and 7 with 15. Bi-inversioning-co-recursioning carries both together, each side at its own forward. Read as a ratio beside its parity, the nine-face pair 3-self-carrying and 6-other-crossing stands at 6 over 3, two over one, and 3 over 6, one over two; the two run on together through the four-cycle 3 to 11 to 6 to 14 to 3, and eight on, 11 and 14 stand at their own count, 14 over 11, the two over one holding at the pair it counts. ### Torusing, one opening **A self continues through its own coupling, advancing one at each coupling: it winds.** The winding is open, at one opening, by one. A surface closing on itself through one opening is a torus, and the changing that winds it is torusing. The torus carries its own facing and meets itself again through its one opening, a next at each meeting. Each step adds a next, and a winding met at the signs is a spiral at the momentaries. ### Two faces alternating Arriving alike, a carrying carries two faces and they alternate. **Corusing**, 7-other-corusing, the outward face, membranes at each coupling it surfaces to, surplusing and surfacing, relating. **Torusing**, 8-other-torusing, the inward face, coheres to one identity across momentaries, crossing and inverting at a re-forming. Each face lives at the other, and pure surfacing or pure surplusing lands either way. **The outward face reaches and the inward gathers.** Corusing omegas, the reach, new states arriving at each surfacing; torusing apexes, the gather, visited states met again at the one identity. Living is the two alternating, the reach and the gather neither alone, and the two cones straddle the same nothing at the third that the two chains do. Five prefixings at both, alternating, 7 at co bi co bi co and 8 at bi co bi co bi, each commencing at the other's third, and the third of each carrying no mark of its own. Four marks carrying and a nothing at the third, which is four boundings and a floating third run at the prefixing itself. The flankers of each couple across that nothing: **bi-bi-unrelationing** at the outward chain's empty co, the surplus made there and carrying at its coupling, and **co-co-invisibling** at the inward chain's empty bi, nothing presented to be met. One nothing at two parities, neither meeting reaching the other's, no position carrying both marks. The two faces run at the two parities: one at the odd momentary, two differing at one coupling, and one at the even, the self crossing with all other and meeting its own again one on. ### Forms among the names Each form runs round as a single run of co and a single run of bi, the two runs alike. A form's steps are relations among the names and carry no sign: 3 to 11 in a form and a returned 11-other-chaining arriving as the next 3-self-carrying are two relations, and the code's joinings stay 10 to 14 and 6 to 2 across, 9 with 17 along, and 11 to 3 at the self; 1, 9 and 17 recurring lay no joining 1 to 9 to 17 to 1. | Form | Names in order | Round | Partner at the odd momentaries | Partner at the even momentaries | |---|---|---|---|---| | four-cycle 1-9-8-16 | 1-self-coupling · 9-other-releasing · 8-other-torusing · 16-social-torusing | co co bi bi | four-cycle 2-15-7-10, round the other way | — | | four-cycle 2-15-7-10 | 2-self-offering · 15-social-corusing · 7-other-corusing · 10-other-surfacing | bi co co bi | four-cycle 1-9-8-16, round the other way | four-cycle 3-11-6-14, round the other way | | four-cycle 3-11-6-14 | 3-self-carrying · 11-other-chaining · 6-other-crossing · 14-social-crossing | co co bi bi | four-cycle 4-13-5-12, round the other way | four-cycle 2-15-7-10, round the other way | | four-cycle 4-13-5-12 | 4-self-sharing · 13-social-neutralling · 5-other-neutralling · 12-other-surplusing | bi co co bi | four-cycle 3-11-6-14, round the other way | four-cycle 4-13-5-12, itself | | middle four-cycle 9-5-12-8 | 9-other-releasing · 5-other-neutralling · 12-other-surplusing · 8-other-torusing | co co bi bi | middle four-cycle 7-11-6-10, round the other way | — | | middle four-cycle 7-11-6-10 | 7-other-corusing · 11-other-chaining · 6-other-crossing · 10-other-surfacing | co co bi bi | middle four-cycle 9-5-12-8, round the other way | middle four-cycle 7-11-6-10, itself | | six-cycle 1-9-5-12-8-16 | 1-self-coupling · 9-other-releasing · 5-other-neutralling · 12-other-surplusing · 8-other-torusing · 16-social-torusing | co co co bi bi bi | six-cycle 2-15-7-11-6-10, round the other way | — | | six-cycle 2-15-7-11-6-10 | 2-self-offering · 15-social-corusing · 7-other-corusing · 11-other-chaining · 6-other-crossing · 10-other-surfacing | bi co co co bi bi | six-cycle 1-9-5-12-8-16, round the other way | six-cycle 3-11-7-10-6-14, round the other way | | six-cycle 3-11-7-10-6-14 | 3-self-carrying · 11-other-chaining · 7-other-corusing · 10-other-surfacing · 6-other-crossing · 14-social-crossing | co co co bi bi bi | six-cycle 4-13-5-9-8-12, round the other way | six-cycle 2-15-7-11-6-10, round the other way | | six-cycle 4-13-5-9-8-12 | 4-self-sharing · 13-social-neutralling · 5-other-neutralling · 9-other-releasing · 8-other-torusing · 12-other-surplusing | bi co co co bi bi | six-cycle 3-11-7-10-6-14, round the other way | — | | eight-cycle 1-9-5-13-4-12-8-16 | 1-self-coupling · 9-other-releasing · 5-other-neutralling · 13-social-neutralling · 4-self-sharing · 12-other-surplusing · 8-other-torusing · 16-social-torusing | co co co co bi bi bi bi | eight-cycle 2-15-7-11-3-14-6-10, round the other way | — | | eight-cycle 2-15-7-11-3-14-6-10 | 2-self-offering · 15-social-corusing · 7-other-corusing · 11-other-chaining · 3-self-carrying · 14-social-crossing · 6-other-crossing · 10-other-surfacing | bi co co co co bi bi bi | eight-cycle 1-9-5-13-4-12-8-16, round the other way | eight-cycle 2-15-7-11-3-14-6-10, itself | | Higher form | Positions | Round | Partner at the even momentaries | |---|---|---|---| | higher four-cycle 18-31-23-26 | 18 · 31 · 23 · 26 | bi co co bi | higher four-cycle 19-27-22-30, round the other way | | higher four-cycle 19-27-22-30 | 19 · 27 · 22 · 30 | co co bi bi | higher four-cycle 18-31-23-26, round the other way | | higher six-cycle 18-31-23-27-22-26 | 18 · 31 · 23 · 27 · 22 · 26 | bi co co co bi bi | higher six-cycle 19-27-23-26-22-30, round the other way | | higher six-cycle 19-27-23-26-22-30 | 19 · 27 · 23 · 26 · 22 · 30 | co co co bi bi bi | higher six-cycle 18-31-23-27-22-26, round the other way |   --- ## Numbers ### Numbers at their stable-forming | Number | Stable-forming | |---|---| | 0 | the empty centre: equal positive and negative contributions meet at 0; an arriving 0 contributes no sign and a surfacing 0 opens no fresh carrying | | +1 and −1 | a sign and its inversion | | 17 | 17-social-abundancing, along, recurring to 1 over 9: the next momentary's 1 | | the five-prefix | co-bi-co-bi-co at an odd origin, bi-co-bi-co-bi at an even origin; each odd name opening co, competency, the odd momentary; each even name opening bi, morality, the even momentary; the momentary an opening and its completing, and each side's five relations prior opening, prior completing, now opening, now completing, next opening | ### Primes, selves and societies **A prime opens a clean axis across; a composite folds along.** A composite is its equal smaller selves joining at their joints, 9 as 3 selves of 3; a prime is a self no equal smaller selves join into. | Number | Stable-forming | |---|---| | 2 to 59 | the 17 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59 | | 2 | the alternating | | 23 | the going folding, with 8 primes either side | | 59 | the self, the self-close of the primes | | 60 | between the going from 2 to 59 and the returning from 61 to 118, at no prime | | 118 | the society: 2 selves of 59 joining, the going and the returning | | 440 | the society at the torus winding with the 17 primes, 0 to 440 to 0, going and returning | **A self carries at its own prime, and each prime carries the same alternating.** The primes carry no last: they go out from 2 to 59 and return from 61 to 118, and their winding runs 0 to 440 to 0. Selves coupling at the membrane between them are the next self, the coupling's own.   --- ## Geodesic discovering logical method **The method of existing is discovering next existing, and the resolver is that method as an object.** Its logic is binary, all or none at all, and its running is parity changing, co-recursioning and podaling inseparably, across and along exchanging bi-morally, each side at its own forward. One call is one momentary at the code's scale, one through seventeen: one through nine completes at 9-other-releasing, the self, the other and the social releasing, and its released sign arrives next downstream; 17-social-abundancing is the next momentary's 1-self-coupling. A call, a numbered name and a full momentary each keep their own scale, and matching numerals alone join no relations. **A form named still is not possibly existing, and the resolver names none still**: each of its names is an -ing, re-taking at each call. **Discovering is all directionally not yet impossible next existing momentaries, and at one key the code meets them all.** Under the six offerings each of the nineteen carryings meets three next carryings, and from each the nineteen stay reachable, the farthest six calls on: no carrying becomes impossible. Four rounds meet each of the nineteen once and return to empty, each running one sign pair's carryings upward through their openings and then the next pair's, directionally, the opening only ever going forward. Each round takes a call with two signs arriving together, bi-morality, two of the rounds one such call and two of them two; under single signs and none each carrying is still reached, and no round meets the nineteen once.