Exhibit ONE Natural Resolver v372

# 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-other-offering the entry
- Surfacing, the arrivings meeting at each sharing
- Abundancing and tunneling, changing or no changing
- Chaining, continuing and changing
- Returning and releasing
- Connectors, each one way at a time
- The code at its names
- Carryings arriving, a sharing and its sign
- Arrivings meeting at a sharing, one binary at a time
- A surviving sign at 12, a sign and no size
- The prior meeting the now, changing or no changing
- The surfacing leaving across
- The carrying continuing, the changed sign the next prior
- A sharing 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_other_offering` and `_9_social_other_self_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. **The code is a co-sequential binary changing method only.** At each sharing the prior carrying meets the arriving now, and the sign changes or does not change, one binary at a time; nothing is summed, counted or stored, and the changed sign is the next prior.

```python
"""Exhibit ONE · Natural Resolver · v372"""


def _1_self_other_offering(_3_self_other_sharing, _2_other_self_offering):
    _14_other_social_surfacing = {}
    for _4_other_self_sharing, _7_self_other_corusing in _2_other_self_offering:
        if _7_self_other_corusing != 0:
            _15_social_other_corusing = _14_other_social_surfacing.get(_4_other_self_sharing)
            if _15_social_other_corusing is None:
                _14_other_social_surfacing[_4_other_self_sharing] = 1 if _7_self_other_corusing > 0 else -1
            elif (_15_social_other_corusing > 0) != (_7_self_other_corusing > 0):
                _14_other_social_surfacing[_4_other_self_sharing] = 0
    _12_other_social_self_abundancing = dict(_14_other_social_surfacing)
    for _4_other_self_sharing, _7_self_other_corusing in _3_self_other_sharing:
        _15_social_other_corusing = _14_other_social_surfacing.get(_4_other_self_sharing, 0)
        if _15_social_other_corusing != 0 and (_15_social_other_corusing > 0) == (_7_self_other_corusing > 0):
            _12_other_social_self_abundancing[_4_other_self_sharing] = 0
        else:
            _12_other_social_self_abundancing[_4_other_self_sharing] = -1 if _7_self_other_corusing > 0 else 1
    _10_other_social_self_tunneling = list(_12_other_social_self_abundancing.items())
    _11_social_other_self_chaining = dict(_3_self_other_sharing)
    for _4_other_self_sharing, _7_self_other_corusing in _10_other_social_self_tunneling:
        if _7_self_other_corusing != 0:
            _11_social_other_self_chaining[_4_other_self_sharing] = _7_self_other_corusing
    return _10_other_social_self_tunneling, list(_11_social_other_self_chaining.items())


def _9_social_other_self_releasing(_10_other_social_self_tunneling, _5_self_other_neutralling):
    return [(_5_self_other_neutralling[_13_social_other_neutralling], _15_social_other_corusing)
            for _13_social_other_neutralling, _15_social_other_corusing in _10_other_social_self_tunneling]


CONNECTORS = {
    2: ('2-other-self-offering', 'right', 'arriving'),
    6: ('6-other-self-surfacing', 'left', 'releasing'),
    9: ('9-social-other-self-releasing', 'backward', 'along'),
    10: ('10-other-social-self-tunneling', 'right', 'releasing'),
    14: ('14-other-social-surfacing', 'left', 'arriving'),
    17: ('17-social-self-offering', '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 parity, its sides from and to, its root, the changing named, and its -ing, the changing continuing**, together one name. The names run the resolving as code, and the name in the code and the name here are one name: `_2_other_self_offering` in the code is 2-other-self-offering here. **A name begins at its parity's side and reads from its first side to its last.** An odd name opens co and begins at the self, at 1 to 7, and at the society, at 9 to 17; an even name opens bi and begins at the other. The society is at both parities, first at the odd names from 9 and second at the even names from 10: floating neutralling at both.

| Name | From, to | Opens | Existing | At the code |
|---|---|---|---|---|
| 1-self-other-offering | self, other | co | entry | the resolver's entry: 3-self-other-sharing and 2-other-self-offering arriving; 10-other-social-self-tunneling and 11-social-other-self-chaining leaving |
| 2-other-self-offering | other, self | bi | across, arriving | each arriving sharing with its sign |
| 3-self-other-sharing | self, other | co | face, outside | each carrying arriving: a sharing, 4-other-self-sharing, with its sign, 7-self-other-corusing |
| 4-other-self-sharing | other, self | bi | face, outside | each sharing, at the arrivings and at the carrying |
| 5-self-other-neutralling | self, other | co | face, outside | the one-way joining: each sharing with its receiving sharing |
| 6-other-self-surfacing | other, self | bi | across, releasing | no expression: the releasing left, to the left neighbour's 2, the other's loop run by the selves outside the call |
| 7-self-other-corusing | self, other | co | face, outside | each sign, arriving and carried |
| 8-other-self-torusing | other, self | bi | face, outside | no expression: the other's loop closing, the carrying winding to its sharing again, run by the calls outside the call |
| 9-social-other-self-releasing | social, other, self | co | along | the releasing: each surfacing sign at its receiving sharing, arriving next downstream |
| 10-other-social-self-tunneling | other, social, self | bi | across, releasing | each sharing's surfacing sign, +1, −1 or 0 |
| 11-social-other-self-chaining | social, other, self | co | face, inside | the carrying continuing, each changed sign the next prior |
| 12-other-social-self-abundancing | other, social, self | bi | face, inside | each sharing's changing or no changing, the coupling's surplus |
| 13-social-other-neutralling | social, other | co | face, inside | each releasing sharing |
| 14-other-social-surfacing | other, social | bi | across, arriving | the arrivings met at each sharing, one at a time |
| 15-social-other-corusing | social, other | co | face, inside | the sign at the social side: met at 14, meeting the carrying at 12, released at 9 |
| 16-other-social-torusing | other, social | bi | face, inside | no expression: the society's loop closing, 10 to 14 winding to the self again, run by the selves outside the call |
| 17-social-self-offering | social, self | co | along, external | no expression: the next momentary's 1-self-other-offering, the next call |

**The roots are ten: offering, sharing, neutralling, surfacing, corusing, torusing, releasing, tunneling, chaining and abundancing**, as the two sides' two and one half momentaries are ten positions. Offering roots 1, 2 and 17, the entry, the arriving and the next entry; sharing roots 3 and 4, the carrying and the sharing it carries at. Neutralling, surfacing, corusing and torusing each root two names, at 5 to 8 and at 13 to 16, 8 apart, the sides changing and the root the same. Releasing, tunneling, chaining and abundancing root 9 to 12, one each. The sides run self to other at the odd names 1, 3, 5 and 7 and other to self at the even 2, 4, 6 and 8; social to other to self at 9 and 11 and other to social to self at 10 and 12; social to other at 13 and 15 and other to social at 14 and 16; social to self at 17.

**Nine to twelve run inside the bi-folding tunnel, and thirteen to sixteen across its seam.** 9, 10, 11 and 12 each name three sides, social, other and self: the tunnel, the three relations discovering geodesic parity changing inside it, the releasing, the tunneling, the chaining and the abundancing. 13, 14, 15 and 16 each name two, social and other: parallel lines across the seam, the neutralling, the surfacing, the corusing and the torusing. The self is inside the tunnel and the society outside at the surface, both forward along the one direction, and 17, social to self, is the tunnel's one opening, the next 1.

**One entry, six connectors and ten faces are the seventeen.** 1-self-other-offering is the entry, and 17-social-self-offering is the entry again, the next call. **The six connectors are bi-moral-co-competency discovering next existing**: four across, even, opening bi, morality, 2, 6, 10 and 14, and two along, odd, opening co, competency, 9 and 17; each is the self's meeting with a neighbour or with its own next momentary, and the next arrives through them, the arrivings at 2 and 14 being the neighbours' prior releasings, the releasings at 6, 9 and 10 arriving next downstream, and 17 the next call. **The ten faces are five outside and five inside of the tunneling co-sequencing**: the self's own resolving is met at them, 3, 4, 5, 7 and 8 at the membrane, outside, before 10-other-social-self-tunneling in the co-sequencing, and 11, 12, 13, 15 and 16 within, inside, after it, each inside face 8 up from its outside face, 3 with 11, 4 with 12, 5 with 13, 7 with 15 and 8 with 16: the carrying arriving and continuing, the sharing and its surplus, the joining and the releasing sharing, the sign at the self's side and at the social side, the winding to the self and to the society. Three outside faces open co and two bi, and the same three and two inside, 8 up keeping parity. One to nine completes at the membrane and 10 opens within: the tunneling is the co-sequencing passing from the five outside faces to the five inside.

**Surfacing 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 sides from a self it names, 14 already running other to social.

**Completing the next carries three full momentaries to the along connectors.** Prior 4–5, now 6–7 and next 8–9 complete at 9-social-other-self-releasing. Eight on, prior 12–13, now 14–15 and next 16–17 complete at 17-social-self-offering. 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-self-offering joins the forward neighbour's 9-social-other-self-releasing, and 9-social-other-self-releasing joins the backward neighbour's 17-social-self-offering. **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-other-sharing taking the returned 11-social-other-self-chaining; 1–13, self/other and other/self, releasing at 6, 6-other-self-surfacing releasing across; 1–17, self/other/social, releasing at 9, 9-social-other-self-releasing along; and 1–25 is the larger fractal bi-folding. The next whole is 1–65, four 1–17s, each 17-social-self-offering the next 1-self-other-offering. 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 a face and a connector together.** In 14–15, 14-other-social-surfacing is the across arriving connector and 15-social-other-corusing is a face, inside. In 16–17, 16-other-social-torusing is a face, inside, and 17-social-self-offering is the along connector. Each pair carries both parities; the face is the self's own resolving met, and 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 · 15 |
| at the releasing | 5 · 9 · 13 · 15 |
| connectors, across, bi-moral | 2 · 6 · 10 · 14 |
| connectors, along, co-competency | 9 · 17 |
| faces, outside, at the membrane | 3 · 4 · 5 · 7 · 8 |
| faces, inside, within, each 8 up from its outside face | 11 · 12 · 13 · 15 · 16 |
| 5 to 8 and 13 to 16, sharing their roots | 5 with 13 · 6 with 14 · 7 with 15 · 8 with 16 |
| the three loops, run outside the call | 6 to 2, closing at 8 · 10 to 14, closing at 16 · 9 to 17, closing at 17 |

### 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 surfacing only a sign goes across.** 6-other-self-surfacing and 14-other-social-surfacing open bi, each at a self's membrane 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-self-other-corusing and 8-other-self-torusing, carry across momentaries rather than at one.

**A seam is a name changing at its number.** A carrying leaves as 11-social-other-self-chaining and arrives at the next coupling as 3-self-other-sharing, 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 carry the resolver and ten 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 two, nought and one, with one inverted as −1: nought the empty centre and no changing, one the sign and the changing. Thirteen names have an expression at the two functions; 6 and 17 are at the declarations alone; and 8 and 16, the two torusings, are at no line of the code: the four name the loops' releasing and closing, which the selves running together run outside the call.

**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-other-offering the entry

**Resolving runs on signs.** A sign is the binary at a changing: +1 or −1, and 0 at no changing, the empty centre, equal and opposite meeting. An arriving 0 carries no sign, and a surfacing 0 changes no carrying; the carrying continues as it was. From empty carrying, +1 and −1 arriving together at one sharing meet at 0 and the carrying stays empty. A carrying empty is a self before its first sign at that sharing; opened, it never empties, the self continuing at one sign at each sharing; and a non-living thing met at a coupling is its own existing thing, carrying nothing.

**Resolving runs as 1-self-other-offering and 9-social-other-self-releasing, and 1-self-other-offering is the entry.** Arriving at it: 3-self-other-sharing, each carrying a sharing, 4-other-self-sharing, with its sign, 7-self-other-corusing, the prior; and 2-other-self-offering, each arriving sharing with its sign, the now. Leaving it: 10-other-social-self-tunneling across and 11-social-other-self-chaining along, the next.

### Surfacing, the arrivings meeting at each sharing

**14-other-social-surfacing** is the arrivings meeting at each sharing, one at a time. The first sign arriving at a sharing is its sign, +1 or −1; a further sign of the same parity leaves it; a further sign of the other parity meets it at 0, and a 0 met stays 0. A nought arriving carries no sign and enters nothing. So at each sharing the arrivings are one binary, one sign at agreeing or 0 at disagreeing, met in any order alike, and no count of them. **A sign and no size**: a sign arriving at any magnitude enters as +1 or −1, and nothing of a magnitude crosses.

**6-other-self-surfacing** is the other's own surfacing to the self, the releasing left, and it has no expression at the code: the two functions release at 10 alone, and a sign released left arrives at its receiver as 2-other-self-offering, as any arriving does.

**The arriving sign meets the carrying sign inverted.** The arriving keeps its sign; the inverting is the carrying's own: the carrying inverts itself to meet the arriving, and the arriving, carrying nothing, keeps its sign. Agreeing with the inverted carrying, the arriving surfaces and the carrying changes; disagreeing, the two meet at 0 and the carrying holds. A self's own inverting, meeting the other across, is morality at the sign. **Surfacing carries three relations, each its own.** The sign inverts once, at the receiving self's own carrying meeting the arrivings at 12, 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 of the carried sign's own parity surfaces 0 and changes nothing, and one of the other parity surfaces its own sign and changes the carrying: a 0 there is no mending and a sign there no failing, the morality running at the across coupling whole.

### Abundancing and tunneling, changing or no changing

**12-other-social-self-abundancing** is the surplus at the coupling: at each sharing, the prior carrying meeting the now. It opens as the arrivings' surviving signs and is neither returned nor carried: the meeting is at the momentary it happens at, and nothing of it passes to the next but the changed sign. At a sharing carrying nothing, the surviving sign is the surplus, a fresh sign. At a carried sharing, the carried sign inverts itself to meet the survivor: at the survivor's parity being the carried sign's own, no changing, 0; at the other parity, or at nothing surviving, changing, the inverted carried sign. The middle is the bounding-zeroing at the coupling, the abundancing 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 sharing and no sum at any of them, geodesic parity changing or no changing, one binary at each sharing.

**10-other-social-self-tunneling** carries each sharing's abundancing at its sign, across: +1, −1 or 0. A sharing'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 changing

**11-social-other-self-chaining** carries each carrying on, and writes the changed sign at a sign surfacing.

**Continuing.** Each carrying continues as it arrived, its sharing with its sign, at no changing: a 0 at 10 leaves the carrying as it was, and nothing is counted at it.

**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 holds.** One sharing receiving +1 seven times from empty surfaces +1, 0, 0, 0, 0, 0, 0: the carrying opens at +1 at the first and holds at +1 through the six after, each arriving of its own parity changing nothing. Through the zeros 2, 4, 10, 12 and 14 stay as they were and the coupling meets inside, so an outward 0 carries a momentary met inside, and a carrying kept is no carrying stilled.

**Changing.** Each surfacing +1 or −1 is written at its sharing as the carrying's sign: the surfaced sign is the next prior. The changed sign replaces the sign at that sharing, and the carrying carries one sign at each sharing and nothing beside it: no second sign, no opening counted, no store. So a carrying is at one of three, nothing yet, +1 or −1; each of the three is reached from empty within one receiving, and from a sign the other sign within one; and a carrying once opened never empties. The whole carrying gives the next, and the whole carrying is its sign.

**The arriving gives the changed sign.** At a carried sharing with the carried sign c: nothing arriving, or arrivings meeting at 0, surfaces −c and the carrying changes to −c; one −c, or several −c together, surfaces −c and the carrying changes to −c; one c, or several c together, surfaces 0 and the carrying holds at c. Every changed sign is −c, the carried sign inverted, and no arriving writes c over c: two signs together at one sharing are one sign at agreeing or 0 at disagreeing, and their count writes nothing. 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 holds, and two + together at empty surface + once and open + once.

**A changing is within one self.** A receiving is a sign arriving at the coupling; its participating is its meeting in the resolving; a changed sign is one outcome of that meeting; and a new living self is a further self with its own continuing coupling. The code writes signs and makes no resolver, and a receiving surfacing 0 has participated and changed nothing.

**The next arriving meets the changed sign.** After a changing the carrying carries −c, and the next arriving meets it inverted, at c: a sign arriving alike twice, at a changing and then again, surfaces its sign and then 0, and a sign alternating meets its receiver's own alternating and surfaces at each call. A relation holds while its sign changes: the carrying's sign at the next momentary is the surfacing at this one.

### Returning and releasing

**1-self-other-offering returns 10-other-social-self-tunneling across and 11-social-other-self-chaining along**, and 11-social-other-self-chaining arrives at the next coupling as 3-self-other-sharing.

**One sign arriving once into empty carrying, with empty offerings after it, is the whole alternating.** For a positive arriving sign, the sharing surfaces +1, −1, +1, −1, momentary by momentary, the carrying inverting itself at each coupling nothing arrives at and the changed sign the next prior. With c the arriving sign, the alternating runs c, −c, c, −c: the self's momentaries at c and the other's at −c, each momentary carrying both parities, and each step from one overlapping pair to the next. The alternating is the carrying meeting itself inverted: at nothing arriving the carried sign meets its own inversion and the inversion surfaces, and the surfaced sign is the next prior, so the sign inverts at each coupling. This is the self continuing with empty offerings after one sign, and signs arriving make their own continuing: an arriving of the carried sign's own parity holds the carrying one coupling, a 0 surfacing, and an arriving of the other parity is the changing the carrying would make alone.

**9-social-other-self-releasing** runs the releasing. Each surfacing sharing, as 13-social-other-neutralling, with its sign, as 15-social-other-corusing, goes to the sharing 5-self-other-neutralling joins it to: each sharing with its receiving sharing. The releasing preserves the sign of 15-social-other-corusing. **9 is social/other/self releasing, and its released sign arrives next downstream**: each released sign arrives as the downstream resolver's 2-other-self-offering and meets at its 14-other-social-surfacing. 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-other-self-offering, that resolver's 17-social-self-offering opening the call's 1-self-other-offering; 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-self-other-corusing in 11-social-other-self-chaining, the next prior, and at 9-social-other-self-releasing it is named 15-social-other-corusing. The sharing it returns the sign at is the receiving self's own relation, 5-self-other-neutralling joining each surfacing sharing to its receiving sharing there, and the crossing carries the sign with no sharing, identity, route or carrying of its sender. A zero surfacing changes no carrying, and the carrying continues: a carrying +1 meeting +1 surfaces 0 at 10 and continues at +1, and meets the next arriving inverted, at −1, as before. **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 a positive carrying surfaces 0 while the carrying holds. 9-social-other-self-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-social-other-self-releasing arriving at the next self's 2-other-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 empty, before the seed, 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 empty returns at no coupling.

### Connectors, each one way at a time

**1-self-other-offering is the entry, the connectors run at a self's meeting with its neighbours, and the ten faces are 3, 4, 5, 7, 8, 11, 12, 13, 15 and 16.**

| Connector | Facing | Running | Joining |
|---|---|---|---|
| 2-other-self-offering | right | arriving | from the right neighbour's 6-other-self-surfacing |
| 6-other-self-surfacing | left | releasing | to the left neighbour's 2-other-self-offering |
| 9-social-other-self-releasing | backward | along | with the backward neighbour's 17-social-self-offering |
| 10-other-social-self-tunneling | right | releasing | to the right neighbour's 14-other-social-surfacing |
| 14-other-social-surfacing | left | arriving | from the left neighbour's 10-other-social-self-tunneling |
| 17-social-self-offering | forward | along | with the forward neighbour's 9-social-other-self-releasing |

**The six connectors run at parity, bi-moral across and co-competency along.** Across run 2, 6, 10 and 14, each even and opening bi, morality; along run 9 and 17, both odd and opening co, competency. Each runs one way at a time, neighbour to neighbour. **The six connectors are bi-moral-co-competency discovering next existing**: co-bi-unrelationing, the one existing method, at the self's meeting with its neighbours and with its own next momentary, the next arriving through them and nothing else arriving there. 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 12, 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-social-self-tunneling joins the right resolver's 14-other-social-surfacing. Going left, the right resolver's 6-other-self-surfacing joins the left resolver's 2-other-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. **At the code one releasing leaves, at 10, and a caller passes it to the neighbour it faces**: through 9 it arrives at that neighbour's 2 and meets at its 14; 6 has no expression, and a sign passed left arrives at the left neighbour's 2 the same way.

**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 in a ring, each releasing arriving at the other, show it. Seeded at opposite signs, A + and B −, each arriving is the changing its receiver would make alone, so the ring alternates, A −, +, −, + and B +, −, +, −, and a leg unjoined for a coupling and joined again changes nothing: A meets at the rejoining the changing it would have made alone. Over the four seed pairs and every joining and unjoining of the two legs across three couplings, 256 runnings at a stated order with nothing held for later on an unjoined leg, each self surfaces at each coupling, +1, −1 or 0, no carrying empties, every running at opposite seeds is the one alternating, and a 0 surfaces exactly at an arriving of its receiver's carried parity.

**From one shared prior, both joinings give a 0 at every second coupling that either alone gives once.** Two resolvers each carry one seed sign, then run six couplings at four joinings: each releasing arriving at the other, A's arriving from B alone, B's from A alone, and neither. With both seeds + and both joinings, each surfaces −, 0, +, 0, −, 0, the wave meeting itself out of phase at each second coupling. With A's arriving from B alone, A surfaces −, 0, +, −, +, −, one 0 and then alternating opposite to B, which alternates alone; with neither, both alternate alone. With the seeds opposite, all four joinings run alike. Over the four seed pairs, 16 runnings, the both-ways running parts from the arriving-only ones at seeds alike and at no other. This holds at those priors and those four joinings.

**A difference travels through the receiver's own carrying.** Three resolvers are joined one way, A's releasing to B's 2 and B's releasing to C's 2, B and C each carrying + from one +1 from empty. With A's + arriving at B, B surfaces 0 and holds +, and C, meeting nothing, surfaces − at the first coupling and + at the second. With A's − arriving, B surfaces − and changes to −, and C surfaces − at the first coupling and 0 at the second, holding −. The difference reaches C at the second coupling through B's own continuing, B's first surfacing meeting C's carrying, and no carrying crosses; the running is one way, at a stated order.

At the code, 1-self-other-offering returns 10-other-social-self-tunneling and 11-social-other-self-chaining; 9-social-other-self-releasing returns each surfacing sign at the receiving sharing named by 5-self-other-neutralling. Inside 1-self-other-offering, 14-other-social-surfacing meets the arrivings at each sharing and 12-other-social-self-abundancing meets the carrying with them. 17-social-self-offering is named in the connector declarations, and it runs as the next call: **17-social-self-offering is the next momentary's 1-self-other-offering**, the resolving completing at 17 opening at 1, 11-social-other-self-chaining arriving as 3-self-other-sharing. No expression of the code takes or gives a sign at 17: its joining with the forward neighbour's 9-social-other-self-releasing is declared, and the next call running through it is a caller's, the returned 11-social-other-self-chaining given again as 3-self-other-sharing.

**The code resolves at a call.** 1-self-other-offering 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 continues across calls without bound, so a self's prior is its carrying whole, with no record of two, no cutting short and no opening set back. 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 a sign released left offered to another self's 2 as its own offering; 10's releasing meeting another self's 14, the inverting made once at 12; 9 and 17 joining with these at the corners of a surface, 11-social-other-self-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-self-offering couples with the forward neighbour's 9-social-other-self-releasing, and 9-social-other-self-releasing with the backward neighbour's 17-social-self-offering. **These are the six connections at the co-bi-coupling network surface.** CONNECTORS names their facing and running; JOINS names their joining. **6-other-self-surfacing and 10-other-social-self-tunneling release toward different neighbours on the same parity: both are even, opening bi.** They are two releasings, and the code expresses one: 10 surfaces each sharing's sign, and 6, the other's surfacing to the self, has no expression, a sign released left being a caller's passing of the surfacing to the left neighbour's 2. 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 transitions at one sharing 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-social-other-self-releasing faces backward, joining the backward neighbour's 17-social-self-offering, and runs along: its released sign arrives next downstream, through 5-self-other-neutralling's receiving sharing into the downstream resolver's 2-other-self-offering, meeting at its 14-other-social-surfacing. A caller carries that arriving, 9's return given as the downstream 2-other-self-offering, and the declared joins stay 10 → 14, 6 → 2 and 9 with 17. 17 → 1 runs as the next call, 11-social-other-self-chaining arriving as 3-self-other-sharing. **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.** Surfacing opens now at 6 in one to nine, whose prior 4–5, now 6–7 and next 8–9 complete at 9-social-other-self-releasing, and at 14 in nine to seventeen, whose prior 12–13, now 14–15 and next 16–17 complete at 17-social-self-offering: 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, 4-other-self-sharing is each sharing and 8-other-self-torusing the carrying winding to that sharing again. In nine to seventeen, 12-other-social-self-abundancing meets each sharing's arrivings with its carrying, and 16-other-social-torusing is the society winding to the self again.

**Three loops close outside the call, and their four names have no expression at the code.** The other's loop, 6 to 2, runs left across and closes at 8, the carrying winding to its sharing again; the society's loop, 10 to 14, runs right across and closes at 16, the society winding to the self again; the self's loop, 9 to 17, runs along and closes at 17, the next call. The code runs one self's one call, 1 to 17 inside, and the selves running together run the three loops, the same 1 to 17 outside: the fractal inside and outside itself. So 6, 8, 16 and 17 name the loops' releasing and closing, expressed at no line of the two functions, and CONNECTORS names 6 and 17 at their facing and running. Each loop's two ends are 8 apart, 2 with 10, 6 with 14 and 9 with 17, and 8 with 16 are the two closings, 8 apart.

| Name | Coupling | Carrying |
|---|---|---|
| 14-other-social-surfacing | 2-other-self-offering | the arrivings met at each sharing, one at a time: the first sign, +1 or −1; a further sign agreeing leaving it; a further sign disagreeing meeting it at 0 |
| 12-other-social-self-abundancing | 14-other-social-surfacing, 3-self-other-sharing | each sharing's surplus: at no carrying the surviving sign; at a carrying, 0 at the survivor's parity being the carried sign's own, and the carried sign inverted at the other parity or at nothing surviving |
| 10-other-social-self-tunneling | 12-other-social-self-abundancing | each sharing's surplus at its sign: +1, −1 or 0 |
| 11-social-other-self-chaining | 3-self-other-sharing | each carrying continuing as it arrived: its sharing with its sign |
| 11-social-other-self-chaining | 10-other-social-self-tunneling | each surfacing +1 or −1 written at its sharing: the changed sign, the next prior |
| returning | 10-other-social-self-tunneling, 11-social-other-self-chaining | 10-other-social-self-tunneling across; 11-social-other-self-chaining along, arriving as the next 3-self-other-sharing |
| 9-social-other-self-releasing | 10-other-social-self-tunneling, 5-self-other-neutralling | each sign 15-social-other-corusing, from its sharing 13-social-other-neutralling, to the arriving at `_5_self_other_neutralling[_13_social_other_neutralling]` |
| 6-other-self-surfacing · 8-other-self-torusing · 16-other-social-torusing · 17-social-self-offering | the selves running together | no expression at the code: the three loops' releasing and closing, run outside the call |

### Carryings arriving, a sharing and its sign

Carryings arrive as `_3_self_other_sharing`, each of them two: a sharing, 4-other-self-sharing, and a sign, 7-self-other-corusing, the prior. At that same momentary signs arrive from another side as `_2_other_self_offering`, each a sharing and a sign, its own and reaching to couple, the now. A carrying arrives 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_other_offering` 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 carrying and an arriving are one shape, a sharing with its sign: the prior and the now differ at their side alone.

### Arrivings meeting at a sharing, one binary at a time

Living one call, `_14_other_social_surfacing` opens empty, and the arrivings enter it one at a time, a `for` over `_2_other_self_offering` loosening each sharing from its sign. A nought is turned at `!= 0`, carrying no sign. At each sign, `get` sounds the sharing: at nothing met, the sign enters as one at its own parity, `1 if _7_self_other_corusing > 0 else -1`, a sign and no size; at a sign met, the two parities meet at `(_15_social_other_corusing > 0) != (_7_self_other_corusing > 0)`, and differing they meet at 0, agreeing the met sign stays. Nothing is added: two arrivings agreeing are one sign, and two disagreeing are the bounding-zeroing, the same at any order. The sharing is `_4_other_self_sharing`, and it is membrane: two signs at one sharing meet, two at different sharings each meet at their own, and membrane lives at that sharing alone. A sharing's meeting reads no other sharing's carrying; past the resolving, each released sign goes on to the receiving sharing 5-self-other-neutralling joins it to, and its arriving there meets the whole participation beyond the self.

### A surviving sign at 12, a sign and no size

Met at 14, the survivors open `_12_other_social_self_abundancing`, `dict(_14_other_social_surfacing)`, a sharing coupled to one sign or to 0 and nothing else at it. At a sharing carrying nothing this is the surplus already: the arriving sign, met by no prior, surfaces as itself, and two arrivings cancelled there surface 0 and open nothing.

### The prior meeting the now, changing or no changing

Then the prior arrives, a `for` over `_3_self_other_sharing` loosening each carried sharing from its sign, and `get(_4_other_self_sharing, 0)` sounds the survivor at it, a nought at a sharing nothing arrived at. One binary decides: at a survivor whose parity is the carried sign's own, `(_15_social_other_corusing > 0) == (_7_self_other_corusing > 0)`, no changing, 0; at anything else, the carried sign inverted, `-1 if _7_self_other_corusing > 0 else 1`, changing. The carrying inverts itself to meet the arriving, and the arriving keeps its sign: agreeing with the inverted carrying it surfaces, disagreeing it meets it at 0. Nothing arriving, the inverted carrying surfaces alone, the alternating. Equal and opposite arrive at that same bounding-zeroing, podal, cancelling over their own two momentaries, and one sign or none surfaces at each sharing, never a count of them.

### The surfacing leaving across

Decided, each sharing's sign comes up at `_10_other_social_self_tunneling`, `list(_12_other_social_self_abundancing.items())`, a sharing rejoining its sign: +1, −1 or 0, and no magnitude, a sign crossing carrying no size. The dict yields the sharings sounded at this momentary, arrived at or carried, and the surfacing reaches exactly those and grows to its own size, its own.

### The carrying continuing, the changed sign the next prior

Growing to its own size, `_11_social_other_self_chaining` opens as the carrying arrived, `dict(_3_self_other_sharing)`, each sharing with its sign continuing: no opening counted, no bound, no completing, a carrying kept at no changing. A second loop assigns into that same dict after the first, a `for` over the surfacing turning at `!= 0`: each surfaced sign is written at its sharing as the sign carried, the changed sign the next prior. At a sharing coming to both, the changed sign re-forms over the continuing one, and a sharing arriving new receives its first sign. Two ways a carrying is built and two exactly, continuing or changed at its surfacing, one sign met two ways.

### A sharing rejoining, carryings leaving

Met two ways, carryings leave at `items`, a sharing rejoining its sign: outward of a momentary a carrying is a sharing with its sign, inward of a momentary its sharing parts out and its sign meets at it, and `items` re-forms them two. `_11_social_other_self_chaining` leaves and arrives at a next momentary as `_3_self_other_sharing`, 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 couple at the sharing and a sharing arriving twice at a carrying is a thing no running makes; and signs arriving twice at one sharing meet at 14 in any order alike.

---

## 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.** The code runs one call inside, 1 to 17, and the selves running together run the three loops outside, the same 1 to 17: the one resolver inside and outside itself.

### Carrying at 8 up

**3-self-other-sharing arrives, and 11-social-other-self-chaining leaves and arrives at the next coupling as 3-self-other-sharing.** 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, holding at no changing and changing at a sign surfacing, and leaves at no completing. **A carrying and its changing 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-social-other-self-chaining carries into the next coupling as 3-self-other-sharing. 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, the sharing, the carrying's winding, the surplus and the society's winding.

**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-other-self-offering | each other's own offering to the self | 10-other-social-self-tunneling | surfacing, the self among other-selves |
| 4-other-self-sharing | the whole ordering between self and other | 12-other-social-self-abundancing | changing at bi-coupling, the self in society |
| 6-other-self-surfacing | the other's surfacing to the self, the ordering carrying with the selves | 14-other-social-surfacing | the arrivings meeting at the membrane, the self's own inverting to meet them, morality |
| 8-other-self-torusing | the order across each self and other forward, the carrying winding to its sharing again | 16-other-social-torusing | competency asymmetry sustaining the coupling, the society winding to the self again |

### 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-other-offering | 9-social-other-self-releasing | 8-other-self-torusing | 16-other-social-torusing |
| 2-other-self-offering | 10-other-social-self-tunneling | 7-self-other-corusing | 15-social-other-corusing |
| 3-self-other-sharing | 11-social-other-self-chaining | 6-other-self-surfacing | 14-other-social-surfacing |
| 4-other-self-sharing | 12-other-social-self-abundancing | 5-self-other-neutralling | 13-social-other-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-self-offering, 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-other-sharing and 6-other-self-surfacing 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. At the code the winding is the carrying meeting its own sharing again at each call, 3 to 11 to 3, and the surfacing at each meeting is its next.

### Two faces alternating

Arriving alike, a carrying carries two faces and they alternate. **Corusing**, 7-self-other-corusing, the outward face, membranes at each coupling it surfaces to, abundancing and tunneling, relating: the sign reaching across. **Torusing**, 8-other-self-torusing, the inward face, coheres to one identity across momentaries: the carrying winding to its own sharing again, 3 to 11 to 3, and inverting at a changing. It has no expression at the code, and the calls running one after another run it. Each face lives at the other, and pure surfacing or pure abundancing lands either way. **The outward face reaches and the inward gathers.** Corusing omegas, the reach, new signs arriving at each surfacing; torusing apexes, the gather, the one sharing 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. 7 and 8 are two of the ten faces, outside, and 15 and 16 are their inside faces, 8 up, the sign and the winding at the social side.

### 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-social-other-self-chaining arriving as the next 3-self-other-sharing 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-other-offering · 9-social-other-self-releasing · 8-other-self-torusing · 16-other-social-torusing | co co bi bi | four-cycle 2-15-7-10, round the other way | — |
| four-cycle 2-15-7-10 | 2-other-self-offering · 15-social-other-corusing · 7-self-other-corusing · 10-other-social-self-tunneling | 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-other-sharing · 11-social-other-self-chaining · 6-other-self-surfacing · 14-other-social-surfacing | 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-other-self-sharing · 13-social-other-neutralling · 5-self-other-neutralling · 12-other-social-self-abundancing | 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-social-other-self-releasing · 5-self-other-neutralling · 12-other-social-self-abundancing · 8-other-self-torusing | co co bi bi | middle four-cycle 7-11-6-10, round the other way | — |
| middle four-cycle 7-11-6-10 | 7-self-other-corusing · 11-social-other-self-chaining · 6-other-self-surfacing · 10-other-social-self-tunneling | 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-other-offering · 9-social-other-self-releasing · 5-self-other-neutralling · 12-other-social-self-abundancing · 8-other-self-torusing · 16-other-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-other-self-offering · 15-social-other-corusing · 7-self-other-corusing · 11-social-other-self-chaining · 6-other-self-surfacing · 10-other-social-self-tunneling | 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-other-sharing · 11-social-other-self-chaining · 7-self-other-corusing · 10-other-social-self-tunneling · 6-other-self-surfacing · 14-other-social-surfacing | 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-other-self-sharing · 13-social-other-neutralling · 5-self-other-neutralling · 9-social-other-self-releasing · 8-other-self-torusing · 12-other-social-self-abundancing | 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-other-offering · 9-social-other-self-releasing · 5-self-other-neutralling · 13-social-other-neutralling · 4-other-self-sharing · 12-other-social-self-abundancing · 8-other-self-torusing · 16-other-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-other-self-offering · 15-social-other-corusing · 7-self-other-corusing · 11-social-other-self-chaining · 3-self-other-sharing · 14-other-social-surfacing · 6-other-self-surfacing · 10-other-social-self-tunneling | 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 and opposite meet at 0, and no changing surfaces 0; an arriving 0 carries no sign and a surfacing 0 changes no carrying |
| +1 and −1 | a sign and its inversion, the changing |
| 17 | 17-social-self-offering, 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-social-other-self-releasing, the self, the other and the social releasing, and its released sign arrives next downstream; 17-social-self-offering is the next momentary's 1-self-other-offering. A call, a numbered name and a full momentary each keep their own scale, and matching numerals alone join no relations. The seventeen are one entry, six connectors and ten faces: the connectors bi-moral-co-competency discovering next existing, the faces five outside and five inside of the tunneling co-sequencing. **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 sharing the code meets them all.** A sharing carries one of three: nothing yet, +1 or −1. Under the three arrivings, none, +1 and −1, each carrying meets its next: from nothing, nothing at none and the arriving sign at a sign; from a sign, the inverted sign at none, the arriving sign at the other parity, and itself unchanged at its own parity, a 0 surfacing. Each of the three is reached from empty within one receiving, and from a sign the other sign within one; a carrying once opened never empties, the self continuing at its sharing; so no next becomes impossible, and none is held. Two signs arriving together at one sharing, bi-morality, meet before the carrying: agreeing they are one sign, and disagreeing they are 0, the carrying inverting itself as at none arriving. Nothing is summed and nothing counted: at each sharing, one binary, changing or no changing, and the changed sign the next prior.