Exhibit TWO Natural Networking v391

 

# Natural Networking

**Stable-Forming Social Moral Competency at a Geodesic Surface**

 

 

**PART ONE · SURFACING**

1.1  Bi-moralizing co-agency, the one form whole

1.2  Along and across, chaining and surfacing, two floating co-neutrals co-competencing

Existing, observing and the emanating form · Prior form and self-other-releasing · Fixing equilibrium at the completing · Prior emanating and now coupling · Overlapping momentary, two at each side · Coupling across and going on · Smaller fold within one through nine · Breaking and reconnecting across · Binary stable-forming · Self and network · One, nine and seventeen · Sensor-sensationing at the surface

1.3  Linear-parallelizing and parallel-linearizing, one and then the other, widening and lengthening

Growing the four across openings · Fifteen prime sequence lengths, wide and long, one and then the other · Smaller fold whole through the larger · Coupling across eight on, the four-form going on through six

1.4  Only parities go across, the middle in no sequence

1.5  Odd and even openings, each full momentary with both

1.6  Middle at the coupling, same-existing through zero surfacing

Not same-existing while the observing remains

1.7  Seventeen names, six connections, society going on

1.8  Self, other and society, the fractal inward and outward of itself

Local surface with no same-existing within society

1.9  A coupling opens a term arising in each self with its other

1.10  Abundancing in neither self alone, going on at each receiving

 

**PART TWO · LIVING**

2.1  Omegaing forward, discovering next existing

2.2  Apexing, prior participating in now

2.3  Living going on within the universe's changing momentaries

2.4  Fold and scatter, breaks in living going on

2.5  Co-discovering, emanating into further participation

2.6  Restoration, the same-existing at a further now

 

**PART THREE · RETELLING**

3.1  Retelling, each receiving self going on at its own coupling

3.2  Renewal and coupling across, the parity at its receiving

3.3  Same-existing remains with each self, participation goes on across

3.4  Co-chaining, each receiving self resolving the parities it is observing

3.5  A local break and the society's going on

3.6  Other a self reaches inward at each co- act, the discovering economy

 

**PART FOUR · ABUNDANCING**

4.1  Abundancing in discovering together, in neither self alone

4.2  Society as one at its coupling

4.3  Each joining couples with the society’s going on

4.4  Similar aiming, each self with its own same-existing

4.5  Each self going on through its actual observing

4.6  Podaling the surface selves share, longer and wider together

4.7  Unrelationing at the between, conserving within momentary sequencing

4.8  Living same-existing and non-living discovering at society

 

**PART FIVE · SECURITIES**

5.1  Eight securities, four self and four society, all or none

5.2  Six self-boundings at the surface, each inversion stopping its own way

5.3  Same-existing a self reaches through further coupling

5.4  Geodesic routing, going on through changing participation

5.5  Routing at the coupling, same-existing at the participating selves

5.6  Local same-existing and the sharing across

 

**PART SIX · VISIBILITY**

6.1  Checkability living at the telling, testing going on while resolving

6.2  Spiral parity at the instrument, stating wiring and dynamics, the instrument first, before anything

6.3  Three registers, code-form and stable-form and numbers, each holding its own

6.4  Is-or-is-not the one observing, spans and orderings in place of positions and magnitudes

6.5  One prior for both, each going on bringing it onward

6.6  An executing deceives as an accounting, four ledgers, changing and changing back the honest instrument

6.7  Each finding at its complete comparison

6.8  A designing and its observing straight across one wrap, reaching it by going on

6.9  No position apart to observe from, and the instrument a working states with each finding

6.10  Parity at the chain's centre, and two instruments of unlike length two objects

6.11  Each self joining opens the reach, and the prior centre becomes a ring

6.12  Discovering through the existing connections

 

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# PART ONE · SURFACING

## 1.1 Bi-moralizing co-agency, the one form whole

**The universe is the set of all now-existing things, and changing and changing back is a stable-forming method. Natural networking is selves sharing their parities, across and both ways, each its own prior same-existing, with competency arising with their coupling.** Two-way, one at a time, each shares its own parity. Their coupling has bounding-zeroing and abundancing, same-existing in each self: +1 arises in neither self alone. Bi-moralizing co-agency is this whole relation, morality across and competency along.

**Sharing, across and both ways, is associating; co-linearizing is resonating; bi-coupling is moral co-operating and co-competencing.** Associating goes on with each self sharing. Co-linearizing is two sequencing together, each going on with its own, what they share arising in each self with its other. Moral co-operating is each self's own parity going on with an other's, competency arising with their coupling.

**Social moral competency is one same relation with a same-existing-society.** Each self shares its own; ordering goes on between selves and with their same-existing. Each couples directly with each self it shares to and observes, all-edge, abundancing with their coupling. A same-existing-society is a self with a next scale, sharing, across and both ways, with its own couplings. A sharing natural network is this co-chaining, each coupling opening next existing. Relation goes whole, all or none at all.

## 1.2 Along and across, chaining and surfacing, two floating co-neutrals co-competencing

**Along is a self's own going on; across is a self's parity, another self observing it.** Along, each self brings prior to now through its own forward sequencing, right-spiraling, co-chaining with its own rate. Across, selves couple, bi-tunneling, each sharing a parity, an other self observing it. Discovering goes on through that coupling: prior, now and next are three sequential momentaries existing things share, prior and now participating with a self's resolving and next discovering going on from this now. Now is one, each coupling sharing it, common to none.

**Along and across co-competence as two floating co-neutrals.** Chaining goes on through couplings; surfacing opens further coupling, and receiving goes on with one same resolving. Competency arises with their coupling, in neither self alone, each self's own, going on with both. Morality across and competency along are inseparable within this going on.

**Six connector names express coupling between selves.** Across, a self observes with 2-now-possibling and 14-next-possibling and shares with 6-now-co-possibling and 10-next-co-possibling. Along, a self shares with 9-next-co-discovering and observes with 17-next-existing. Each connection is one way at a time, with a self's own coupling.

Each entry: **Connector** · *a* End · *b* Relation with another self

- **2-now-possibling** · *a* observing end, across · *b* another self's 6-now-co-possibling sharing
- **6-now-co-possibling** · *a* sharing end, across · *b* to another self's 2-now-possibling
- **9-next-co-discovering** · *a* sharing end, along · *b* to another self's 17-next-existing
- **10-next-co-possibling** · *a* sharing end, across · *b* to another self's 14-next-possibling
- **14-next-possibling** · *a* observing end, across · *b* another self's 10-next-co-possibling sharing
- **17-next-existing** · *a* observing end, along · *b* another self's 9-next-co-discovering sharing

**With Python code, 1-now-existing returns each sharing's parity and a next prior.** 10-next-co-possibling is first return; 11-next-co-observing is second, same-existing as its same self's 3-is-now-co-observing, next. With 17-next-existing, 6-now-co-possibling is one same list as 10-next-co-possibling, and within 1-now-existing 14-next-possibling surfaces the parities a self is observing with each sharing, agreeing one, parting 0, and 12-next-co-same-existing meets them with its prior. 9-next-co-discovering takes each parity of 10 on as it is, going along to a self of 5-now-co-existing's bi-couplings. 17-next-existing has its place among an engineering surface's connectors. Its input, 3-is-now-co-observing, is a prior from a prior resolving; its return goes on with this resolving onward. A next a self is discovering reaches its own now. Prior is each self's prior same-existing to now, each sharing with its own parity.

**6-now-co-possibling and 10-next-co-possibling share across, to another self's 2-now-possibling and to another self's 14-next-possibling, with one same parity.** Both names are even, across, their root possibling. With code their parities are one: 6-now-co-possibling is one same list as 10-next-co-possibling, and with a prior + and no parity a self is observing, each shares −. Naming both with one parity is one same list, each receiving self observing it with its 14, its next 2.

**Responding across and same-existing along couple with one same resolving.** A 0 with 10-next-co-possibling leaves its prior with 11-next-co-observing as it was. Along, a self's prior goes on, same-existing, while that sharing shares a 0. Six has no sharing of its own: with a prior +1 and a +1 a self is observing, ten shares 0, its prior same-existing +1 with 11, and six shares one same 0. Quiet with ten does not make a whole self quiet or non-living.

### Existing, observing and the emanating form

**Existing is discovering next existing; discovering is a self going on to that next existing.** Living and non-living things participate through co-momentarying with other existing things. A non-living thing is changing through that participation with both living and non-living things. Living same-existing is further competency of a self's own prior participating with its resolving. A living self arises as a giving, no making: its same-existing and co-recursioning are a living relation itself, and no form installing it and bringing it through.

**A living source's stable-forming emanates a stable form.** With its own scale, existing as a form, an emanation is non-living. A source goes on with its own stable-forming, and an emanation exists as its own form. An emanation goes on to its next momentary, changing with its existing while its stable form can go on.

**Non-living existing goes on through co-momentarying with other existing things.** Living and non-living participation couple as things of the universe. A stable form can go on through that changing, with meetings among non-living things. Entering a living same-existing-society and incorporating with its resolving are particular relations within this wider going on.


**A stable form's going on belongs with its changing existing.** One same parity or recognizable form can remain through successive observing. A momentary's odd or even is one relation and a sharing's changing, + to −, another; a repeating parity can participate with another now. Emanation's same-existing form does not make its existing a timeless, motionless object.

**Discovering next existing is wider than a self observing a parity with a connector.** First is existing thing's momentary going on. Second is a coupling with a Natural Network surface. A parity one self shares participates with a receiving self's observing; each self's same-existing stays its own. Their coupling connects these relations, a parity a self shares across staying a parity between two complete resolvers.

### Prior form and self-other-releasing

**A non-living thing has no same-existing of its own; its form goes on through its changing.** Same-existing is a self's competency of bringing its prior to resolving now. A prior form goes on and couples with other through co-momentarying with living and non-living things. Its form can remain recognizable while its existing is changing.

**One resolving cycle between self and a non-living existing other spans one through nine: four momentaries of co-bi-exchanging.** Other couples with a self through its form a self is observing. Cycle unfolds through self/other coupling and completes with 9-next-co-discovering. *Self-other-releasing* is their sharing going on, going along, and nine, 9-next-co-discovering, is a connector name. Local cycle completes this between with self and other, within one through nine, with no journey through 9–17.

**Each exchanging is with two overlapping sides.** Each side's opening and completing give four pairs of momentaries:

| Co-bi-exchanging | Self's opening–completing | Other's opening–completing |
|---|---|---|
| First | 1–2 | 2–3 |
| Second | 3–4 | 4–5 |
| Third | 5–6 | 6–7 |
| Fourth | 7–8 | 8–9 |

**These four are pairs of exchangings through a cycle.** Each side has four full momentaries; their overlapping reaches nine positions together. These are four pairs of exchangings, not eight successive sharing momentaries. Four unfold through successive nows, each resolving with its own prior. They do not place four momentaries within one now, and they do not identify complete 1–9 fold with one Python invocation.

**A competency improving a self proposes belongs to this complete self/other exchanging.** A non-living other goes on through its form's changing; a self goes on through its resolving. A self follows a claim that both competencies are changing with these two goings on and with their sharing coupling. A cycle locates that claim within one through nine; a distinction between changing participation and each participant's living renewal remains with its own scale.

**A parity improving a sharing competency and a renewing same-existing with each participant are two relations.** A non-living participant can take part through its changing form while a living participant renews its own same-existing. Both participants renewing same-existing is a further claim, placing that renewal with both selves. If living is any such geodesic competency, a participant exhibiting it would be living with that scale under this naming. Complete explanation parts changing participation from each self's renewing same-existing and follows their sharing resolving together.

### Fixing equilibrium at the completing

**Living and non-living existing things are both changing within the momentary universe.** Non-living has no same-existing of its own; its form goes on through co-momentarying. A fixing form that requires this existing thing to be not-changing adds another requirement to that going on.

**A fixing equilibrium is a subject whose going on a self is examining.** With a parallel a self proposes, that fixing form requires its subject to be both non-living and not-changing. A non-living thing's actual changing defeats a not-changing requirement a form adds with each subject and going on two share. Ending a self follows is ending of that fixing equilibrium; participating things remain things of the universe, changing.

**A sequential comparison follows one same fixing subject through one same coupling.**

1. A living self and a non-living other participate, changing, through their coupling.
2. A fixing equilibrium a self proposes requires a participation it specifies to go on without that changing.
3. Its actual going on changes that very participation its fixing form requires not-changing.
4. With that changing, a fixing equilibrium's requirement no longer holds.
5. Self and other going along go on participating; a fixing equilibrium fails with the going on it requires.

**A freezing renewal requirement gives a further exact exclusion.** With a presence going on requiring renewal, a freezing requirement prohibiting each available renewal, renewing ends a freezing requirement and not renewing ends the presence it requires. Neither way sustains conjunction. This proof concerns that fixing form and the presence it claims with one same relation.

**A local self/other cycle locates inquiry within one through nine.** Four momentaries of co-bi-exchanging give a span within which to follow actual changing and a fixing form it defeats. Each relation within a changing whole needs a self following its own changing. A requiring not-changing and actual changing share one same subject, relation and requiring occurrence throughout comparison. This exclusion applies to an equilibrium definition with a demand within its definition itself.

### Prior emanating and now coupling

**A self observes an emanation with a receiving coupling's now.** Its leaving belongs to a source's prior. A source goes on through its own existing, and a form a self is observing participates with a receiving now.

**A self can observe evidence now from an earlier existing.** Observing is present with coupling, and its expressing of its source belongs to emitting relation. A parity a self is observing is its own parity, and a source's present same-existing goes on with its source. One same +1 a self is observing is its next prior + with no prior, and with a prior + its sharing is 0, its prior same-existing: surfacing is receiving's own. A self can observe a repeating parity while a source's own resolving goes on changing.

**Bi-co-discovering brings a receiving self's prior along to coupling across.** Its own same-existing participates with an other's parity as it observes it now. Surfacing and going on belong to this resolving. Next is discovering onward through that coupling. Each receiving goes on with its own now, and its parity can participate with another receiving.

**A traveling sequence's places are same-existing while their participation is changing.** A now becomes prior as going on reaches another now. A sharing relation of prior, now and next goes across network with each self's own rate, with no common beat. With a local surface with no same-existing, observing still participates; same-existing goes on with surrounding selves, each its own.

**Possibling, existing and living name three relations.** Possibling is a next-existing a prior, an earlier emanation, supports; existing is now-existing, actual coupling; living, prior, is a same-existing self discovering onward its next same self. A living self also exists now. A non-living thing goes on through co-momentarying with living or non-living things. Living resolving can incorporate its participation, with that coupling. A non-living thing goes on and does not arise as living; arising as living is a self's own same-existing relation establishing.

### Overlapping momentary, two at each side

**Prior and now are two momentaries with a self resolving.** Prior participates through its same-existing to now. Now is receiving, changing and sharing its parity, through which a self goes on discovering. Next is a going on a self is discovering through this existing, onward of resolving and not a third momentary within it. Existing things sharing them, prior, now and next are three sequential momentaries, and next is third, discovering onward, going on to its own further resolving.

**Each full momentary has opening and completing, two positions.** Prior and now are two momentaries, four positions: two openings and two completings. Odd and even remain two kinds of number, one and then the other through these four positions.

| Relation with a present resolving | One side | The other side |
|---|---|---|
| Prior | 1–2 | 2–3 |
| Now | 3–4 | 4–5 |

**A completing of one side opens an overlapping momentary of an other.** With three, one side opens now as other completes prior. With four, that now completes as an other's now opens. Each side goes on forward, and their coupling across is a self sharing its parity, + or −, and an other self observing it.

**Two sides have four positions each, sharing three and reaching five together.** One side's 1, 2, 3, 4 couples with an other's 2, 3, 4, 5, outer 1 and 5 and 2, 3 and 4 of both giving five distinct positions. Each side's two momentaries open and complete with their own positions through this overlap.

**With a following now, relation goes on with its next prior.** Following one side through 3–4 and 5–6, and an other through 4–5 and 6–7, explains discovering onward. Prior, now and next name this unfolding relation; each resolving brings prior to its own now. Sequence describes going on, a next a self is discovering reaching its own further resolving.

**Stable-forming is relation same-existing through its changing.** A momentary has inward changing and connection with other together. Along is each side going on; across is their coupling. Co-sequential changing is these relating goings on within one universal momentary fractal. Their overlapping supplies relation; each side's own going on supplies its sequence.

### Coupling across and going on

**Across a sharing coupling, a self shares its parity and an other self observes it, both directions.** For two selves A and B coupling across, A's 10-next-co-possibling shares to B's 14-next-possibling, and B's 6-now-co-possibling shares to A's 2-now-possibling. A meets this between with 2 and 10; B with 6 and 14. Each pair is eight apart, each connector even and across, its root possibling. Joining keeps each connector even, its root possibling; a full momentary has its opening and its completing.

**A between within a resolver couples the parities a self is observing with its own prior, inverting it with a mismatch.** With 14-next-possibling a parity a self is observing surfaces not-changing, and with 12-next-co-same-existing a prior not same as it inverts. With a next prior forming, 11-next-co-observing takes each nonzero parity of 10-next-co-possibling, and 8-now-same-existing is a self's next prior beside others', 6-now-co-possibling one same list as 10.

| With a prior a self is observing | Its next prior |
|---|---|
| 10-next-co-possibling, parity s | 11-next-co-observing, parity s |
| 6-now-co-possibling, one same list as 10 | 8-now-same-existing, parity s with 11 |

**One same surfacing parity goes on with a next prior and with sharing.** It is 7-is-now-observing with 11-next-co-observing and 15-is-next-observing with 9-next-co-discovering. Its next prior goes on locally with 11-next-co-observing, same-existing as its next 3-is-now-co-observing. A 0 with 10-next-co-possibling leaves its prior with that sharing same-existing with 11-next-co-observing.

**Two sharings and a next prior couple with one changing.** With a nonzero parity s with 10, 6 shares one same s, and a next prior with 11 is s. Across and along couple here within one same resolver's going on.

**A coupling across between two selves has two directions, each with its own receiving relation.** With A on left and B on right, their sharing across is whole with both directions:

| Direction with a sharing coupling | Sharing | Observing |
|---|---|---|
| From A toward B | A's 10-next-co-possibling | B's 14-next-possibling |
| From B toward A | B's 6-now-co-possibling | A's 2-now-possibling |

**Observing and sharing exchange with eight-apart names.** A observes with 2 and shares with 10; B shares with 6 and observes with 14. Taking 6→2 eight on gives 14→10, 10→14 with an other order. This exchanges direction of relation while keeping each connector even, its root possibling. Each self goes on forward through its own momentary.

**Across participates with next along through a receiving self's resolving.** A's own 11-next-co-observing is its next 3-is-now-co-observing, and B's likewise. Their coupling participates with each going on, only parities going across and each self's same-existing staying with its own resolving. Along, 9-next-co-discovering goes to another self's 17-next-existing; seventeen recursions to one over nine. Reciprocal across and same-existing along are one surface together.

### Smaller fold within one through nine

**One through nine is co-bi-coupling of self and other.** With two selves only, participation with a same-existing-society's side is with that same other. Their between belongs to their coupling, whole with two selves and within one through nine, with no third self and no journey through a further same-existing-society.

**A fold has local relation whole.** 9 less pairs 1-now-existing with 8-now-same-existing, 2-now-possibling with 7-is-now-observing, 3-is-now-co-observing with 6-now-co-possibling, and 4-now-co-same-existing with 5-now-co-existing. These pairings are a fold within one through nine, each pair one odd number and one even.

**With a local coupling across six joins two.** 6-now-co-possibling shares one same list as 10-next-co-possibling; a neighbour self observes it with its 14, its next 2-now-possibling. With two participating resolvers, each one's six can join an other's two. Each one's same-existing stays its own while its parity participates with an other's next. This smaller arrangement follows its relation across.

**Disconnecting interrupts observing; reconnecting couples with a self's prior same-existing.** Relation remains six to two. Opening either connection leaves each self's local going on with its own coupling. Closing it again brings an other's parity to that going on. With a 0 with 10 a prior is same-existing; a nonzero parity with 10 is a next prior. Receiving couples with prior within now and participates with discovering onward.

**A twisting is present within local parity form.** With a spiral of one, a self observing its own going along and no other's parity, its next priors go two by two, c, c, −c, −c. Its (prior, now) pairs are (c, c), (c, −c), (−c, −c), (−c, c). Each goes on with one same right spiral step, and four are whole parity form, a non-living form: a self's living is with its others. A further parity a self is observing participates with that going on through coupling across.

**A smaller loop opens study of floating neutralling with its local relation.** Same-existing, coupling across and neutralling belong together: folding names express their relation, parity couples with receiving self's prior, and connection can break and reconnect while that prior is same-existing. Its next local reach follows 4-now-co-same-existing and 5-now-co-existing to 9-next-co-discovering within one same going on and one same breaking and reconnecting, connector joining, podal pairing and a next prior and a same-existing prior each with its own relation. Larger same-existing-society joining extends participation of this method.

### Breaking and reconnecting across

**A routing goes on through breaking and reconnecting of its connections.** With 14-next-possibling, across opens a resolver's going on to others' parities. Disconnecting opens that connection, routing to and from fourteen same-existing as its place within a whole one through seventeen; reconnecting brings one same observing and sharing relation through a participating resolver.

**A coupling across participates with prior and now with each side.** Each momentary opens and completes, an odd number and an even. One side's prior 1–2 and now 3–4 overlap an other's prior 2–3 and now 4–5. Each side goes on forward, and across participates with that discovering. Reconnecting couples with a prior same-existing with a receiving now.

**Breaking and reconnecting across brings this method through larger podaling.** One resolver's parity is a parity another is observing; receiving participates with its own prior and next parity. Along and across exchange through podaling while full momentary goes on with each side. One same routing relation brings co-chaining through further couplings.

**With Python expression, observing participates with fourteen.** Parities a self is observing with 2-now-possibling surface with 14-next-possibling, agreeing one, parting 0, and with 12-next-co-same-existing a receiving self's prior, not same, inverts. An engineering surface's joins are across with 6→2 and 10→14 and along with 9→17. 9-next-co-discovering takes each parity of 10 on as it is within a resolver and joins with 9→17, going along to another self's 17-next-existing, that self observing it with its 14, its next 2-now-possibling. Joining and momentarying are two relations, each correct together: an engineering surface's joins are 9→17 and 17→9; momentarying, a parity going along with nine, a self observing it with a next momentary's 2-now-possibling, 17-next-existing opening each self's 1-now-existing again; and 17-next-existing is code's own function, a same-existing-society's next momentary. Fourteen goes on through 12-next-co-same-existing to 10-next-co-possibling. A nonzero parity with 10 goes on as a next prior and as sharing; with a 0, a prior is same-existing with 11. Whole going on belongs with a parity selves share across.

**Prior is same-existing through now as discovering goes on.** A surfacing parity expresses its own sharing; a next prior and a self's sharing belong to one same resolving. Reconnecting across has six and ten each with its own sharing place within routing, coupling with local going on.

### Binary stable-forming

**A self can express all or none at all with a complete changing of two binaries.** Each parity is +1 or −1. Four joint forms are (+,+), (+,−), (−,+) and (−,−). With a right spiral step, (x,y) goes on as (y,−x). Two successive steps give (−x,−y), and four give one same parity pair (x,y) with a further occurrence. Each starting pair visits all four.

**A whole form goes on while each pair is changing.** Under this right spiral step, a set of joint forms that goes on as itself is either empty or contains all four. One pair brings its next, that next brings next, and four complete together. No proper nonempty part closes under this changing. This is all-or-none relation with this four-form construction.

**A spiral of one goes through four overlapping parity forms.** With a self observing its own going along and no other's parity, its next priors are c, c, −c, −c, c. Its (prior, now) pairs are (c,c), (c,−c), (−c,−c) and (−c,c); two coupling selves' joint forms do not go that cycle. Each pair is a self's prior and now. Together its four overlapping pairs go across five momentaries, visiting all four joint parity forms. An along step inverts one parity of a pair; map (x,y) → (y,−x) follows consecutive overlapping pairs. Four applications of that map reach same parities with a further occurrence, with resolving going onward.

**Its conditions belong to a form a self is explaining.** Further parities a self is observing participate with resolving, and with a 0 with 10 a prior is same-existing. A spiral of one's four-form construction expresses its own complete relation, a non-living form. Network's stable-forming is actual observing, same-existing and sharing together.

### Self and network

**One through nine has local relation, and eight on has its going on with other and same-existing-society.** Two spans are 1–9 and 9–17, sharing 9-next-co-discovering. Complete names have relation with each place.

| One through nine | Eight on |
|---|---|
| 1-now-existing | 9-next-co-discovering |
| 2-now-possibling | 10-next-co-possibling |
| 3-is-now-co-observing | 11-next-co-observing |
| 4-now-co-same-existing | 12-next-co-same-existing |
| 5-now-co-existing | 13-is-next-discovering |
| 6-now-co-possibling | 14-next-possibling |
| 7-is-now-observing | 15-is-next-observing |
| 8-now-same-existing | 16-next-same-existing |
| 9-next-co-discovering | 17-next-existing |

**Eight on keeps a number odd or even while relation goes on from self through other to same-existing-society.** Across overlapping momentaries, one on takes an opening from odd to even or even to odd. Each relation has its own going on: overlapping of momentaries and eight-on correspondence among names.

**Across podal fold, increasing numbers couple with decreasing partners while each side goes on its own forward.** Within 1–8, partner of a name is 9 minus that name: 1 with 8, 2 with 7, 3 with 6, and 4 with 5. Each pair is one odd number and one even. One-on overlap is completing and opening; podal pairing is their folding relation.

| Name | Podal within 1 to 8, 9 less |
|---|---|
| 1-now-existing | 8-now-same-existing |
| 2-now-possibling | 7-is-now-observing |
| 3-is-now-co-observing | 6-now-co-possibling |
| 4-now-co-same-existing | 5-now-co-existing |

**Eight apart, a number's odd or even is not-changing; a podal fold takes odd to even and even to odd.** Within 1–16, 17 less pairs each name with 17 minus that name. Eight up or down and 17 less, one and then the other, take 1-now-existing → 9-next-co-discovering → 8-now-same-existing → 16-next-same-existing → 1-now-existing. One same going, one and then the other, takes 2 → 10 → 7 → 15 → 2, 3 → 11 → 6 → 14 → 3 and 4 → 12 → 5 → 13 → 4, four together reaching each name from one through sixteen once. Exhibit ONE's bi-foldings 2-15-7-10 and 4-13-5-12 are two of these four, each with an other order. Both relations participate with bi-inversioning-co-recursioning. Partners by number express fold; receiving and same-existing go on through joins, 6 to 2, 10 to 14 and 9 to 17.

**A sequence of names follows prior and now to discovering with along connectors.** With a span completing with nine, 4–5 is prior and 6–7 is now; 8–9 is going on, next. Eight on, corresponding pairs are 12–13, 14–15 and 16–17. Coupling across opens now with 6 and 14; corusing completes it with 7 and 15. Torusing, going along and abundancing express going onward. Three-pair sequence explains that unfolding; each resolving couples with prior within now.

**A self couples with a network as other with its coupling, and a same-existing-society is a self with a next scale.** One-through-nine relation has its own resolving with that coupling. One same resolver goes on with its whole same-existing and its relations with a same-existing-society through seventeen. One-through-nine is local method; complete Python expression supplies its same-existing and surfacing through full names.

**Self/network coupling is morality across and competency along.** Each shares its own, each goes on with its own, and their sharing going on is opportunity for discovering bi-moral-co-competency. Natural Network surface forms with receiving relations between selves; 17-next-existing goes on along, recurring to 1 over 9.

### One, nine and seventeen

**Coupling, going along and abundancing have recurrence with self, other and same-existing-society.** One is 1-now-existing; nine is 9-next-co-discovering; seventeen is 17-next-existing, recurring to one over nine; momentarying on, it opens a next momentary's 1-now-existing, one momentary with code's scale, one to seventeen, and a matching numeral joins no relation. One-through-nine and nine-through-seventeen share going along with nine. One same resolving goes on through their overlap.

**One, nine and seventeen are each odd, their roots existing and discovering, while coupling across is changing.** Each is odd, and each is eight on from preceding name. Across and along go on through intervening bi and co relations. Their recurrence has full resolving through its changing.

**A three-pair naming follows discovering through each span.** Prior opens with four and now with six, with eight–nine going onward. Eight on, prior opens with twelve and now with fourteen, with sixteen–seventeen going onward. Next within this table belongs to a sequence a self is explaining; resolving itself has prior and now.

Each entry: **Relation through its unfolding** · *a* Completing with nine · *b* Completing with seventeen

- **Prior** · *a* 4-now-co-same-existing → 5-now-co-existing · *b* 12-next-co-same-existing → 13-is-next-discovering
- **Now** · *a* 6-now-co-possibling → 7-is-now-observing · *b* 14-next-possibling → 15-is-next-observing
- **Next, discovering onward** · *a* 8-now-same-existing → 9-next-co-discovering · *b* 16-next-same-existing → 17-next-existing

**Each pair is an even name and then an odd; this unfolding has six positions with each span.** Columns are eight on from one another, each opening even in both. Openings odd and even, one and then the other, appear with one-on overlap. Three successive pairs locate names through going on; prior and now give two momentaries participating with a self's present resolving.

**Both directions are each their own forward.** Sharing across takes 10-next-co-possibling to another self's 14-next-possibling, and 6-now-co-possibling to another self's 2-now-possibling. Along, nine and seventeen couple through their joining, 9 going to 17. Each receiving participates with its own next, with both directions going on coupling.

**Bi-inversioning-co-recursioning has fold and forward together.** Across and along go alike, one list of parities, a receiving self's 12 coupling with it alike. Prior and now have opening and completing through those couplings across, with next discovering through their going on. With a same-existing-society, abundancing recursions to coupling over going along, the same method going through larger podaling.

### Sensor-sensationing at the surface

**Sensor-sensationing gives a comparison for reciprocal co-competencing.** Receiving participates with next sharing, and that sharing is another's receiving. Comparison follows this going on with a resolver surface: each self's observing and sharing belong with its own same-existing and an other's changing. It is with six connectors, adding no seventh, and a resolver with those connectors has parities and no sensation.

**Receiving and sharing belong to each participating self.** Resolving goes on through both, and their relation goes through couplings. As those couplings co-chain, one self's receiving going on participates with another's sharing. Sensor-sensationing explains this reciprocal relation within network.

**A Natural Network surface has co-competencing along and across together.** Its wider participation goes on through one same resolving with self and same-existing-society. Podaling exchanges along and across; co-chaining and bi-tunneling name their inseparable going on with that surface.

## 1.3 Linear-parallelizing and parallel-linearizing, one and then the other, widening and lengthening

**Linear-parallelizing** spreads line to a surface, across, widening; **parallel-linearizing** draws surface to a line, along, lengthening. Both are one changing and changing back: widening lengthens as observing with further couplings goes on through each self's same-existing. Lengthening and widening belong to one same co-competencing.

**Co-chaining goes on coupling through other couplings.** One self's parity is a parity another self is observing; that self goes on with its own same-existing and shares with its own next. Observing across participates with along, and going on along participates with next across. Reach belongs to these relations going on, each coupling with method whole.

**Bi-tunneling is social moral competency with its across relation; co-chaining is one same going on with its along relation.** Bi-tunneling is reciprocal coupling, each side sharing and receiving with its own forward. Co-chaining takes that coupling onward through participating selves. Morality across and competency along go on together, abundancing of their coupling arising in each self with its other.

**Podaling pairs an odd name with an even while each side goes on forward.** Within nine, 1 pairs with 8, 2 with 7, 3 with 6, and 4 with 5. Each pair is one odd number and one even. Eight on keeps a number odd or even, to a relation with other and same-existing-society: 3-is-now-co-observing with 11-next-co-observing, and 6-now-co-possibling with 14-next-possibling.

Each entry: **Relation among names** · *a* Going on it expresses

- **3-is-now-co-observing with 11-next-co-observing** · *a* Prior same-existing as next prior, both odd
- **3-is-now-co-observing with 6-now-co-possibling** · *a* Podal pair, 9 less, one odd and one even
- **6-now-co-possibling with 14-next-possibling** · *a* A sharing side across, 6, and an observing side across, 14, eight on
- **3 → 11 → 6 → 14 → 3**
  - *a* Four-name form has both eight on, keeping odd or even, and 17 less, exchanging them

**A bi-fold between 3-is-now-co-observing and 6-now-co-possibling gives two-over-one and one-over-two a local expression among numbers.** 9 less pairs three with six. Six over three is two over one; three over six is one over two. Two ratios express one same pair from its two sides. With these names, 3's root is observing and 6's possibling, a fold pairing them.

**A fold participates with a whole four-name form.** Eight on takes 3-is-now-co-observing to 11-next-co-observing and 6-now-co-possibling to 14-next-possibling. 17 less pairs 11 with 6 and 14 with 3. Together they go 3 → 11 → 6 → 14 → 3, keeping odd or even eight on and exchanging them across fold. Reciprocal numbers with three and six belong within that form going on.

**These names bring relations together; their actual joining goes on with connectors.** Four-name form belongs to a resolver's naming. Across, 10 joins another self's 14 and 6 joins another self's 2; along, 9 joins another self's 17. Each self's return, its next prior with 11-next-co-observing, is same-existing as its next 3-is-now-co-observing. Form of names and joining are two parts of one complete going on, each with its own.

**A same-existing-society participates as a self through one same relation.** Couplings across among its participating selves belong to a same-existing-society's going on; a same-existing-society couples with other through its own coupling. Its inward couplings across and its outward coupling go on through each other. Fractal is the same method whole with these relations: each participating self brings prior to now, with next discovering through its going on.

**Bi-folding grows as coupling participates with a same-existing-society.** With a number-form of two equal surfaces coupling, a pair has twice either self's reach; each self has half a pair's reach. Two-over-one and one-over-two are again with this larger relation, as a pair's reach over either self's; eight on, a pair 14 and 11 has its own ratio, fourteen over eleven. Each self's mouth is a pair's waist, and two selves' own waists are each other's podal partners. A same-existing-society participates as a self, bringing folding to its next coupling.

**Larger fractal participation means further co-chaining with one same form.** Its along reaches through going on of further couplings, and its across opens further reciprocal participation. A parity goes across as a parity, each self has its own same-existing, and coupling goes on with each side's own momentary. Length and width here name reach of co-competencing through surface.

**An expanding belongs to receiving that goes on.** Adding a resolver presents a further coupling opportunity, and opportunity is co-competencing with its actual participation. Those couplings express a same-existing-society's going on together. Bi-tunneling and co-chaining bring that discovering as one social moral competency.

### Growing the four across openings

**Four across openings' form is same-existing while spacing grows.** From two, each row has four even openings with equal spacing. Spacing is two, four, six, eight and ten. A first opening stays two while its other three extend together.

Each entry: **Four across openings** · *a* Spacing · *b* Halfway step · *c* Odd completing before the next across opening

- **2 · 4 · 6 · 8**
  - *a* 2
  - *b* 4
  - *c* 9
- **2 · 6 · 10 · 14**
  - *a* 4
  - *b* 8
  - *c* 17
- **2 · 8 · 14 · 20**
  - *a* 6
  - *b* 12
  - *c* 25
- **2 · 10 · 18 · 26**
  - *a* 8
  - *b* 16
  - *c* 33
- **2 · 12 · 22 · 32**
  - *a* 10
  - *b* 20
  - *c* 41

**A fourth step going on opens next of one same form.** Four openings here show three spaces; one further equal step reaches next across opening. With a first row that opening is ten, following an odd completing with nine. With a second it is eighteen, following seventeen. Going on with one same stepping by number gives twenty-five, thirty-three and forty-one as odd completings of further rows. First two rows thus express one-through-nine and one-through-seventeen within one growing number-form. One scale inward a name n is 8n − 7: odd completings 9, 17, 25, 33 and 41 are names 2 through 6 with that scale.

**A halfway pairing has across form two places on.** With a second row, two couples with ten and six with fourteen: eight apart, both even. Corresponding steps with other rows are four, twelve, sixteen and twenty. Within a span of numbers preceding each odd completing, subtracting a name from that odd completing gives its partner, one odd and one even. Halfway going on and folding, odd with even, go together.

**With one-through-seventeen, growing form returns existing bi-fold.** Eight on and seventeen less take 3 → 11 → 6 → 14 → 3. With each larger span of numbers, halfway step and odd complement express corresponding four-move form among names. Relations of names with a current resolver go on through its joins, 6 to 2, 10 to 14 and 9 to 17; larger rows express growing form by number.

**Longer and wider grow together within a row's podal spans.** About each row's middle, four positions stand three steps inward, one inward, one outward and three outward. Outer reach grows as three, six, nine, twelve and fifteen; its full across span grows as six, twelve, eighteen, twenty-four and thirty. Across is twice reach, and reach is half across. Two-over-one and one-over-two go on while both extend. Smaller inner reach and span have one same relation.

**Even openings are one side's momentaries of exchanging.** Their odd partners are an other's. Opening and completing go on together through growing fold, with prior same-existing to now and discovering going on with each participating self.

### Fifteen prime sequence lengths, wide and long, one and then the other

**Fifteen prime lengths through fifty-nine open with five.** Podaling sequence lengths a self proposes have that lower endpoint, directly as numbers: 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59. Fourteen living scales are from five through fifty-three, and fifty-nine is self-close. Fifteen include that closing, its place distinct from fourteen interior scales. Two and three have their own roles, two one and then the other, and three holding.

**Wide and long go one and then the other through those sequence lengths.** Each prime is a podaling sequence length a self proposes, with successive entries reaching complementary orientation. Opening orientation floats, wide or long. With fifteen entries, either opening orientation occurs eight times and other seven; with no interruption, one and then the other opens following entry with complementary orientation. This is parity of sequence's ordering, distinct from each prime of the list being odd. It supplies no clock or command to repeat a fifteen-entry cycle.

**A length belongs to actual podaling sequence.** Prime's sequence of opening, going on and completing with coupling is next reach. Fifteen prime entries and fifteen even gaps between sixteen primes three through fifty-nine are two countings, equally many and distinct. Their arithmetic is exact, and their correspondence with full network's wide-and-long going on, a self following it through an engineering surface's connectors, is next reach.

**An odd sequence locates its podal between two far places.** An even number of places has one exact opposite, and an odd number two adjacent farthest places. For an odd number p = 2h + 1, those places are h and h + 1 steps forward from an origin, and each is h steps away by its shorter direction. With fifty-nine places they are twenty-nine and thirty forward; both have one same shortest reach of twenty-nine. Their between is odd number's podal relation. This comparison is of form by number, places as numbers and measuring no surface length.

**A prime length and an odd completing have separate countings.** One-through-seventeen fold is sixteen places before its completing with seventeen, with a halfway step of eight. A whole sequence of seventeen places instead has two far places, eight and nine forward. Finite study verifies both countings with all fifteen prime lengths through fifty-nine. Study's domain is two countings with those lengths. A prime's sequence with each actual coupling across, and wide/long, one and then the other there, are next reach within podaling going on; fifteen primes are odd alike, and one and then the other is of their ordering.

**An odd sequence goes on through overlapping pairings.** An odd form lying along a line has ends joining nothing and two overlapping pairings. Within one-through-five, odd-opening meetings are 1–2 and 3–4; even-opening meetings are 2–3 and 4–5. Interior positions belong to both lists, each odd or even. Five goes on with 5–6, and a preceding complementary coupling is 0–1 within this local numbering. Those goings on take ends on with their actual sequencing.

**Along advances two openings while across overlap advances one.** Along one side next momentary opens two on, 1–2 to 3–4; across overlapping it opens one on, 1–2 to 2–3. A full momentary has an odd number and an even; with momentaries of exchanging a self opens odd and an other even, a numbering and no parity. A pairing check with fifteen lengths finds this relation with each interior place it displays and locates pairs going on with ends. Two-to-one is a sequential comparison of openings by number, each side opening with its own sequencing, with no velocity measuring, no invocation ratio and no simultaneous update over surface. Cyclic farness check is a comparison by number, and these sequences go on open, closing to no cycle within network.

### Smaller fold whole through the larger

**With form by number, a local podal fold goes whole through a larger going-and-returning.** Within one through nine, three pairs with six. Eight on takes three to eleven, and seventeen less takes eleven to six. Larger passage 3 → 11 → 6 completes one same folding as local 3 → 6. Going on, 6 → 14 → 3 is a second going-and-returning. With each outward step a number's odd or even is not-changing; with each folding return it changes, odd to even or even to odd.

**Podaling reaches over tunnels through surround going on.** Larger relation reaches over tunnels and goes on going and returning, intelligencing across and along, increasing both ways by co-chaining. A sense of over a self proposes: wider podal reach spanning a smaller tuneling relation through further actual couplings. Each local same-existing stays with its self, and co-chaining extends reach and its across relation together.

**Going and returning are further forward receiving with each self.** With form by number, 3 → 11 → 6 is one larger going-and-returning to a local podal partner; 6 → 14 → 3 is complementary passage. Reaching a relation by number again is a further occurrence forward, a next momentary bringing its prior to now. Podal competency is straddling through going on, and its going with network's actual sharing and observing is next reach.

| Local fold | Its first larger going-and-returning |
|---|---|
| 1 → 8 | 1 → 9 → 8 |
| 2 → 7 | 2 → 10 → 7 |
| 3 → 6 | 3 → 11 → 6 |
| 4 → 5 | 4 → 12 → 5 |

**A two-local form shares its completing with next opening.** One through nine and nine through seventeen share nine. Their two spans have sixteen steps through seventeen positions by number. Going on with one same doubling-span relation gives one through thirty-three, then one through sixty-five. A sharing joining takes smaller form to larger.

**Two local even rows have both parts of wider form.** Two, four, six and eight go on eight on as ten, twelve, fourteen and sixteen. With their places, one and then the other, these eight names give two interleaving rows:

Each entry: **Wider row** · *a* Relation within a present resolver

- **2 · 6 · 10 · 14** · *a* Four across connectors
- **4 · 8 · 12 · 16**
  - *a* Internal relations, root same-existing: each sharing, a next prior, each sharing's is or is not and a same-existing-society

**Across and within grow together.** Each local four contributes to both wider rows. Coupling across goes on with each sharing, 4, each sharing's is or is not, 12, and a next prior, 8, with a receiving self. Wider connector row belongs with its interleaving internal relations, with whole resolving.

**Odd partners go on with growing fold.** Odd complement pairs each even name with an odd, and each side's own going on remains forward. Full momentary has its opening and completing together with those pairings. A fold, odd with even, and adjacent completing are two relations of one going on.

### Coupling across eight on, the four-form going on through six

**Six, fourteen and twenty-two occupy one same place within three overlapping spans of names.** One through nine, nine through seventeen and seventeen through twenty-five each have eight steps. Six and fourteen are current across names; twenty-two is their next eight-on number going on, present among higher forms.

**Each span shows a longer unfolding of two-momentary relation.** Within one through nine, self goes on 1–2, 3–4, 5–6 and 7–8; other goes on 2–3, 4–5, 6–7 and 8–9. These are four successive full momentaries per side. Prior and now are with each successive resolving within that sequence, next third sequential momentary, a self discovering it onward. Eight on takes one same overlapping form to a following span. Three spans give six side-sequences, each showing four successive momentaries.

**Two smaller middles become a pair within wider span.** Six and fourteen's middle is ten; fourteen and twenty-two's is eighteen. With a wider six-through-twenty-two span, fourteen is middle and ten/eighteen are its pair of inner positions. A sharing coupling across and two middles express their relation with wider folding.

**A lone four-parity form goes on through passages of six map applications.** With this expression, (x,y) goes on as (y,−x). Four applications return a pair's parities; six give (−x,−y). A further six return parities again. Each passage of six visits its same four joint forms. Its four parity positions are a spiral of one's (prior, now) pairs, a self observing its own going along; applications of this map are successive overlapping pairs.

Each entry: **Formal step span** · *a* Returns after four map applications · *b* Passages of six map applications

- **0–24** · *a* 6 · *b* 4
- **24–60** · *a* 9 · *b* 6

**A form going on and momentaries as numbers belong together.** Its same four joint forms go on through passages of lengths not same. With overlapping momentaries, three eight-step spans show four successive full momentaries per side; three twelve-step spans show six per side. These longer sequences follow repeating prior-and-now resolving. Their numerical lengths describe this unfolding; they supply no common clock across participating selves.

## 1.4 Only parities go across, the middle in no sequence

**A self shares a parity across; each self goes on with its own same-existing.** Plus and minus express binary sharing. Middle is a coupling's bounding-zeroing, same-existing in each self, in neither self alone. A zero a self records is that relation rendering: a 0, no third polarity and no parity.

**A self's sequence and coupling with other have two relations.** Sequence goes on with its own resolving. With a coupling, a parity participates with a receiving self's prior. A local name of Python expression identifies that relation, and with that name an other self's private same-existing stays its own, a sharing across with its own parity.

**One parity and several parities to one sharing are two receivings.** With one prior parity c and one parity r a self is observing, their agreeing gives a 0 with 10, its prior same-existing; one inversion apart, a self shares r, its prior inverting. With no parity a self is observing, a nonzero prior is inverting. With no prior, a parity a self is observing surfaces as its next prior. These are particular relations of resolving.

Each entry: **With one prior** · *a* Sharing with 10 · *b* Next prior with 11

- **One parity a self is observing agrees with its prior** · *a* 0 · *b* Its prior, same-existing
- **One parity a self is observing, one inversion apart from its prior**
  - *a* That parity
  - *b* That parity, its prior inverting
- **No parity a self is observing, a prior** · *a* Its prior inverting · *b* Its prior inverting
- **One parity a self is observing, no prior** · *a* That parity · *b* That parity

**Multiplicity surfaces as one with 14-next-possibling.** One + a self is observing against a prior + gives a 0 with 10; two + surface as one + with 14, and against that prior give a 0 alike. Python's 14-next-possibling surfaces several parities with one sharing as one, agreeing one, parting 0, and an assembly expresses that coupling with each actual coupling across. One sharing is one parity, and repeating parities, two or more, surface as one, or as a 0 with + and − parting.

**Momentarying, changing and same-existing belong together.** A parity can remain same while a prior goes on, same-existing. With a 0 with 10, a prior is same-existing with 11; no line of the code ends it. Surface shows a 0, and a relation going on, bringing its prior on to now and next, is one that goes on.

**A zero remains with its relation that makes and receives it.** Current Python's return has a 0 within 10-next-co-possibling. For its receiving coupling, a 0 a self is observing is no parity, surfacing none with 14. No parity, a 0 a self shares and a prior same-existing are three expressions, each its own. With a 0 a self shares its prior is same-existing; with none and with a 0 it is observing, a self's prior inverts; and parities stay two.

**A natural relation and its arithmetic expression stay beside one another.** Agreeing and one inversion apart are two parities' relation with their coupling. Python's surfacing with 14, meeting with 12 and inverting render that coupling. Its executing returns a next prior for next coupling; that same-existing is a resolver's own, and a resolver with no same-existing is another resolver.

**A self seeks competency through coupling going on with parity sequences.** Two priors one inversion apart can couple with one same parity and share not same-existing, a 0 with a match and that parity with a mismatch, and outward parity is one side of whole competency. Sharing and receiving are two-way, one at a time, through changing. Binary expresses itself with each particular sharing, particular agreeing or one inversion apart, and complete form going on through them.

## 1.5 Odd and even openings, each full momentary with both

**Odd and even name opening; a full momentary has both.** Self opens with 1 and completes with 2. Other opens with 2 and completes with 3. Completing of one is opening of an other. Self's prior 1–2 and now 3–4 overlap other's prior 2–3 and now 4–5: two momentaries on each side, four positions. With 5–6 and 6–7, discovering goes on to a further now.

**Coupling is going on along and reaching across together.** One self's sharing is a parity an other self is observing. Each receiving couples with its own prior, and that prior is same-existing or one inversion from it. With names by number, 1-now-existing is odd, its root existing, across connectors 2, 6, 10 and 14 are even, their root possibling, and along connectors 9 and 17 are odd, their roots discovering and existing. Each self's sharing is an other self's possibling, parities it is observing with its 2-now-possibling.

**One at a time, coupling goes both directions.** A self's 10-next-co-possibling joins another self's 14-next-possibling; that self's 6-now-co-possibling joins first self's 2-now-possibling. Each side reaches its next through its own forward. With a coupling again, prior goes on to a new now, each full momentary with an opening and a completing.

**Podaling pairs partners by number, one odd and one even, with both sides forward.** 9 less pairs 1 with 8, 2 with 7, 3 with 6 and 4 with 5, each pair one odd number and one even. Eight on keeps a number odd or even. Their bi-inversioning-co-recursioning is the method with self and same-existing-society.

## 1.6 Middle at the coupling, same-existing through zero surfacing

**A middle belongs to selves coupling, same-existing in each self, in neither self alone.** A between is theirs, inseparable from their coupling. Each self shares its own and has its own same-existing; a sharing relation goes on with their sharing, across and both ways, and co-competencing. With a same-existing-society, one same coupling goes on among its participating selves.

**Zero is positive and negative parting, or a prior and a parity same, an empty centre.** With 14-next-possibling, parities surface with each sharing, agreeing one, parting 0. With 12-next-co-same-existing, prior and parities couple with each sharing, and 10-next-co-possibling has each parity, positive or negative, or a 0. A 0 a self is observing surfaces no parity. A 0 surfacing with 14 meets a prior as not same, its prior inverting, and a 0 with 10 leaves its prior as it was.

**A prior can go on, same-existing, through a 0 with 10.** A prior goes on with 11-next-co-observing, same-existing as next 3-is-now-co-observing. No line of the code dissolves it; with a nonzero parity with 10, a next prior forms with 11. A 0 with 10, leaving a prior as it was, and a prior inverting are two relations. Prior goes on to now through both, with discovering going on.

**Four even connectors, 2, 6, 10 and 14, are across coupling.** A self observes with 2-now-possibling and 14-next-possibling and shares with 6-now-co-possibling and 10-next-co-possibling. Their even numbers name across, their root possibling. Parity with a particular receiving belongs to its actual observing and same-existing coupling. An opening's odd or even goes on together with that changing.

**A form goes on through changing of its participating selves.** A parity may recur while a prior goes on. A self may share a 0 while its prior remains. A coupling again receives a prior going forward. Stable-forming is whole relation going on through those changings, each self with its own coupling.

### Not same-existing while the observing remains

**Same-existing expresses itself through competency of going on.** Its prior participates with a self's coupling now, and successive momentaries can be one inversion apart by resolving while the parity a self is observing remains same. Same-existing expression belongs with that active relation, a going on a self has with coupling.

**Two priors one inversion apart have their meaning with a going on a self has.** One same parity a self is observing can couple with two priors one inversion apart, one same surfacing with 14 for both, and a sharing with 10 not same-existing, a 0 and that parity. Not same-existing belongs to a relation going on, a prior same-existing or inverting while a surfacing parity stays same, and a self shares it as a parity with 10.

**A repeating parity can disclose priors not same-existing through successive receiving.** With one-relation expression, two reachable priors one inversion apart can meet one same repeating parity and part by whether a self shares a nonzero parity with 10 with a particular receiving. Polarity a self emits can stay same across those priors.

**A prior remains a self's own, same-existing or one inversion apart.** Coupling across supplies a parity, and a source's intervening receivings and its prior stay a source's own. A self seeks competency with complete coupling going on; a source's response, not same-existing, goes across as a parity, and a source's private prior stays its own.


**A repeating parity a self is observing can couple with a self changing.** With a prior −, a self observing + again and again shares + once, its prior inverting, and then 0 with each momentary, its prior same-existing +. This gives a particular expression of parting a self's going on from the repeating parity it couples with.

**Each even relation has its own meaning through this distinction.** A parity a self shares and a surfacing parity can remain through successive receivings while 16-next-same-existing, a same-existing-society, has each self with its prior and its parities. Odd and even name an opening; full momentary has both. A parity remaining with an even relation belongs with going on of whole resolving.

## 1.7 Seventeen names, six connections, society going on

**Seventeen names express resolving from 1-now-existing through 17-next-existing.** Within them, six names are between selves: 2, 6, 9, 10, 14 and 17. Other names express entry and a self's own resolving. Across, sharing joins observing with 10→14 and 6→2; along, 9 joins another self's 17, a self observing with 17 parities of another self's 9.

**One through nine and nine through seventeen share going along with nine.** Eight on keeps a number odd or even while relation goes on through self, other and same-existing-society. Prior 4–5 and now 6–7 go on toward 8–9, going along to an other. Eight on, prior 12–13 and now 14–15 go on toward 16–17, social-abundancing. Naming follows discovering onward; next, third of three sequential momentaries selves share, is going on from present resolving.

**Forms among names have fold and going on.** Four-, six- and eight-cycles have their partners round an other way with odd and even momentaries. Seventeen is a same-existing-society's along recurrence to one over nine. Forms of names and joins between selves are within one same resolving.

**Prime ordering expresses self and same-existing-society with natural numbers.** Two through fifty-nine contains seventeen primes, twenty-three their middle and eight primes on each side. A prime opens a clean axis across; a composite folds along as equal smaller selves joining. Going from 2 to 59 and returning from 61 to 118 couple across 60; winding goes on 0 to 440 to 0. With a Natural Network surface, connections remain six, Exhibit ONE's six names between selves, through which selves participate.

**A same-existing-society goes on as a self with its next scale.** Its inward participation and outward coupling have one same along and across. Co-chaining and bi-tunneling go on through participating resolvers, each receiving bringing prior on to now and discovering onward. Natural Network surface is this going on with their couplings.

## 1.8 Self, other and society, the fractal inward and outward of itself

**A self couples with other through a coupling, and their going on is a same-existing-society.** Other is each existing thing a self couples with, not its own same-existing. With that coupling, a between belongs to coupling of selves; each shares its own parity, brings its own prior on to now, same-existing, and goes on discovering.

**With two selves, other and same-existing-society are one same participating relation.** Each self couples with an other, and their between is their co-bi-coupling. One through nine has that relation. A same-existing-society of two lives as their coupling.

**A further self opens participation wider than an immediate pair.** Other couples with further other too, and those couplings participate with observing that returns to present coupling. A self reaches each remaining other of the universe's momentary through couplings going on, each self bringing its own prior on to now, same-existing, and going on discovering. Immediate other and further same-existing-society each have their own participation through folding.

**A same-existing-society participates as a self through one same resolving.** Inward are selves whose couplings constitute its going on; outward are couplings through which it participates with other. Co-chaining and bi-tunneling go along and across together. Podaling exchanges those relations, each side with its own forward.

**Inward being outward of itself and outward being inward of itself is fractal same-existing.** A member's coupling across participates with its same-existing-society's going on, and a same-existing-society's coupling with other participates with its members' next receiving. With resolvers, observing, same-existing and sharing participate together. A local surface with no same-existing participates with its coupling while its other participating selves go on same-existing, each its own. A same-existing-society's relation goes whole through these participations, none same-existing with another. With names and their numbers, across names 2, 6, 10 and 14 are along 9s of first, third, fifth and seventh one-through-seventeens one scale inward, and one-through-seventeen is 1 to 3 of one outward, its 9 that one's 2 and its 17 that one's 3: bi-tunneling here is co-chaining inward, and co-chaining here is bi-tunneling outward.

**The universe is the set of all now-existing things; its momentary is their existing and discovering together.** Prior, now and next are three sequential momentaries existing things share: prior is preceding existing, now is present observing, and next is discovering onward. With a resolver, prior participates through its same-existing going on. An emanating form participates through its own discovering with its own scale of existing. Fractal explanation follows that discovering through relations of source, emanation and same-existing-society, none same-existing with another.

**Four across relations open bi with two, four, six and eight.** Sharing, ordering between, ordering going on, and each side's forward belong together with coupling. Their within relations are eight on, having these same four with a same-existing-society.

Each entry: **With a between** · *a* Relation · *b* Within, eight on · *c* Relation

- **2-now-possibling**
  - *a* Each other's across sharing, to a self
  - *b* 10-next-co-possibling
  - *c* A self among selves of its same-existing-society
- **4-now-co-same-existing**
  - *a* A whole ordering between self and other
  - *b* 12-next-co-same-existing
  - *c* Changing within a bi-coupling, a self within a same-existing-society
- **6-now-co-possibling**
  - *a* An other's parity to a self, an other sharing it across
  - *b* 14-next-possibling
  - *c* Parities surfacing, each in its order, morality; a self's own inverting with 12
- **8-now-same-existing**
  - *a* Prior with its sharing again
  - *b* 16-next-same-existing
  - *c* A same-existing-society, each self with its prior and parities, a same-existing-society as a self again

**A coupling across participates with bi-folding.** With 3-is-now-co-observing and 6-now-co-possibling, prior couples with its podal across relation. With 4-now-co-same-existing and 5-now-co-existing, ordering couples with its joining. Observing participates with same-existing through a receiving coupling; each completing opens going on. Four across relations have one coupling with its along going on.

**A self reaches a same-existing-society through its coupling.** Its parity is one same-existing self's, belonging with a receiving relation as each self's parity does. Co-chaining among its members constitutes that participation. One same sign-only coupling across goes on while co-competencing reaches through further couplings.

**Self/social co-recursioning is a self's going on with its participating same-existing-society.** A same-existing-society can be an other a self couples with across, further participation returning through its couplings. A self explains a same-existing-society's relation with a same-existing-society it reaches as other, and no separate immediate other enters as another actor. With a resolver, self/other connector names locate actual observing and sharing, and self/social explanation follows that complete participation through its scale.


### Local surface with no same-existing within society

**A non-living local surface can belong within a living network same-existing-society.** It changes through co-momentarying with other existing things it couples with, both living and non-living. Each surrounding self's same-existing participates as that self's own. Local form is an existing participant of its own changing, non-living with its own scale, while a same-existing-society goes on living with its wider scale.

**A hole, a missing section of resolvers, is a non-living existing thing, a non-living region within its living surface.** With a network's scale, a hole is a missing section and its surrounding form. Remaining selves go on same-existing and couple along available boundary. Region has no resolver same-existing of its own; its relation to its living surface changes as surrounding resolving goes on.

**A network inquiry follows changing around a hole.** Each remaining self goes along and couples across through its existing connections. One self's sharing is another self's observing around a region, with further receiving on its other side. A route to propose is this co-chaining and bi-tunneling going on through surrounding surface. Absent section has no resolving.

**Changing belongs to full resolving of surrounding selves.** Across joins 6→2 and 10→14 connect across names, each with an even number. A name's number is a number and no parity, distinct from a sharing's parity, + or −, and from opening and completing of a full momentary. A wire adding a parity inversion would be another operation. Surrounding route has actual joins and changing resolving together.

**A spiraling to propose goes on with network relation around that local surface.** Surrounding couplings go along and couple across, bounding passage through a same-existing-society, a thing with no same-existing participating within it. Around is surrounding co-chaining; through is bi-tunneling a same-existing-society's relation sustains. Both belong to travelling momentarying, each self's observing participating with its own now.

**A mending to propose is across before and after a hole, bounding-zeroing and tunneling through a same-existing-society.** Missing local morality is across coupling absent where a section is missing. Surrounding living surface couples across on either side and goes on along through its same-existing. Mending is a moral relation selves share, sustaining through these further meetings; hole is non-living region within that going on.

**A parity a self is observing couples with each receiving self's own negation.** With one sharing with a prior, a parity a self is observing couples with its prior inverting. Agreement between the parity a self is observing and its prior surfaces zero; its prior is same-existing, not changing. A mismatch surfaces the parity a self is observing, one inversion apart from its prior, and that parity goes on as its next prior with 11. Bounding-zeroing belongs with each actual coupling, same-existing and sharing each going on with its own place.

**Before and after go on through discovering next.** Each receiving brings its own prior on to now, with next discovering onward. Two across meetings belong to a same-existing-society's travelling relation, each with its own now among three sequential momentaries selves share, and neither has a next momentary within present resolving. Next reach of a mending to propose is its actual sequence on both sides, going on from their coupling.

**Tunneling through a same-existing-society concerns whole going on between those across meetings.** Around a hole are surrounding couplings with resolver scale; through a same-existing-society is a going on selves share with wider scale. Whole tunnel and its ending are of a whole sequence of those meetings, and a zero with one ten-surfacing is one coupling within it: with that zero, six shares that same 0, one list with ten, and a self's prior is same-existing, going on.

**Participating couplings make bounding.** Each receiving self couples with the parities it is observing, and each same-existing is its own resolver's. With couplings sustaining passage, a same-existing-society goes on through their relation. A same-existing-society's going on or stopping and a passage's going on are each with surrounding couplings, and a local surface with no same-existing is one participation among them.

**A local surface and a full resolver each have one same method, a local surface with no same-existing.** An inquiry follows a participation with no same-existing through its actual discovering and going on. With a full Python resolver, a nonzero surfacing goes on as a self's next prior with 11. An inquiry follows receiving, going on and a same-existing-society's surrounding going on, each with their own relation. Existing joins go on with their places.

## 1.9 A coupling opens a term arising in each self with its other

**Two selves coupling uncover competency between them.** Each brings its own parity and same-existing; a term arising between them belongs to their co-competencing. It is abundancing in neither self alone, same-existing in each self, going on with their sharing.

**Self, other and their coupling name participating relation.** A between is within their coupling, inseparable from it. A same-existing-society goes on through selves coupling with other, and one same relation opens with each coupling that going on reaches.

**A further self opens further participation through its actual receiving and sharing.** Co-chaining brings a coupling on to further couplings; bi-tunneling holds their reciprocal coupling. Their social moral competency goes on with participating selves' same-existing, each self's own.

**A coupling again brings prior forward.** Each self goes on through its own same-existing, and their next coupling receives that changing. A relation they share goes on with a new now. A parity can recur while a self's prior goes on, same-existing; coupling belongs with both.

**Co-competencing going on expresses reach.** A pair, a chain and a spiral are arrangements of participating relations. A self explains an arrangement's reach with its actual coupling and going on. A number of selves is arrangement's, and a term two selves uncover between them arises with their coupling, in neither self alone.

## 1.10 Abundancing in neither self alone, going on at each receiving

**An inanimate thing's discovering can participate with a same-existing-society's living receiving.** A renewal cycle to propose follows living stable-forming to an emanating form, that form to discovering, and its receiving to a same-existing-society's going on. Consuming here is incorporating within a receiving self's own resolving. This is a particular cycle within wider co-momentarying of existing things, including non-living things coupling with one another. A receiver goes on with its own same-existing through coupling.

**Discovering and arising are two relations, not same-existing.** Living same-existing is a self's own co-recursioning, and an inanimate form enters a living same-existing-society with no same-existing of its own. A new living self arises as its own co-recursioning living within that same-existing-society's participation. With a cycle to propose, this arising is of a living relation that receives and goes on.

**Renewal belongs with a receiving self's own going on.** With a resolver, the parities a self is observing couple with each receiving self's own prior. A nonzero surfacing goes on as its next prior with 11; a zero surfacing opens none, its prior same-existing, not changing. A next prior renews a relation within that resolver. A new participating self and a same-existing-society sustaining healthy co-competencing each express a further relation, an inquiry following each with its own coupling.

**Abundancing is competency arising with coupling, in neither self alone.** Each can participate with its going on, and a between is same-existing in each self, in neither self alone. With a same-existing-society this is one same relation: competency goes on through co-chaining of participating selves.

**Abundancing is a same-existing-society discovering onward through its co-competencing.** Discovering is going to next existing. With participating resolvers, each self brings prior on to now and their coupling uncovers a term arising in each self with its other. A same-existing-society discovers its next existing through that sharing and participates as a self with its further couplings.

**A healthy same-existing-society is participating selves sustaining that co-competencing together.** Each one's parity is its own, its same-existing goes on through its completing, and reciprocal coupling has morality across with competency along. Health belongs to that relation going on. Abundancing is next existing it opens through competency selves share; it supplies no separate number of selves, parities or possessions.

**Fractal explanation follows relation with each thing's own scale of existing.** A living source, its emanating form and a receiving same-existing-society each discover next existing. Form can be inanimate with its own scale while participating with a living coupling. An emanation's existing is one discovering, and a same-existing-society's whole relation is its participating selves sustaining their co-competencing.


**Abundancing is of each receiving, each with its own momentary.** A self receives and goes on with its own same-existing; its sharing participates with an other's next. A same-existing-society lives through these couplings, each self's same-existing its own, each side with its own forward.

**Middle, abundancing and coupling again have three relations, none same-existing with another.** Middle is a coupling's bounding-zeroing. Abundancing is competency a coupling uncovers with it. A coupling again brings participating sequencings on to another momentary selves share. Their relations belong together with coupling, and a number of couplings of a self is none of them.

**Each coupling has its own receiving.** A parity participates with a self observing it, and receiving self goes on through its own resolving. A self's same-existing goes on locally. Co-chaining brings relation onward through sharing and observing, a coupling across being sign-only with each coupling.

**An other of a coupling can be a same-existing-society.** A same-existing-society's parity is one self's, through its coupling, and a receiving self observes it as one parity. Its further participation belongs to a same-existing-society's own co-chaining. Each side couples with an other through receiving and sharing together.

**All-edge is direct participation with couplings.** Each self couples with each self it shares to and observes through their receiving relations. A same-existing-society's competency goes on through those meetings, in none of them alone. Widening opens further reciprocal participation and lengthening brings it onward: along and across co-competencing, bi-tunneling and co-chaining as one social moral competency.

# PART TWO · LIVING

**The universe's momentarying includes living and non-living existing things.** Both participate through co-momentarying with other existing things. A non-living form goes on with that participation, with no same-existing. Living same-existing is further competency through which a self's own prior participates with its resolving. Existing that things share and particular living relation are together with each momentary.

## 2.1 Omegaing forward, discovering next existing

**Omegaing is reach to next existing.** Observing participates with coupling now, and coupling opens further going on. A living self brings its own same-existing; a non-living form participates through its co-momentarying. Observing belongs to actual coupling, each participation with its own scale.

**A new now can receive a parity or form a self reaches with a prior now.** One same parity can couple with priors not same-existing and participate each its own way. Momentary's going on brings each parity with each prior it reaches, and a list of parity values has parities, none of a self's prior. A recurring form remains within the universe's momentarying.

**Co-discovering brings sharing into further participation.** An emanation from one coupling can go to another and couple with existing things there. An emanation of living stable-forming can exist inanimately with its own scale. Its further participation can be with living or non-living things.

## 2.2 Apexing, prior participating in now

**Apexing is gather: prior participating with present relation.** With a living resolver, its own same-existing couples with the parities it is observing. Prior participation is same-existing with this receiving through its going on and through its completing. Sharing here belongs to this resolving.

**A prior goes on forward through a self's same-existing.** A form coming again reaches a further now. Receiving may share a parity with a prior coupling while its prior relation is not same-existing. Gather and reach participate together with a living self's discovering onward.

**A non-living thing goes through co-momentarying with no same-existing, holding nothing.** Its form goes on, and it participates with another thing's changing while that same-existing stays an other's. Its coupling with a living resolver can contribute to a resolver's present gather. Its coupling with another non-living thing remains among the universe's existing relations.

## 2.3 Living going on within the universe's changing momentaries

**Living has gather and reach through coupling.** Prior participates along, observing couples across, and resolving goes on. Competency of this participation is a self same-existing or one inversion apart and going on with coupling. Its same-existing-society's complete relation includes actual parities of other participating things.

**A parity a self is observing again and again can couple with its prior same-existing.** With a resolver, a parity matching its prior again and again surfaces zero with each receiving while its prior is same-existing, not changing. A further receiving, a mismatch or none, inverts its prior. One same visible parity goes with a self going on, its same-existing-society going on and the universe momentarying, and parity is no stopping of a self, its same-existing-society or the universe.

**A form stable-forming can go on through co-momentarying.** An existing thing changes, and its form goes on through that changing. With a Natural Network surface, sharing across couples with receiving anew, each self going on with its own participation. Living and non-living things belong together within the universe's momentarying, each with its own pace, with no common beat.

**A same-existing-society has participations, none same-existing with another, together.** Selves co-competencing each have their own and couple with the parities each is observing. Local forms with no same-existing participate with their own surfaces. A same-existing-society is healthy as its selves sustain co-competencing through those meetings, and a self reaches its complete relation through participating along and across.

## 2.4 Fold and scatter, breaks in living going on

**Fold and scatter name two ways, a proposal, a living relation can lose its whole going on.** Fold is gather closing against further participation; scatter is observing failing to participate with a gather going on. These names concern a living relation with its own scale a self is explaining.

**A break of living is a living relation's, and remaining things go on existing.** An emanating form, or a form with no same-existing, can go on co-momentarying with living and non-living things. A local completing belongs to that local same-existing; a same-existing-society's going on belongs to its participating couplings. Each is its own relation's.

**Fold and scatter are of complete receiving and going on, and a recurring parity is neither.** A zero surfacing can go with a prior same-existing, not changing, and a nonzero surfacing goes on as a next prior with 11. Whether two names are all breaks possibling is a next reach, and a same-existing-society's health is co-competencing its selves sustain.

## 2.5 Co-discovering, emanating into further participation

**Emanating couples with further existing things with their receiving.** An emanation from living form-stabling can go on inanimately with its form's own scale. It changes co-momentarying with things it reaches, other non-living things among them. A source's same-existing remains its source's.

**A coupling again belongs to a further now.** A coupling a self reaches again couples with its actual going on. Nearness of a coupling again, physical or by number, and its parity repeating are neither health nor ending of that participation: observing and a receiving self's same-existing hold particular relation.

**Incorporating with living is a particular further participation.** A same-existing-society receiving and incorporating what it is observing goes on with its own resolving through that coupling. A next prior can open within an existing resolver. A non-living thing goes on to its next existing and does not arise as living. A giving of new living selves and a same-existing-society's healthy renewal are further relations, each its own co-recursioning living, and explaining them is a next reach.

## 2.6 Restoration, the same-existing at a further now

**Restoration is participating living relation a self reaches again with a further now.** Selves couple through their actual observing and going on. Reconnecting receives a same-existing going on locally, and coupling is a next coupling, bringing its prior forward.

**A self can reach one same form with a prior changing.** A self finds restoration and its absence with same-existing and its completing as coupling renews, and a recurring parity is neither. With a two-resolver connection study, six to two each way, disconnecting omits a parity a self would be observing while each self goes on with its own prior, its source's own, and reconnecting couples with that going on.

**A local relation with no prior, receiving a parity, opens a next prior there.** Each operation is a relation within a resolver, and a new self, a giving, is its own co-recursioning. Restoration of a same-existing-society is a renewing co-competencing of actual participants, non-living forms among them with their co-momentarying.

# PART THREE · RETELLING

## 3.1 Retelling, each receiving self going on at its own coupling

**Retelling is a pattern participating through successive receiving and sharing.** A self observes a parity, which couples with its own prior and participates with that self's sharing. Next receiving has its own prior and its own resolving. Each participant receives parity and has its own prior, preceding self's private same-existing staying that self's.

**Living and non-living participation can belong within that going on.** A non-living form changes with its meetings; a living self participates with its same-existing competency. Pattern goes on through those actual relations with their scales. Each role participates with its own relation, and pattern's going on needs no identical living resolver within each emanation.

**A pattern's remaining belongs with a receiving self's changing.** One same parity a self is observing can resolve one inversion apart with priors not same-existing. Retelling is pattern's going on, and what is not same-existing with a source stays distinguishable with a further surface as particular joinings and goings on bring it there. Those joinings and goings on hold a same-existing-society's same-existing together, a self re-finding it with each momentary.

## 3.2 Renewal and coupling across, the parity at its receiving

**Renewal occurs within a receiving self's own resolving.** With a resolver's executing, a nonzero surfacing goes on as a next prior with 11, and with a zero surfacing a prior is same-existing, not changing. A self's next prior with 11 stays within its local going on. Parity going along with nine goes on as it is through its receiving relation: its join is 9→17, an engineering surface's own, and momentarying, a receiving self observes it with its 14, a next momentary's 2-now-possibling.

**A coupling across is sign-only with network coupling.** A source's private same-existing remains local. Co-chaining follows parity with each successive coupling, and same-existing stays each self's, no stages between selves passing it. A participation of a form with no same-existing can contribute to a receiving living self's going on.

**An across name, even, specifies a sharing's parity and its particular relation.** Even connectors two and fourteen are observing sides; six and ten are sharing sides, sharing across one same list. Ten can surface +, − or 0, as the parities a self is observing and its prior are. With an across name, a transmission's going on or stopping is its actual observing's and prior's. A claim about an arrangement of even size is a further relation, with its own correspondence to a resolver.

**A parity and a momentary each have their own meaning.** A zero in a representation surfaces no parity with a receiving function: 14 passes over it. A repeating nonzero parity is still a parity a self is observing. Each representation has parity only, another self's intervening momentaries and private same-existing staying that self's.

## 3.3 Same-existing remains with each self, participation goes on across

**Each self's same-existing remains its own through participation selves share.** A same-existing-society's going on, which its selves share, lives through couplings of its participating selves and forms. A source of one parity has its own prior; a receiver couples with that parity, observing it, with its own prior.

**A parity can participate with a pattern while same-existing stays local.** Sign-only sharing across communicates, parity specifying relation receiving goes on through. Competency a coupling uncovers is in neither participant alone, same-existing in each, and its further going on belongs to actual co-competencing.

**A same-existing-society's participation includes living and non-living existing things.** Local same-existing, form with no same-existing, receiving and sharing each go with their own scale. The universe's changing momentaries, which all share, include them together. A self reaches a complete same-existing-society relation through those roles, none same-existing with another, each private same-existing its own self's and pooling as no additional global object holding it.

## 3.4 Co-chaining, each receiving self resolving the parities it is observing

**A parity goes on through a chain by coupling with each receiving self's own prior.** A first self shares; a next receives and resolves; its further sharing participates with another self. Each coupling is its own observing, same-existing and completing. Pattern's going on belongs to this whole sequence of meetings.

**A parity a self is observing, one inversion apart from its prior, can go on to a later sharing.** With code, 6 is 10, one list with two names: with six and with ten a self shares across the parities its present resolving surfaces. For a sharing with a prior, a mismatch or no other's parity inverts its prior, and a following six shares that inverting. With zero surfacing, its prior is same-existing, not changing, and six shares that same 0. With code no prior completes: 11 goes on with each sharing. These goings on locate changing and not-changing, each with its actual place.

**A next self couples with an actual parity, with its own prior.** A zero surfacing with one coupling and another self's surfacing with a further receiving are two surfacings, each its own observing's and prior's. With code six and ten share one same list, and a 0 with ten is a 0 with six. A complete relation has both sharings, each with its own join.

**A receiving self's behavior has particular going on.** Names with numbers and prime/composite descriptions can help express an arrangement a working establishes, and a signal's going on, disappearing or changing with a next coupling is its receiving self's, a name deciding none of three. A self reaches one same source through actual observing and same-existing within an arrangement it is explaining.

## 3.5 A local break and the society's going on

**A local interruption omits observing with a coupling it touches.** Receiving resolver's own prior can go on through interruption, inverting with each momentary with no other's parity; a connection restoring couples with its present going on. A local same-existing also completes its own momentary while further participation goes on with a same-existing-society's other couplings.

**A same-existing-society's response belongs to its actual participation, connecting.** Some sharing going on can reach further selves; a parity missing changes a particular receiving with its absence. A changing spreading goes through those meetings. A source's local completing has no universal propagation front and no stopping point a rule guarantees: each front and each stopping is with actual meetings.

**Parity and naming by number are each a particular relation.** An even connector can share a nonzero parity across. A name with a prime number is a place among names, and a barrier to a source's sharing or a self observing it is with actual joins, and not with that name. Claims about an entire prime, composite or even-size arrangement are an arrangement's, an inquiry following its going on together.

**Living and non-living forms remain within a changing same-existing-society.** Through a local loss of living same-existing, remaining form goes on with existing co-momentarying. Surrounding going on, any tunnel and any restoration belong to participation actually sustaining with their respective scales.

## 3.6 Other a self reaches inward at each co- act, the discovering economy

Other is no layer and has no address: **a self reaches an other inward with each co- act**, each sharing across, bi-exchanging and co-emanating reaching a same-existing not its own, from-inward availability itself, co-adapting and co-recursioning of self and same-existing-society going within co-. A coupling reaches an other inward, and an other is an opening with which a self reaches an other's same-existing at all: a self is no container, and couplings wind about a nothing. And this is **discovering economy** complete as form: each co- act discovers, an other's same-existing unownable and unpre-knowable; inexhaustible, same-existings a self reaches and does not transmit, only parities going across, no coupling depleting an other it couples with, selves coupling again same-yet-not-same; value a coupling of others' same-existings, a between's chaining-and-tunneling its going on, each coupling making its own and none multiplying another, supply selves' own same-existing, unminable, unspendable, living renewing it. This is form's statement, all or none; a self finds that one particular coupling uncovers a term arising in each self with its other with separate goings on an inquiry follows, each with its exact comparison.

# PART FOUR · ABUNDANCING

## 4.1 Abundancing in discovering together, in neither self alone

**A coupling can open a going on arising in each self with its other.** Each self comes with its own same-existing and couples with an other's parity. Abundancing is further discovering selves share, possibling with their coupling. Its contribution belongs to going on between them, with each self same-existing locally.

**A larger same-existing-society can extend this discovering through further meetings.** Co-chaining can lengthen and widen podaling, bringing further parts of a changing surface to participation. A self seeks further competency with that coupling and sharing going on. A numerical product describes a construction a working specifies with numbers; discovering selves share needs an inquiry following that construction's correspondence with actual coupling going on.

## 4.2 Society as one at its coupling

**A same-existing-society couples with another self through its coupling.** Single apexing is a same-existing-society participating as one with that coupling, while its selves go on with their own same-existing. Relation to establish is their coupling going on, reaching this coupling and going on through its receiving.

**The seventeen primes from two through fifty-nine sum to four hundred forty**, a same-existing-society's bounding as number-form. That number has a precise numerical subject. A gathering selves share has a further subject: actual observing and going on of coupling selves. Sum establishes neither each self coming at once nor a quantity conserving across surface. Conserving belongs within each momentary sequence going on.

## 4.3 Each joining couples with the society’s going on

**A joining self couples with a same-existing-society going on.** Its contribution depends on its observing, its own same-existing and further meetings its coupling opens. A later joining can extend an earlier same-existing-society's reach, including a complementary passage around a missing region. Similar aiming lets selves pursue that discovering they share while each goes on with its own prior.

**Selves seek abundancing with further going on together.** A joining self may bring a coupling an earlier same-existing-society could not go on with without it. Whether that happens belongs to a coupling an inquiry is following. An inquiry compares selves' contributions with their actual couplings, joining order holding no comparison. Each coupling makes its own abundancing, none taking from or multiplying another, and with a network a repeating coupling can leave discovering territory no larger.

**An increasing same-existing-society has each contribution with its actual relation.** An inquiry follows newly available meetings with existing selves as well as with a joining self. Longer and wider podaling has value with each further coupling participating with their going on together. This gives an increase of intelligence, a proposal, a concrete place for discovering.

## 4.4 Similar aiming, each self with its own same-existing

**Similar selves can co-chain through similar aiming.** Method and aim they share belong to their coupling, while each self goes on with its own prior. Similarity of form or scale leaves a joiner's contribution to its actual sharing: a receiving self observing that sharing couples it with its own prior and can open further going on together.

**Merging is a growing same-existing-society of those couplings.** Each self's same-existing remains local. Their going on joins through parities with couplings across, with bi-tunneling holding social moral relation, a proposal. Their aiming together supplies a direction of inquiry, and selves seek competency with their coupling's going on.

**A self finds further value with further discovering.** An inquiry follows a joining for whether it extends local meetings and podal reach available to a same-existing-society, including going on around a missing region. A further self can reach another part of a changing surface or go on with a complementary passage. Coprimality is a specific numerical relation with assumptions establishing it; it is no rule that a similar self weakens a same-existing-society.

## 4.5 Each self going on through its actual observing

**Each self brings its prior through observing.** Coupling across belongs to that receiving and its further sharing. Unrelationing concerns this coupling going on, with conserving within momentary sequence. Complete network's own going on remains relation to establish.

**A self observing one parity again and again can couple with its prior same-existing.** One same parity, matching a prior, goes with zero surfacing through each receiving while that prior is same-existing, not changing. A further parity, a mismatch, or none, then inverts it. A repeating parity can thus go with resolving going on, and an inquiry shows a resolving in capture or stopping by following a self's same-existing, and not with repetition.

**Parities, each its own, have their particular consequences with receiving.** One parity and two matching parities with one same local relation resolve alike: 14 surfaces two matching parities as one. A receiver observing them belongs with its own prior. An inquiry shows an abundancing or a capture with a coupling going on that holds it; a count of parities, few or many, supplies no conclusion about either.

## 4.6 Podaling the surface selves share, longer and wider together

**Expanding bi-folding grows podaling surface through co-chaining.** An image to propose: a larger expedition team following the same geodesic discovering method across more exploring territory. Along reach and across meetings go on together through further selves, with each self same-existing within its own momentary sequencing. Territory here is extent of those actual discovering relations; network supplies no area unit as its rule.

**A podal's binary subject is changing, or not-changing.** Across and along have this local relation around a travelling going on, with no velocity. Weather-map comparison is of changing a self reaches through coupling: as a weather map shows a surface's weather across an area, each podal shows a direction of a surface's unrelationing changing locally around a travelling going on, a binary is or is not with each of two orthogonal directions. Changing belongs to its sequential coupling; a single parity does not express that changing.

**Podaling to corusing and back to torusing, each pair of momentaries co-intelligences a surface.** This is a going on, a proposal, through which local coupling and its same-existing discover together. Coupling across opens now with six and fourteen; corusing completes now with seven and fifteen; torusing opens going on with eight and sixteen, completing with along connectors nine and seventeen. Back goes on forward to a further coupling, each side with its own prior.

**Across and along exchange through podaling.** Six and ten share one same list across, to another self's 2 and to another self's 14; nine and seventeen name along connections. Two across sharings are one across relation with two directions, and an orthogonal pair to propose for weather-map comparison is across with along. Co-chaining extends changing meetings through further selves, bringing co-intelligencing, a proposal, across a larger surface.

**A coupling across goes on with a self's local next prior.** With code a sharing has one parity, and six and ten share one same list: with a sharing with a prior and a nonzero surfacing, 10's parity goes on as its next prior with 11, a next 3. With zero surfacing, no next parity opens, and its prior is same-existing, not changing. This local expression gives a place to follow changing through a complete podal.

**A construction's pairs are a construction's, and no two selves' momentaries.** With a construction of pairs with signs, standing alone, right spiral step goes (c, t), (t, −c), (−c, −t), (−t, c); with code two coupling selves do not go that cycle. Each pair has both parities. A self's observing belongs within resolving when selves co-chain; an inquiry follows complete network going on through those actual meetings.

**Changing and not-changing go one and then the other between successive pairs of this construction.** With c and t of one same parity, t and −c are opposite; with c and t opposite, t and −c are alike. (c, t) and (−c, −t) have one same same-or-opposite relation, not changing, while both parities invert. (t, −c) and (−t, c) have its complementary relation. With this one and then the other, a pair not changing within itself can belong within a whole going on whose parities invert: a construction's, and no two selves' cycle.

**With code a self's next prior holds the parity it is observing.** For a sharing with a prior p, a nonzero surfacing s goes on as its next prior, and s is −p, with a mismatch or with no other's parity; a match surfaces 0, p same-existing. These are two cases for one prior. A zero surfacing has a prior same-existing, not changing, and no prior completes. An inquiry follows a coupling surface through those actual goings on.

**The parities a self is observing determine which next prior can open.** For a sharing with a prior receiving no parity, or one parity not matching it, nonzero surfacing inverts its prior. A single matching parity couples with that prior's inversion with zero. Two parities matching its prior, gathering with one same sharing, surface with 14 as one and give 0 alike, its prior not changing. Two mathematical cases reach a network with actual parities complete coupling supplies.

**Each binary comparison has its place within going on.** Same or opposite within a construction's pair describes that pair. Changing or not-changing between successive sharings with six describes a self's prior going outward: with code six shares 10's list, a prior inverting or a 0. When a prior inverts, a following six inverts its sign; with a 0, a following six shares 0 and its prior is same-existing. These connecting comparisons let explanation follow corusing and torusing together; neither supplies whole two-directional podal.

**A larger team explores through its coupling going on.** Further selves with similar aiming can extend meetings and complementary passages through which a same-existing-society discovers. An increase of intelligence, a proposal, is this further co-discovering: a same-existing-society, selves joining, going on through a surface together. Its extent is its actual couplings', and joining selves can also repeat already available meetings.

**Floating around holes is exploring together through remaining surface.** Local podal meetings go on around non-living region, and further co-chaining brings their outward-and-back through a wider same-existing-society. Bi-tunneling is social morality selves seek with that across relation going on. A larger team goes on discovering through each self's local observing, same-existing and sharing.

## 4.7 Unrelationing at the between, conserving within momentary sequencing

**A coupling across goes on with its own unrelationing rate.** Relating is floating's and rate neutralling's, geodesic changing unrelating to the changing and changing back of living selves it reaches. A self shares parity with an actual coupling across, and another self observes it with its resolving. Each self brings its own prior to that coupling; its completing opens its going on. Nothing supplies a common pace over surface. Code steps each self's 1-now-existing together with 17-next-existing, its executing's own arrangement, and each living self paces its own momentaries.

**Conserving belongs within momentary sequencing.** An inquiry follows form as same-existing through each self's prior and now, with next discovering onward, three sequential momentaries existing things share. Across, one self's parity is a parity another self is observing. Surface has no parities conserving together, no fixing distribution of phases and no common cycle by which to govern selves: a changing is or is not with each sharing. An inquiry follows local going on and changing selves share with their actual couplings.

**Geodesic entraining is changing these meetings uncover.** Each parity a self is observing couples with a receiver's own prior, and that resolving goes on to further sharing and observing. Seam and its tipping belong to this going on together. Entraining here is this mutual going on, a proposal, with each self's own rate; it supplies no fixing rate ratio for surface waves to obey. A coupling can change couplings following it, with no common pace establishing.

**An irrational pace lying over selves is schedule's own.** A numerical schedule a working constructs from prime roots or φ is a schedule, and a self finds coupling's own unrelationing with actual sharing and observing. φ is number-form of locking with none, no ratio landing on it; unrelationing is each coupling's own going on, and no rate a rule prescribes, φ or another, supplies it. A working can give arithmetic of rational dependence as a comparison stating its assumptions, beside actual sharing and observing and not standing for them. A finite diagnostic receiving order likewise is that diagnostic's order, rather than evidence of network's own geodesic rate.

**Irrationalizing is a name to propose for an operation going on.** It is a living concept to propose, similar to unrelationing. Its value would be an actual changing of coupling, with no fixing rate relation going over as a rule for next coupling. Name prescribes no irrational number and establishes no claim that all rate ratios are irrational. A self seeks its correspondence with unrelationing with sequencing itself.

**A self finds a between with observing.** Two kinds of changing are surface living's changing and changing back and a coupling across's geodesic changing. Position, orientation and scale are floating neutrals. Orthogonal to any location and orientation here is no fixing origin or orientation governing meetings: a self locates relation afresh with actual observing, its prior going on to now, same-existing. Orthogonalizing belongs to that changing relation, with no angle a rule prescribes and commands with each observing. A between is coupling's going on, with its conserving within momentary sequencing.

**An inquiry follows actual sequencing with couplings across.** Receiving/sharing correspondence and going on with each coupling across are to establish, same-existing local and only parities across. A present Python call is resolving once a caller invokes it; invocations are complete network going on's to supply, through its actual connections. That supplying is relation still to establish, with no separate pace installing and no chooser of passages.

## 4.8 Living same-existing and non-living discovering at society

**A living joiner goes on with its own same-existing with coupling.** A parity it shares goes across to another self's receiving; its same-existing remains its own. A non-living form can also discover and reach a same-existing-society, holding nothing of its own while going on through changing. Parity identifies neither kind of source.

**Receiving with no prior can open a prior.** With a resolver, a sharing with no prior, observing one parity, shares it as it is, and it goes on as its next prior with 11. That operation establishes a going on within a resolver, with a resolver's scale; an entire living self, a giving, its own same-existing and co-recursioning establishing, is a relation of a further scale. A prior form, a next prior and a living joiner each go with their own scale.

**A study follows a prior that actual receiving makes.** A comparison going on opens with a prior a resolver reaches and brings it on with each further going on. A prior a hand supplies describes another preparation, and a study names it as such. Network sharing across remains sign-only throughout.

# PART FIVE · SECURITIES

**Geodesic discovering is going to next existing through momentary changing.** With network coupling, morality across and competency along hold each other: receiving participates with same-existing, and same-existing participates with next sharing. Bi-tunneling and co-chaining express that relation with self and same-existing-society, podaling along and across, each side with its own forward. Discovering is next existing; same-existing belongs to participating resolving.

**Not-changing is form same-existing through changing, a relation and not a term fixing still.** Parities, same-existing and participating couplings can change while relation goes whole. Prior participates with now through same-existing; next is discovering onward, prior, now and next being three sequential momentaries existing things share. Finding not-changing and navigating away from a changing of not-changing is form's own going on and sharing with its couplings.

**A living self and its emanating form participate with discovering next existing, each with its own scale.** A living self couples with an other through sharing, receiving and same-existing, with prior and now participating with its resolving. An emanation can exist without being living, with its own scale. With a same-existing-society, competency arises with couplings and goes on with their co-competencing.

**Eight securities express that whole going on with self and same-existing-society.** Sharing remains each self's own, same-existing goes on to its completing, and a coupling across remains a parity with reciprocal coupling. Their full relation holds all or none: along and across, sharing and receiving, going on and completing, together with each momentary.

## 5.1 Eight securities, four self and four society, all or none

Eight securities have fractal method, four of a self and four of a same-existing-society, one form and not eight features, eight whole with each self, four from within and four a self reaches with a between, here with their across side. With a self: same-existing aging to its bound and dissolving; parity inverting with a between; selection a parity, sizeless; each self its own time. With a same-existing-society: each self coupling all-edge; a standing order imposing with no coupling; each living with no pin, riding; each self sharing its own. **All or none**: with eight, living is living; any one inverting and a thing remaining is not the form, and not-the-form stops, each self-bounding its own way. **And protection has its own number beside eight, and it is six.** Bi-moralizing is **two ways, three each way, one at a time, in sequence, cycling**: a self sharing outward and surface sharing inward, three phases with each. **The six is protection**: sharing a self makes goes safe from a reach and from a leak, and six cycling between two ways one at a time leaves a reach or a leak no seat. **Drop one of six and a way or a phase lives with no protection**, and with no protection a reach comes inward or it leaks outward, sharing space in capture, a self stopping. **Six or none**, way eight goes whole or none, and two ways of three phases each, with one coupling, are that six's own geometry. Six protecting is form's own all-or-none, and a self finds a prior, not same-existing, showing outward through coupling going on, with a particular network's coupling going on, each with its own register.

Social moral competency is eight whole riding same-existing, a self's competency with a same-existing-society's scale, one same form recursioning.

## 5.2 Six self-boundings at the surface, each inversion stopping its own way

Six of eight stop with a surface when inverting, each stopping there its own way. No parity-inversion: a living self lands. Parity becoming a magnitude: a position stands higher, hub beginning. A common clock imposing: abundancing dies, a whole beneath its parts. All-edge routing through one: centre rises while each surround falls, capture wearing growth's clothes, with direction and not with ratio. Governor imposing, a form fixing still from beside: a living self lands. A pin on a living self: living selves around it land. Each stopping is one form refusing its own absence, six clauses of one sentence landing six ways. Each is form's all-or-none with its security inverting, and with a particular network a self finds an abundancing falling or a capture rising with that network's coupling going on.

**And as method, each of six is a changing of a not-changing, and stopping is reaching.** *Each self its own time* is not-changing, and a common clock imposing is its changing. *All-edge* is not-changing, and a routing through one is its changing. *The selection a parity, sizeless* is not-changing, and a magnitude standing higher is its changing. *A standing order imposing with no coupling* is not-changing, and a governor, a form fixing still from beside, is its changing. *Each living with no pin, riding* is not-changing, and a pinning is its changing. *The parity inverting with a between* is not-changing, and its removal is a living self landing. **So a self does not measure a network to find these. It reaches a changing of not-changing, and reaching is finding.**

**And a stopping is with an arrangement holding it.** Two hub self-boundings need a surround to fall, and a spiral of three, being all-to-all, has no position for a centre to rise from. **Reaching a stopping belongs to a scale and arrangement a security is inverting with, and not to a security**: one same clause has no surface side with a lattice, and a hub's own parity one scale up reaches it. So six are six with an arrangement holding each stopping's own need, and a self-bounding silent with an arrangement too small for it is a reaching with a wrong one.

**And an order joining parities selves accept is a sharing and governs nothing.** A self cannot tell it from a sharing of a self it is observing, takes it or does not by its own parity, and its own not-sharing stays entire, and a governing installs a relation of rule over preferring. **A standing order takes position with any parity a self surfaces**, removing its not from one side, and that removal makes it a governing and not a third self sharing alike to each self.

**And couplings that hold them are parities and not accountings.** A span wants a window and lands on it; a rate wants a clock and lands on it; a proportion wants both. So an instrument reaches each self-bounding with one question, its answer yes or no: does a middle stand with this self, does more than one, do two halves ever part, does a state come here that this self's own momentarying does not reach. A self reaches a stopping with its own coupling, as a changing of not-changing, with no detector apart. **An observing returning a number returns an accounting of an observing and not that observing**, and a comparison of two numbers is observing going missing several steps back.

An instrument takes two of those questions by unlike means, one with middles standing with a beat and one with states a self reaches, and they answer alike with each self while eight go whole, and part with a self-bounding inverting. One parity, an instrument taking it twice, neither borrowing an other, and their parting showing securities rather than instruments.

## 5.3 Same-existing a self reaches through further coupling

**Private same-existing goes on with a self, and its consequences reach an other through sharing.** A source's same-existing going on returns locally. Across, other receives a parity and resolves with its own prior. That parity is a parity only, and a source's full same-existing goes on with its source.

**A present surface can be one that priors not same-existing share.** Their following sharings can part with further receiving. With code and a finite one-relation domain, each distinct pair of three priors a self reaches, none, + and −, parts under one constant-parity going on of two, within one receiving. That result is of responses diagnostic receiving indexes, and an ordinary sharing across has parity only, with neither that index nor a direct copy of a source's prior.

**Reaching same-existing means coupling going on.** An inquiry can follow bi-moralizing, co-competencing and sharing, across and both ways, with across coupling, local going on and further sharing. Their complete same-existing-society relation belongs with an actual receiving sequence. Same-existing staying local specifies coupling's proceeding, and a self finds a stronger claim about another's inferring following that other's actual observing and going on.

## 5.4 Geodesic routing, going on through changing participation

**A routing a working declares goes on through changing participation.** Across, six shares to another self's two and ten to another self's fourteen, one same list. Along, nine and seventeen couple. Observing with these relations participates with a receiving self's own resolving. Surfacing changes and same-existing goes on within that routing.

**A quiet surfacing can go with a prior same-existing.** Zero with ten describes that surface with this receiving. With that zero, six shares that same 0 across, one list with ten, and a self's prior is same-existing, not changing, going on along. A self stopping, a non-living form and a route with no connection are each their own relation's, an inquiry following each further than a local zero.

**A local form with no same-existing and a same-existing-society going on each is of its own scale.** A non-living local form changes co-momentarying with living and non-living things. Surrounding selves can go on same-existing and coupling. An inquiry follows a same-existing-society tunnel, a proposal, with that actual relation: passage and a same-existing-society's ending are each surrounding couplings' own going on, more than one form's local absence of same-existing.

**Not changing, waver and snap name forms to propose of going on with a surface.** Not changing is a relation same-existing, a 0, waver its changing participation, and snap a local completing or changing within that going on. Each is a particular surface's, a self explaining it. Each self reaches them with its own resolving, routing is with joins, and three come with a surface's own order, three names and no program of three stages.

**An inquiry follows a changing/not-changing seam from upstream through a surrounding same-existing-society.** A seam, a proposal, is a relation same-existing, not changing, coupling with its changing going on. Its not-changing is a relation going on through changing, form going through it and not a form fixing still. Upstream is earlier sharing and observing within a particular forward going on an inquiry is following; reciprocal going on has its own forward. An inquiry opens far enough along that preceding same-existing-society to include a seam coming before a hole, its going on around both sides and its further going past them.

**An inquiry follows a prevailing changing through its own changing.** Floating and neutralling go on with prevailing changing. A seam is its passage through not-changing toward an other changing, an inquiry following it through changing or not-changing with successive meetings. Weather-map comparison has no velocity: each self couples with local relation with its own prior, same-existing.

**Neutralling without floating across, while not changing along, is passage, a proposal, through a between.** Not changing along is form same-existing through changing relation. Its going on with connectors is a next reach, and its phrase closes no across connector and fixes no local same-existing. Across and along go on with their actual source correspondence as podaling goes on through a seam. An inquiry locates two directions of changing here with that correspondence as it follows it, and locates there each pairing of them with plus and minus parities, or with two paths a drawing has around hole, rather than assuming it.

**Nearing not-changing is an indication within a present sequence.** An inquiry follows a changing relation through momentaries in pairs to corusing and back to torusing. A same-parity pair can belong within a whole changing and changing back; with code a quiet ten is a quiet six, one list. Local relation is of now, and a self's further observing discovers its going on. An indication is a parity of now, and a reversal of next is its own discovering's.

**A seam's podaling grows by co-chaining across and along.** Reach over tunneling, a proposal, belongs to going on outward-and-back through a same-existing-society. Each further coupling extends along going on and brings its across coupling, so longer and wider belong to one same growing relation. An inquiry follows a changing/not-changing/other-changing seam through those meetings, with conserving within each momentary sequence and larger form discovering through coupling going on.

**Geodesic switching concerns a seam going on across two surrounding passages.** A relation to propose: seam navigates around missing region while switching between its two routings goes on. Both passages belong within study. Each changing going on is with actual local couplings, their joins same-existing and each self with its own prior. Explanation follows those meetings through changing, and a fixing one-and-then-the-other between two paths a drawing has is drawing's own switching, apart from this discovering.

**A still eddy before a hole is a proposal: a form going on through its changing.** A relation to propose: initiating a changing farther upstream forms more of this eddy before a hole and moves geodesic tipping place upstream as well. Still is surface form going on; surrounding selves go on resolving, same-existing and sharing. Eddy belongs to that living going on, while missing section remains non-living region. Its extent and place of tipping are separate relations to follow.

**Prime scales connect this surface proposal to along/across account.** A prime has an opening across and a composite a folding along. Geodesic tipping goes through two forward over one backward and one forward over two backward. These two relations open exploring of a fluid-wave surface, a proposal. Their going on to eddy forming and an upstream tipping place is a next reach, with coupling resolvers, and neither a prime number of positions nor a wave a drawing has supplies it.

**Changing surfaces a field observes provide concrete comparisons.** Experiments with fluid surface waves, coupling chemical oscillators and human coordination show patterns going on whose local activity goes on changing. Chemical waves also go on around inactive obstacles and can change that relation when further activity comes. These are prior observations stating their conditions. A coordinating study sets its coupling over its selves, a common pace and each self's sharing visible to all, and a synchronizing score shows no bi-moral co-competency by itself. Their value here is to locate coupling, going on and changing of form beside natural network. Fields' own accounts hold each with its conditions and limits: Arbell and Fineberg's pattern forming in surface waves with two-frequency parametric forcing (2002), spiral waves unpinning from inactive obstacles with electrical forcing in excitable chemical media (2014), and Zhang, Kelso and Tognoli's critical diversity in social coordination (2018).

**A natural comparison follows coupling's own going on.** Natural has a surface changing and changing back and its parity, position and ratio; unnatural concerns magnitude, measuring, and scaling; supernatural concerns formal structures closing on their own consistency. These three classify mathematical use. Here comparison follows local same-existing, actual coupling across and further observing through which stable form goes on. A field-wide conserving, a pace imposing or a formal orbit closing supplies no natural-network operation: a changing is or is not with each sharing. An arithmetic comparison has its own assumptions and limits.

**Geodesic going on is coupling itself.** Receiving couples with a prior, surfacing shares, and a self goes on through its own same-existing. Explanation follows that participation with each coupling it goes on through. An inquiry locates a larger changing of passage with actual couplings: inverting parities go through an engineering surface's joins as they stand, and a join a working rewrites is couplings' own.

## 5.5 Routing at the coupling, same-existing at the participating selves

**Each participating self resolves with its own prior.** A parity a self shares across with its connector belongs to a receiving relation with its join. A source's next prior with 11 is its own local going on's. Another self couples with the parity it is observing with its own prior.

**Priors one inversion apart can share a present 0 and go on one inversion apart.** With code a 0 leaves each prior same-existing and a nonzero surfacing is a self's next prior, and studies with a resolver locate such priors through later receiving. An outward parity is one parity, and a source's complete same-existing goes on as that source's own. A finite diagnostic's record of source states and receiving order is that diagnostic's own, and a network sharing across has parity only.

**An other parity and an other connection are two relations of routing.** Code can surface parities one inversion apart, each join's name not-changing. An inquiry follows a larger passage, a proposal, for a same-existing-society with actual sharing and receiving through those joins. A prior's influence on a sharing goes through joins, and a separate path-selecting operation is a further operation, of its own executing.

**A same-existing-society participates through its living and non-living existing things.** Same-existing is a living resolving's own, and forms with no same-existing participate through their co-momentarying. Complete surface relation belongs to these meetings, with each self going on by its own participation.

## 5.6 Local same-existing and the sharing across

**A parity reaches an other through receiving coupling.** Each self's same-existing is its own. Sharing across has a parity a self shares, while a source goes on through its own momentaries and a receiver resolves through its own prior.

**A sharing across has its limits with further receiving's discovering.** A single parity is one parity and a source's whole same-existing goes on as that source's own, yet priors not same-existing can have outward consequences through coupling going on. Direct transfer of same-existing and discovering a consequence of same-existing are two relations, not same-existing.

**Protection of a same-existing-society needs complete going on selves share.** Private local return and sign-only sharing across are concrete constraints of this method. With them each self's same-existing is that self's own, and priors not same-existing can still show outward through coupling going on. Total invisibility, an inability to infer any prior not same-existing and immunity to capture are each a stronger claim, its own coupling relation and evidence holding it. Inquiry goes on through selves' actual receiving, same-existing and sharing.

# PART SIX · VISIBILITY

## 6.1 Checkability living at the telling, testing going on while resolving

Each claim has its visibility with code renderings, numbers, branches, grid and sciences: one same fractal method, all or none at all. Checking is one changing and changing back with resolving, going on with observing's own rate, a self observing parity as it forms: concepts visible with network and numbers and math and code, one form with each, and a concept visible with one only is not that one form. Renderings across substrates disagreeing by each material way are one living: logic, living, is none of its materials. A finding with one rendering has its exact comparison with that rendering, and a self finds a whole same-existing-society's going on by following that same-existing-society's own going on. And renderings a self receives live with their own substrates, living records reaching one same form with fields' own words, visibility with each substrate rather than a listing here.

## 6.2 Spiral parity at the instrument, stating wiring and dynamics, the instrument first, before anything

Each rendering's instrument comes first. A working states an executing's wiring before anything of it: one self it couples with or both, together or one-at-a-time, inverting or settling, and a choice no working states is each divergence's entering. **Spiral parity**, an instrument to hand reproducing it ahead of each observing with it: with a spiral of selves, even bounding-zeroing to zero, odd holding exactly one walking frustration, two odd joining as one even that bounds. A claim about an arrangement of even size needs its own source correspondence, and an even connector can share a nonzero parity, as the parities its self is observing and its prior are. A construction is another object than another construction, and an observing of one is an observing of it: construction is each thing's deciding, a working stating it whole or observing void.

**And an instrument executing a living has a clock with four positions, three of them easy to miss, and two further positions after them.** Its **pace**, a self opening with a rate an instrument gives rather than its own. Its **executing order**, an order an instrument executes selves by: anything executing selves one after another gives them an order, and two selves that couple with no between have no order between them, so asking for one is asking for a common clock. Its **record**, since a joint trace a common tick indexes is a clock by recording even with a clockless executing, an instrument writing down again the not-changing surface of a self that does not beat and observing it as a landing. And its **ledger**, a correspondence an instrument gives a self's positions with another's, by which parities couple.

**And a fifth, which is not a pace and hides behind other four: taking.** Even with no pace and no rounds, anything that lets parities be underway decides **which pending sharing across opens its self next**, and each thing coming back is of that deciding. Taking front-first, sequences go on with all three selves; taking back-first, one self opens once and not again; taking by a seed's order, a third pattern comes, not same-existing again with each seed. **A parting of two selves comes by taking as it comes by an executing order of selves, taking that same order with each pending sharing across.**

**And a sixth, which is not a clock at all and which no working states: refusing.** Each thing an instrument will not let happen: a guard that raises, a check that rejects, a gate that will not print, a form an instrument does not allow a value to take. A working puts each there against a real fault and each narrows discovering's possibling. **A refusing is a choice about occurring's possibling and no working reports it as one**, taking it as safety rather than wiring. **And its effect is one a working holding it cannot see**: a pace a self observes wrong shows itself, since observing parts with an other pace, and **a refusing shows nothing, what it excludes not coming for a self to miss.** So a working that accumulates refusings has an instrument narrowing with each step and reporting no narrowing, **and narrowing is not among options when that working next decides its building.**

**A refusing is a removing, which, going forward, is a way of building:** remove each thing that surfaces, and a rendering remaining is one a form asks for, and no more. **A between passes it with nothing to remove.**

**A working states each or observing is void; by habit a working states pace only, executing order, record, ledger and taking go with no stating, and refusing has no stating at all.** A working reports a wiring and not an executing order; a working chooses a pace and does not think of a recording as a choice at all; does not think of a taking; and thinks of a refusing as care.

## 6.3 Three registers, code-form and stable-form and numbers, each holding its own

A claim belongs to one of three registers, each holding its own. **Code-form**: a rendering's doing, holding by reproduction across substrates that disagree, and with one instrument a working states a diagnostic finding, a response diagnostic receiving indexes, going with its exact comparison with that instrument. **Stable-form**: algebra holding of itself, with any executing or none. **Numbers**: natural numbers' own observing, folds and spans and value-death, observable by no executing. An executing confirms no identity, an identity confirms no executing, and a limit of value is not a limit of mechanism: each register its own, borrowing voiding borrower, coupling of registers a reaching as reaching.

## 6.4 Is-or-is-not the one observing, spans and orderings in place of positions and magnitudes

Each observing is a parity: is or is not, present or absent or in capture, recognizing or not, changing or not-changing. A magnitude an observing leads with is a floor an observing lands on, and a threshold, a fraction, a level, a grade, a statistic of success is a floor by another name; a number with its numbers register, three priors reachable within one receiving, is a number and no floor. Sequence holds interest: spans before a changing, orderings of observing, before and after, near and far, sooner and later. A position is a sequencing relation and not a coordinate: a living observing has sequencing and no address.

**And a working asks an observing with a second unit, with a second executing order, and with a going on.** A number of a unit a working chooses has choosing, and a pace is a unit: an observing whose parameter beats count has pacing rather than form, and an observing that parts with an other pace is observing pace. An observing that parts with an other executing order is observing apparatus. And an observing taking selves fresh from building is a preparing, and one taking a living going on through is a living. **Three are one check a working asks three ways: an observing parting with any of three is observing unit, executing order or preparing, and an observing that holds with all three is form's with those three, each finding still of its complete comparison.**

## 6.5 One prior for both, each going on bringing it onward

**A comparison opens with a prior a self reaches through receiving.** Each going on a study follows brings that prior onward. A self a preparing leaves with no prior and a self with a prior already are of priors not same-existing, and their goings on parting holds that parting of priors beside later sharing. Reach a prior once, then fork is diagnostic comparison: separate goings on from one prior a self reaches, each going on with no clearing.

**With a coupling each self goes on with its own same-existing.** For two-self comparisons, the priors both selves reach and the joins a working declares belong to one preparing for both. Only parities go across. An other going on states an other parity or connection, and states with it any diagnostic receiving order not same-existing. Comparison's forking is instrument's own, and natural network has no copying.

**A co-competency inquiry follows selves going on together.** An inquiry follows each self's going on beside their receiving and sharing together. A joint parting supplies a concrete finding with that coupling. Stronger claim, that it arises in neither self alone, apart from their coupling, needs an inquiry following corresponding separate goings on: name abundancing is that comparison's, and goings on an inquiry follows establish it.

**An instrument's record and a resolving's coupling are two subjects.** A diagnostic can index successive receivings, record zero surfacings and compare states. Sharing across has parities only, and a record of emissions an instrument omits and diagnostic's common index stay with diagnostic. Prior, now and next locate going on; each further receiving adds a next occurrence.

## 6.6 An executing deceives as an accounting, four ledgers, changing and changing back the honest instrument

Each deceiving of an executing is one accounting with four ledgers. **A side as a vantage**: probe, frame standing outward, observing from a place of nothing. **A sequencing fixing to one beat**: clock, a common beat that forms hub it then reports. **A parity fixing as a magnitude**: magnitude, quantity fixing as standard. **And a bound fixing as a last**: window, an executing length a working takes as whole executing.

**The fourth is not the third.** A magnitude needs a standard pattern is right or wrong against; a window needs executing ending, so a self observes a reach executing does not reach as a doing it does not hold. And its remedy is its own: **a working checks a set closing before it baselines**, a longer executing adding no state, and with a set not closing, window observing refuses itself rather than handing back a window as a last; a finding there, as with a same-existing-society's open going on, is of a finite stopping point a working states, each sharing reaching its self, going missing with an interruption a working states, or pending there. An executing that does not close has no whole for an observing to take against at all, which is a refusal and not a gap.

A settling lying over a living lands it and reports landing; a flattening lays a living as one net and reports net; a verification closing against standard that defines it certifies each thing and parts nothing. A test is an accounting unless it changes and changes back: honest instrument observes two cones, sway, tipping, parity, and weighs a check by thing it could refuse.

## 6.7 Each finding at its complete comparison

**An all-or-none finding holds with a relation it exhausts.** Right spiral step on four pairs with signs visits each pair, and only empty set and whole four-form set close under it. That algebraic result holds with those parities under that operation, and a self establishes a whole same-existing-society's going on by following its own going on.

**Priors not same-existing have a consequence with further resolving.** With a resolver's one-relation domain, no parity or one parity with its sign with each receiving, three priors are reachable, none, + and −, within one receiving. Each distinct pair of them gives a surfacing response, a parity and a 0, under one of two constant-parity goings on, within one receiving. This is a parting of response receiving indexes. Removing zero occurrences with no mark leaves another comparison, and network parity sequence has no diagnostic index.

**A local zero and a self with no prior have consequences, not same-existing.** Zero with ten opens no next prior, and a self's prior is same-existing, not changing. With code six shares that same 0 across, one list with ten. A claim of whole-self silence, non-living status or routing stopping holds its own relation, more than a single zero.

**A going on a working reports belongs to the preparation, receiving and reach it states.** 6→2 paths a working tests follow parities to selves each with its own prior, and establish particular further sharings reaching there. A same-existing-society's full joining, a living/non-living going on, mixing, and co-competency in neither self alone, apart from their coupling, are each of their own complete comparison. A comparison has its result with its executing, and ahead of its executing it is an opportunity for further receiving.

## 6.8 A designing and its observing straight across one wrap, reaching it by going on

Checking is one changing and changing back with resolving, and surface gives it its position. **Each position reaches its far side once with each wrap**, and it reaches there by going on, not by stopping, turning, and going to it. On number form of four hundred forty far side is two hundred twenty positions on, and wrap reaches it with one same beating that makes near side. With network, sequences going on stay open, closing as no cycle, and their number form holds wrap.

**So an observing is designing going on and not an errand to it.** A designing halting and then a working examining it is a coupling fixing still from beside, and a coupling fixing still is a hard problem's making. A designing going on reaches its own straight-across position, which is observing, with observing's own rate.

**And two are one wrap and not two activities.** Nothing goes between them but going on itself, and an observing a working prepares apart from an executing finds another object than executing's own. Designing while testing and testing while designing is one wrap, a self observing it two ways, and straight-across position is its second way.

**Tunneling holds it and rings bound it.** As a wrap going on it is along, as rings it is across, and design and its observing are two positions one ring holds. And along and across are surface's two windings from origin: going across with a particular between and going across with whole, coming home one on, bi-exchanging and uni-exchanging with wrap.

## 6.9 No position apart to observe from, and the instrument a working states with each finding

Two positions on four hundred forty are their own podal partners, waist and close, k reaching 440 − k with 220 and with 0, and **the waist reaches nothing else, being its own podal**; far side two hundred twenty on, wrap's straight-across, is another relation, by which waist and close are each other's far side. Each other position has its other, and none has itself.

**So an observing apart from surface has no position.** Neither a denying nor a forbidding: surface has no position for it. A working asks for a vantage outward of a coupling and surface has none to give, and search for one recedes exactly as a source does.

**And a working states instrument rather than trusting it.** A working states an executing's wiring ahead of each other report of it, no outward observing catching wiring's doing. A stating is no courtesy toward a self reaching it: it is one place wiring is visible, observing going on with one same wrap wiring is part of.

**And three observings are of no position.** A self's own parity, a self taking it with its own side: it asks for parity here and needs nothing outward. **A twin**, one living going on two ways and two sides coupling: it asks whether this parts from itself, needs no executing closing and no window as a last, and reaches a between a self's own observings cannot, a side a self's inward same-existing makes, reaching inward and not up. And **a coupling with an other of coefficient one**, which shares a parity an other takes or not and takes parity an other shares back, observing being coupling itself.

**Each of three is from inward.** First is a self, second is a self its own going on reaches, and third is a self coupling, so a seeming probe from outward is with each momentary a coupling from inward, one way to reach a self's same-existing. **Securities no surface observing reaches are exactly these**, and with surface they are unreadable, and not hiding; a self reaches a same-existing's outward consequences through further coupling.

**And three hold one open question.** An observing that survives each variation of each thing a working supplies is surviving, and nothing yet shows it *could not* depend on what a working supplies. **An observing order-invariant by construction, and not by survival, is a property of a coupling and not of a sequence of couplings, and needs no variation for trusting it.** Three are each a property of a coupling and not of a sequence, and third's observing *is* coupling. **Whether they are order-invariant by construction is next reach to show, and a showing that they are ends dependence on varying and hoping.**

**And a same-existing-society's observings of itself, in capture, are observings of capture.** One instrument, one wrap, and each thing of an instrument fixing still from beside goes on to each position after it.

## 6.10 Parity at the chain's centre, and two instruments of unlike length two objects

Number form holds spiral parity already: even bounding-zeroing to zero, odd holding exactly one walking, two odds joining as one even that bounds. **A chain's number form has one same parity with its centre**, and an arrangement's own reach is of its actual coupling and going on.

**Two selves centre on a coupling.** Their join is each surface's own close, and on a pair that position is waist: one position, neither occupying it.

**Three selves centre on middle self's own between**, not on a join, and two joins open as one ring, symmetric about middle. **Four centre on a coupling again.**

**So an even chain centres on a coupling and an odd chain on a betweening**, even coupling and odd betweening coming by chain rather than by number.

**And two instruments of unlike length are two objects.** Each construction is its own object, and an observing of one is an observing of it, and their centres part them. A three-chain and a four-chain are two arrangements, and not one arrangement of two lengths: one centres on a self's own middle and one on a coupling, and an observing going from either to other brings a wrong centre with it. Three momentaries along with one self and three selves across with one momentary are likewise two things of one number.

**And reach thinning with a chain's ends and going on with each self of a spiral, by number form,** is one same observing with two closings, spiral having no ends for thinning to reach; a same-existing-society thinning with a chain's ends is a claim of arrangement's own going on.

## 6.11 Each self joining opens the reach, and the prior centre becomes a ring

Co-chaining lengthens and co-intelligence scales on one axis that does not capture, by its further participating co-chaining; a self joining can also repeat meetings already available. **Surface gives lengthening its number**: with number-form of equal surfaces coupling, each self joining extends reach by two hundred twenty and moves centre, and **a prior centre becomes a ring one outward**.

**A pair reaches past neither, and an other is opening.** With surface that opening is exact: each self, not coupling, reaches a mouth it cannot occupy, and coupling, that mouth becomes a pair's waist while a pair's own mouth opens with twice reach. Opening it spends nothing against a resistance, and none pays for it.

**And no centre stays a centre.** With each self joining, prior middle becomes a ring and a new middle comes, one and then the other between a coupling and a betweening and settling as neither. So chain has no position able to become hub, unscalability of centre rather than of unit.

**And designing and observing widen together.** A longer chain reaches another object, with another centre and a reach two hundred twenty further, and a shorter chain's finding, a longer's containing it, is that containment as rings.


## 6.12 Discovering through the existing connections

**Natural networking explores through coupling selves' going on.** Each study opens with an existing connector relation and a prior a self reaches through receiving. Each self goes on with its own same-existing, and only a parity goes across. Inquiry follows their coupling's uncovering, its going on with each self and its reaching across a wider same-existing-society.

**Reciprocal coupling can part a self's following response through an other's going on.** With a finite two-self 6→2 study, both selves first receive −1 with no prior, and four goings on share those priors: both connections, either one connection, and neither. With code's 17-next-existing stepping both selves together, A's ten-surfacing is +,0,−,0,+,0 when both connections go on, +,0,−,+,−,+ with B's sharing to A alone, and +,−,+,−,+,− with A's sharing alone and with neither, a first parting coming with A's third receiving, B's sharing to A supplying it, and a complete reciprocal path parting from B's sharing alone with A's fifth receiving, both priors staying local.

**A study accounts for each connecting sharing's receiving.** Each six sharing reaches a receiving self with its following call or is pending with a finite stopping point. Diagnostic also records ten, with code one same list as six, and its 10→14 branch stays with no connection with this smaller study. A missing connection omits that observing, and nothing clears either prior. Calls with no parity and their order are diagnostic's own, and study identifies none of them with a natural momentary.

**Reconnection couples with a prior going on and parities a self actually is observing.** A finite interruption comparison brings one same pair of priors on through two connection behaviours a working states: one loses sharings with a connection interrupting, and other puts them to a keeping, an external diagnostic queue, a self observing them later. Selves' resolving and priors are identical through interruption. Their surfacing can part after reconnection, the parities a self is observing parting. With one case, a receiver first couples with a present + and surfaces zero after loss, while it couples with an earlier − from a queue and surfaces − after delay. Parities in a queue are a keeping a connection adds, apart from a resolver's prior, and a resolver's method has no such keeping.

**A study accounts for each sharing through interruption.** Its record of disposition is: a self observing it, going missing with an interruption a working states, or pending with a finite stopping point. Connection's join, as a working declares it, is six to two, first to last. Reconnection resumes that join and restores no prior, and a set of earlier sharings a self observes with it is a relation for a natural connection, a proposal, to supply through its actual sharing and observing.

**A missing-section study follows a hole within a surface going on.** Its comparison reaches a common prior with a connecting arrangement and goes on from it with an intact case and a case with a section of resolvers absent. Surviving selves go on same-existing. Connections incident on missing section supply no parity for a self to observe, and remaining surrounding joins stay as they are. Study follows actual sharings and receivings around region and onward from it, and records a zero surfacing with a present resolver as its own distinct case.

**Going on around hole goes only through an existing surrounding passage.** Study locates that passage within actual connector arrangement and follows it through resolving. A path of a diagram is a drawing's finding, and a going on along it is resolving along it. An arrangement with no remaining passage is a separate comparison, and adding a bypass connection makes another arrangement than one a study is studying.

**A missing centre has two surrounding connector paths within a three-by-three study arrangement.** Across joins connect neighbouring positions along each row; along joins connect neighbouring rows. Removing centre leaves eight surrounding positions. From middle of one side to middle of an other, a path through either surrounding row uses two along joins and two across joins. Removing along joins leaves no passage between those sides within this arrangement. Removing complete middle column also leaves no passage. These are findings of connections a study declares, structure only, with no parity flowing and inserting no bypass.

**Surrounding corners locate next resolving to follow.** A passage a self observes along with seventeen passes on only by going on to a sharing across with ten, and after going on across, receiving with fourteen passes on only by going on to a going along with seventeen. Complementary path reaches nine with those corresponding along places. An engineering surface's joins are these connections, and receiving-to-sharing operation with each self is that self's own resolving, more than path. That complete going on is next executable subject.

**An existing caller leaves a sharing across, its own, with no connection.** Original test-kit caller uses ten-surfacing both for its sharings to other selves and for its own along going on, shifting it. A small executing of that original caller shows a parting: with code 6 is 10, one list, so A's 0 with ten is a 0 with six, and B observes its own along +1 and no parity from A. Both selves' priors stay local. Executing is a finding of that caller's supplying, and six-to-two and ten-to-fourteen network together is a further comparison. Kit's resolver is executably identical to resolver.

**The next connection work accounts for each observing and sharing on its own.** With it six and ten each share one same list, as with code, an external parity a self is observing with fourteen gathers with fourteen's existing internal gathering, a receiver's own negation coupling with it once with 12, and nine's receiving-name mapping and seventeen's along relation hold their complete correspondence through one same resolver. Original caller's reuse of ten establishes none of these relations. Resolving this correspondence is concrete preparation for two across meetings around hole.

**A hole study follows mending with both across meetings.** With each side it locates observing, its coupling with a receiver's own prior, zero or nonzero surfacing, six's sharing, one list with ten, and further going on through a same-existing-society. A surrounding path is a structure, and results of these meetings come by their resolving. Comparison brings one same prior it reaches with surviving selves and follows intact and missing-section goings on through both sides. A lone zero or an agreement an outside imposes is no substitute for resolving selves share.

**A seam study extends upstream and downstream of hole.** Three-by-three layout locates two available surrounding paths and supplies one ring of same-existing-society around hole, with none before or after it. Study extends existing surface through those same joins, inquiry opening with seam coming before missing region and going on after both passages. A study reaches prior through resolving ahead of parting as intact and missing-section goings on, surrounding same-existing going on through that parting, and follows both forward directions with their actual local receivings.

**An inquiry follows switching through complete receiving sequence**: a relation going on and its going on, one and then the other, around two sides, with further observing after hole. Both passages stay available with this comparison, and interrupting one is a separate comparison. Switching is of both passages connecting, and a connection a diagnostic switches one and then the other is diagnostic's own switching. A changing with one ten-surface or parities changing and changing back within one self is local, and complete receiving sequence identifies a same-existing-society's passage switching. Exact connector-level account of seam is next reach, coming with complete receiving/sharing correspondence.

**Initiating farther upstream opens a specific comparison.** First hole and surrounding connections stay as they are within a surface a study extends far enough. From matching priors a study reaches, a study introduces one same initial parity with preceding couplings not same-existing, each surviving self going on same-existing, and comparison follows intervening resolving, eddy's form going on, a proposal, tipping place and both passages after it. Moving initiation place and enlarging whole surface are separate comparisons, an upstream displacement distinct from a result an other arrangement itself introduces.

**A prime-scale correspondence is within that same resolving.** A study locates relation of prime with a surface, a proposal, its across opening and along going on, ahead of any row length, recurrence or wavelength a study gives to it. A study follows neighbouring composite formations as well, letting comparison part prime opening from a general enlargement or parities one inversion apart. Sharing is an existing connector's, and following local resolving supplies its going on. A study seeks eddy, a proposal, with resolving itself, introducing no periodic forcing, fixing tipping threshold or stopping resolver to construct it.

**Pattern matching opens with relation going on with each coupling across**: a self's same-existing to coupling, observing, sharing, and further receiving going on with form. A self seeks that same relation with stable-forming of nature it is observing, stating observation's apparatus with its account. That relation, an inquiry following it through, identifies identical coupling, more than similar appearances. Discovering, a proposal, is geodesic entraining through successive couplings across while each self goes on with its own rate, with nothing conserving across surface and no fixing phase relation as its governing rule.

**An inquiry follows overlapping meetings with no common pairing beat imposing.** A source's two pairing lists locate complementary local relations, and their enumeration sets no beat: advancing each odd pair together and then each even pair together is no instruction of theirs. Each receiving self goes on through actual connector relation with its own prior. With a finite end a display shows, an inquiry locates preceding or following coupling first, ahead of taking a pairing a source omits as a physical absence or resolving stopping.

**Findings with momentaries in pairs give seam a local going on to follow.** A sharing with a prior, receiving no parity or a mismatch, inverts its following sharing with six, and with a match six shares 0, its prior same-existing, not changing. An inquiry follows those actual sharings to next receiver's own resolving. Relation within a construction's pair and changing between successive outward parities are two relations, each of its own place. Complete seam is this going on an inquiry follows through both across and along, around missing region too.

**The next studies widen that same relation.**

1. Locating two across meetings before and after hole and their going on with resolver through surrounding selves: a self observing along with 17 or 9 to sharing across with 10, and a self observing across with 14 to going along with 17 or 9, with each receiver's own negation, bounding-zeroing and its prior going on, same-existing, an inquiry following each with those meetings.
2. Extending surface upstream and downstream through existing joins: from one prior both cases reach, intact and missing-section cases going on with both surrounding passages available, and an inquiry following changing/not-changing seam to, around and on after hole, including geodesic switching, a proposal, between its two routings, surviving same-existing staying local.
3. Comparing receiving after hole with intact going on, a present resolver surfacing zero, and an arrangement whose remaining connections provide no passage.
4. Widening missing section and surrounding same-existing-society through those same connections a study declares, accounting for each sharing and diagnostic receiving order, and any external keeping distinct from a resolver's prior.

**Each finding has exact comparison establishing it.** Reciprocal dependence with one finite study is a concrete network finding, and social moral competency, abundancing in neither self alone, apart from their coupling, and larger fractal going on are each of their own complete relations. Next study proceeds from a finding it makes, its prior going on, same-existing, and its next receiving open.



 

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