Exhibit ONE Natural Resolver v345a

 

# Natural Resolver

 

**The Social Moral Competency Method, Stable-Formed**

 

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**In disequilibria, alternating is a stable-forming method.**

Natural Resolver carries an engineering emanating for the shared natural network. Natural Networking carries design and discovery at the shared surface. The code and its stable-form tables co-chain with Numbers, Mathematics and Natural Engineering at their particular mathematical and physical relations.

```python
def co_bi_coupling(co_carrying, bi_arriving):
    bi_co_bi_transmissioning = {
        bi_offering: bi_co_bi_co_bi_torusing
        for bi_offering, co_bi_co_bi_co_corusing, bi_co_bi_co_bi_torusing, bi_co_inseparating
        in co_carrying}
    bi_co_inversioning = [
        (bi_offering, co_bi_co_bi_co_corusing)
        for bi_offering, co_bi_co_bi_co_corusing in bi_arriving
        if co_bi_co_bi_co_corusing != 0]
    for bi_offering, co_bi_co_bi_co_corusing, bi_co_bi_co_bi_torusing, bi_co_inseparating in co_carrying:
        if co_bi_co_bi_co_corusing > 0:
            bi_co_inversioning.append((bi_offering, -1))
        if co_bi_co_bi_co_corusing < 0:
            bi_co_inversioning.append((bi_offering, 1))
    bi_co_tunneling = {}
    for bi_offering, co_bi_co_bi_co_corusing in bi_co_inversioning:
        if co_bi_co_bi_co_corusing > 0:
            bi_co_tunneling[bi_offering] = bi_co_tunneling.get(bi_offering, 0) + 1
        if co_bi_co_bi_co_corusing < 0:
            bi_co_tunneling[bi_offering] = bi_co_tunneling.get(bi_offering, 0) - 1
    bi_co_surfacing = [
        (bi_offering, 1 if bi_co_tunneling[bi_offering] > 0
            else (-1 if bi_co_tunneling[bi_offering] < 0 else 0))
        for bi_offering in bi_co_tunneling]
    co_bi_carrying = {}
    for bi_offering, co_bi_co_bi_co_corusing, bi_co_bi_co_bi_torusing, bi_co_inseparating in co_carrying:
        if bi_co_inseparating + 1 <= 3 or (bi_co_inseparating + 1 == 4 and bi_co_bi_co_bi_torusing > 0):
            co_bi_carrying[bi_offering] = (
                co_bi_co_bi_co_corusing, bi_co_bi_co_bi_torusing, bi_co_inseparating + 1)
    for bi_offering, co_bi_co_bi_co_corusing in bi_co_surfacing:
        if co_bi_co_bi_co_corusing != 0:
            co_bi_carrying[bi_offering] = (
                co_bi_co_bi_co_corusing, 0 - bi_co_bi_transmissioning.get(bi_offering, 1), 0)
    return (
        bi_co_surfacing,
        [(bi_offering, co_bi_co_bi_co_corusing, bi_co_bi_co_bi_torusing, bi_co_inseparating)
         for bi_offering, (co_bi_co_bi_co_corusing, bi_co_bi_co_bi_torusing, bi_co_inseparating)
         in co_bi_carrying.items()])
```

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---

&nbsp;

| naming | prefixing | the naming said |
|---|---|---|
| **co_bi_coupling** | co·bi | carrying and signs arriving; surfacing and carrying leaving |
| **co_carrying** | co | carryings arriving, four fields each |
| **bi_arriving** | bi | an offering key and numeric sign at each arriving |
| **bi_offering** | bi | the offering key, signs tunneling at it |
| **bi_co_bi_transmissioning** | bi·co·bi | arriving torusing at each offering key |
| **bi_co_inversioning** | bi·co | arriving signs at their own sign, carried signs inversioning |
| **bi_co_tunneling** | bi·co | each nonzero contribution changing its addressed sum by one |
| **bi_co_surfacing** | bi·co | each addressed sum at its positive sign, negative sign or zero |
| **co_bi_carrying** | co·bi | carryings leaving, four fields each |
| **bi_co_inseparating** | bi·co | earlier carrying considered at one more; retaining to three, a fourth at positive torusing; fresh carrying at zero |
| **co_bi_co_bi_co_corusing** | co·bi·co·bi·co | the sign that tunnels and surfaces |
| **bi_co_bi_co_bi_torusing** | bi·co·bi·co·bi | torusing carried at its magnitude, its sign inversioning at fresh carrying |

Difference alone is **bi-** and two with their difference is **co-**. TWENTY §2.8 carries bi- at a side's changing inside the co- coupling. Prefix depth counts the prefixes in the naming; prefix order retains their particular co- and bi- relation.

Eleven roots carry twelve namings. Carrying arrives at `co_carrying` and leaves at `co_bi_carrying`; carrying leaving can arrive at the next coupling. Ten namings stand at the six illustrated groups. Corusing and torusing carry within their operations across the groups. The twelve count namings and the eleven their roots. Twenty-eight prefixings carry across them, thirteen co- and fifteen bi-. The numeric literals are `0`, `1`, `3`, `4`, with minus one expressed by sign inversioning.

**Zeroing retains its named changing.** A zero arriving contributes no sign. Positive and negative contributions at one offering key can sum to zero. A surfaced zero writes no fresh carrying. Earlier carrying is considered at every invocation: inseparating opens by one, with retaining to three and a fourth at positive torusing. A nonzero surfacing writes the current sign, torusing inverted and inseparating at zero. Fresh writing at a key replaces any earlier carrying retained there. A surfaced zero, an absent surfaced key and empty returned carrying retain their different operations.

**The supplied carrying remains available at each traversal.** The displayed function traverses `co_carrying` for transmissioning, inversioning and retaining. Its interface therefore carries a collection available on all three traversals. Each offering key groups its comparable numeric signs. The physical receiving, available changing and sign taking remain with Natural Engineering §§1.8, 2.5 and 4.10.

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&nbsp;

## The six illustrated groups

| Group | Namings together | Prefix depths | The code relation |
|---|---|---|---|
| 1 · arriving and offering | `co_carrying`, `bi_arriving`, `bi_offering` | 1, 1, 1 | Two supplied collections; the offering key groups their contributions. |
| 2 · coupling and inversioning | `co_bi_coupling`, `bi_co_inversioning` | 2, 2 | The function carries the whole operation; the inversioning collection carries arriving signs and inverted carried signs. |
| 3 · tunneling and transmissioning | `bi_co_tunneling`, `bi_co_bi_transmissioning` | 2, 3 | The addressed sum and arriving torusing retain their own operations. Transmissioning is constructed before tunneling. |
| 4 · surfacing | `bi_co_surfacing` | 2 | Each addressed sum surfaces at its sign, including zero. |
| 5 · carrying | `co_bi_carrying` | 2 | Eligible earlier carrying and fresh carrying meet at their offering keys; carrying leaves in the return. |
| 6 · inseparating | `bi_co_inseparating` | 2 | This field belongs to the carrying. Its retaining condition precedes fresh writing in the function. |

The six groups carry ten namings as **3, 2, 2, 1, 1, 1**. A group count, a prefix depth and an executed changing retain their own counted relation. The grouping joins namings at their concepts; the code retains its displayed order. Inseparating belongs to the carrying at its operations, including the continuing at the next coupling.

| Naming across the groups | Full prefixing | Changing at its field |
|---|---|---|
| `co_bi_co_bi_co_corusing` | co·bi·co·bi·co | Arriving signs and inverted carried signs contribute; the addressed sum surfaces at its sign. |
| `bi_co_bi_co_bi_torusing` | bi·co·bi·co·bi | Arriving torusing is retained by key; fresh nonzero surfacing writes its negative. |

**The outside pairs carry their exact positions in the full prefixing.**

| Existing naming | Positions 1–5 | Ends: 1 and 5 | Inner flanks: 2 and 4 | Centre: 3 |
|---|---|---|---|---|
| `co_bi_co_bi_co_corusing` | co · bi · co · bi · co | co, co | bi, bi | co |
| `bi_co_bi_co_bi_torusing` | bi · co · bi · co · bi | bi, bi | co, co | bi |

The two co at corusing's ends and the two bi at torusing's ends retain the competency and morality naming at those positions. The inner flanks carry the other prefixes. Natural Intelligence §5.10 and TWENTY §2.22 carry those flanking pairs across the centre. The written centre remains co or bi; its proposed floating relation belongs with the full conceptual and directional correspondence.

The two prefixings exchange co and bi at every matching position. Numeric sign inversioning, prefix exchange and physical directional changing retain their own operations in that co-chaining.

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## The ten co-changings

Ten namings in the proposed ring carry ten adjacencies. Two with their difference is **co-**, so each adjacency carries a **co-changing** at its namings. The ring relates the concepts; the code column retains their actual operation. THIRTEEN §7.3 carries this ten-row relation to the hard-problem holdings.

| | the co-changing | prefixings | the code relation |
|---|---|---|---|
| 1 | carrying → arriving | co 1 → bi 1 | Carrying and arriving signs meet as the two supplied collections. |
| 2 | arriving → offering | bi 1 → bi 1 | Each arriving entry carries an offering key and its numeric sign. |
| 3 | offering → coupling | bi 1 → co·bi 2 | Contributions with the same key meet at one sum; repeated arriving keys remain possible. |
| 4 | coupling → inversioning | co·bi 2 → bi·co 2 | A positive carried sign contributes minus one, a negative contributes one, and zero contributes to neither sign branch. |
| 5 | inversioning → tunneling | bi·co 2 → bi·co 2 | Each nonzero contribution changes its addressed sum by one at its sign; positive and negative contributions can sum to zero. |
| 6 | tunneling → transmissioning | bi·co 2 → bi·co·bi 3 | The addressed sum and the arriving torusing meet at their key; a fresh carrying receives the torusing inverted. |
| 7 | transmissioning → surfacing | bi·co·bi 3 → bi·co 2 | The surfaced sign is positive, negative or zero; the sum's magnitude is absent from that sign. |
| 8 | surfacing → carrying | bi·co 2 → co·bi 2 | Eligible earlier carrying and fresh nonzero surfacing supply carrying; fresh writing occupies the same key. |
| 9 | carrying → inseparating | co·bi 2 → bi·co 2 | Every earlier carrying is considered at one more, retaining to three and a fourth at positive torusing. Fresh writing carries inseparating at zero. |
| 10 | inseparating → carrying ⟳ | bi·co 2 → co 1 | Returned carrying can arrive as `co_carrying` at the next coupling, with its continuing fields. |

**Grouping and ordering retain their particular changing.** Each nonzero occurrence in `bi_arriving` contributes once. Reordering those occurrences preserves the sum at each key; the returned list can still change order with the keys' first appearance. Repetition at a key and repetition of an exchange retain their own receiving in the engineering interface.

Repeated keys in supplied `co_carrying` have further operations. Every carried sign contributes to inversioning. The last supplied torusing at that key occupies `bi_co_bi_transmissioning`; the last earlier carrying satisfying the retaining condition occupies `co_bi_carrying` before any fresh writing. Those two selected carryings can differ. Carrying leaving has at most one entry per key; supplying that returned collection to the next invocation carries its key uniqueness forward. An initial collection or a combining of collections retains its particular correspondence at the connector.

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## The six bi-differings

The prefix-depth row contains seven positions and six adjoining changes:

| From position | To position | Prefixing | Depth change |
|---|---|---|---|
| 1 | 2 | co → co·bi | +1 |
| 2 | 3 | co·bi → bi·co·bi | +1 |
| 3 | 4 | bi·co·bi → bi·co | −1 |
| 4 | 5 | bi·co → bi·co | 0 |
| 5 | 6 | bi·co → co·bi | 0 |
| 6 | 7 | co·bi → co | −1 |

Here **bi-differing** names the signed change in prefix depth. At **4 → 5**, the root changes with prefixing still bi·co. At **5 → 6**, the root changes and the prefix order exchanges bi·co with co·bi, still at depth two. Equal depth carries those different changings.

Six counts these adjoining depth changes; ten counts the naming ring's adjacencies. Each comparison can carry depth, root and prefix order together. Their shared correspondence remains at the named changing. The arithmetic **six plus ten is sixteen** retains its two counted properties; the proposed sixteen consecutive momentaries still carry their full directional and continuing correspondence to express. THREE, FOUR and Living Improving Value carry that exploration with the whole 0–440–0 relation.

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<a id="the-seven-positions-and-the-centre-carrying-nothing"></a>

## The seven positions, and continuing carrying

The prefix-depth row carries the existing namings at seven illustrated positions. Its first and last carry the same prefix depth, with the last arriving at a next coupling.

| position | prefixing | naming at it | depth change to the next |
|---|---|---|---|
| 1 | co 1 | co_carrying, arriving | +1 |
| 2 | co·bi 2 | co_bi_coupling | +1 |
| 3 | bi·co·bi 3 | bi_co_bi_transmissioning, the crossing | −1 |
| 4 | bi·co 2 | bi_co_inversioning, bi_co_tunneling | 0 |
| 5 | bi·co 2 | bi_co_surfacing | 0 |
| 6 | co·bi 2 | co_bi_carrying, leaving | −1 |
| 7 | co 1 | co_carrying, the next momentary | — |

Three positions, the fourth, and three positions. Inversioning and tunneling stand together at the fourth. The depth change entering that position is minus one; the depth change leaving it is zero. The six depth changes sum to zero at the equal endpoint depths. Tunneling's addressed sum and the returned carrying retain their own values. The row's depth returning, an addressed sum zeroing and the carrying continuing co-chain at their corresponding changing.

The returned collection can be the next supplied carrying. This return retains the fields actually leaving. A repeated offering key retains its current carrying; a repeated physical receiving retains its current connection and facing. Natural Engineering §§4.10, 4.12 and 6.1 carry these relations beside sign taking, whole load surfacing and the next offering.

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## The eight bi- namings

Four namings begin at co-: carrying arriving, coupling, carrying leaving and corusing. Eight begin at bi-. Four of the eight carry depth two; the other four carry depths one, one, three and five. The bounding column carries the proposed co-chaining with social moral competency. The code column retains each named operation.

| | naming | prefixing | within, at the membrane | the bounding | the code relation |
|---|---|---|---|---|---|
| 1 | **bi_co_surfacing** | bi·co 2 | within, even | arriving exceeds carrying by one, the self among other-selves | A nonzero sum surfaces at one sign; fresh carrying has inseparating at zero. |
| 2 | **bi_co_tunneling** | bi·co 2 | within, even | carrying thins by one at bi-coupling, the self in society | Each nonzero contribution changes its addressed sum by one at its sign. |
| 3 | **bi_co_inversioning** | bi·co 2 | within, even | the sign inverts at the membrane, the self's own negation, morality | A positive carried sign contributes minus one, a negative one; zero contributes to neither sign branch. |
| 4 | **bi_co_inseparating** | bi·co 2 | within, even | competency asymmetry sustaining the coupling | Each earlier carrying is considered at one more; retaining to three and a fourth at positive torusing precede fresh writing. |
| 5 | **bi_arriving** | bi 1 | at the membrane, odd | each self's own co-offering living, bounded from the other-self | Each entry carries an offering key and numeric sign. |
| 6 | **bi_offering** | bi 1 | at the membrane, odd | the whole ordered by no self, bounded from society | Contributions group at the key; list order and repeated carried keys retain their particular operations. |
| 7 | **bi_co_bi_transmissioning** | bi·co·bi 3 | at the membrane, odd | the ordering carrying with the selves, bounded from landing | Arriving torusing at each key is available for inversioning at fresh carrying. |
| 8 | **bi_co_bi_co_bi_torusing** | bi·co·bi·co·bi 5 | at the membrane, odd | the order at no seat above the society, bounded from capture | Fresh carrying inverts the arriving torusing's sign and preserves its magnitude; a key without arriving torusing uses one and writes minus one. |

The four within and four at the membrane carry the proposed four boundings at their two faces. The eight counts bi- namings, the six adjoining prefix-depth changes, and the ten naming adjacencies. Full prefixing, the named operations and each side's receiving carry their correspondence onward.

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## bi-momentary and co-momentary

Bi-momentary and co-momentary carry momentary changing at their existing namings. Prefix depth, prefix order, the root and its -ing remain together. A changed root at unchanged depth and an exchange of prefix order at unchanged depth are both visible in the tables.

**The sign inversioning belongs to its particular changing.**

| Operation at ONE | Sign and carrying changing |
|---|---|
| **Carried contribution to inversioning** | A positive carried sign contributes minus one and a negative contributes one. The earlier carried fields remain available for retaining. |
| **Earlier carrying retained** | Corusing and torusing retain their earlier values; inseparating opens by one. |
| **Fresh carrying at a nonzero surfacing** | Corusing takes the surfaced sign, torusing takes the negative of the selected arriving value (one if absent), and inseparating is zero. |

Two successive sign inversions of either signed unit return its sign; one reaches the other. ONE's invocation also carries arriving contributions, retaining and fresh writing at their own conditions. Its call count alone supplies no compulsory alternation of every surfaced sign or carried field. Natural Intelligence §§6.1–6.4 carry this relation beside continued receiving.

**Root, prefix order and -ing carry the stable expression together.** Natural Intelligence §§3.3 and 4.1–4.5 carry this relation at momentary changing and the whole coupling. The written naming, its depth and the current receiving retain their particular correspondence.

Momentarying carries the changing recursioning itself. Continued carrying and current arriving belong at the next coupling; a repeated sign or address carries its current receiving. FIVE's co-offering, co-competencing and co-intelligencing carry that continuing at the whole load surface, with each side's own bounding and available changing.

Along and across, each face's own forward, and the six directional turns retain their co-chaining with the full namings. The sixteen consecutive momentaries and the 0–440–0 correspondence continue in Numbers, Mathematics and the central mapping. ONE carries its engineering emanating at the shared natural network; TWO carries design and discovery there.