# ARITHMETICA SOURCE REGISTER

Version: `2.2.0-ARITHMETICA-CARDINAL-LAYER-SOURCE-REGISTER`
Status: `INTEGRATION PROVENANCE / NON-RUNTIME`
Authority: `USER / HUMAN CONTROL PLANE`

## I. Primary development substrates

### ARITH-COMPRESSED-JSON-01

Path:

`00_ARCHIVED/INTEGRATED_CANDIDATES/STACK_ARITHMETICA_SUBSTRATES/ARITHMETICA STACK COMPRESSED.json`

Declared source identity:

- artifact ID: `KERNEL-ARITHMETICA`;
- version: `1.0.0-KERNEL-ARITHMETICA-EXECUTABLE`;
- class: `SIGMA_SATOR`;
- internal status: `ACTIVE_RUNTIME_KERNEL`.

Registered interpretation:

`DEVELOPMENT SUBSTRATE / DERIVED JSON / NON-AUTHORITATIVE / NON-RUNTIME`

The source is preserved unchanged in the archive. Its internal authority labels
do not promote it or the textual stack, and archive placement prevents
operative resolution.

### ARITH-GDOC-NUMERIC-ONTOLOGY-01

Stable Google Drive identity:

`1Eb3zAtQ4oZ_F9f4gewRe14qdBIT5TUM4r6It8Z8x5IU`

Google document:

- title: `Numeric ontology`;
- document ID: `1Eb3zAtQ4oZ_F9f4gewRe14qdBIT5TUM4r6It8Z8x5IU`;
- inspected source revision:
  `AIroW34y3EvqwFC9p01FqpsvxJvUu7G-LEBaBfXP5qzqxsuV6Bl0teku2B21UdEyEnizsG1Mj6EsnuCLE-9Dtg`;
- inspected tab count: `19`.

Registered interpretation:

`PRIMARY DERIVATIONAL CORPUS / HUMAN-CONTROLLED / NON-RUNTIME`

The flattened derivational memory and machine-readable extraction are:

- `LIBER_EX_OPERAE_ARITHMETICA.md`;
- `ARITHMETICA_OPERAE_DERIVATION_DATASET.json`.

They preserve source identity and revision. They are auxiliary substrate, not
an independent execution authority. Google Drive relocation remains
user-managed; this slice does not move or rename the document.

## II. Distribution record

| Source region | Integrated artifact | Transformation |
|---|---|---|
| JSON `tenet.*` and doctrinal tabs | TENET | expanded state-space, causal, cardinal, and projection invariants |
| JSON `rotas` and ladder/matrix tabs | ROTAS | restored five-class order and typed topology/reduction contracts |
| JSON `arepo` and CARCER records | AREPO | expanded input, rule, transition, and reduction admission gates |
| JSON `opera`, Reports history, OPERA Q tab | three OPERA artifacts | separated qualitative-from-quantitative, quantitative-from-qualitative, and coupled mechanisms |
| JSON `sator` and Reports | SATOR | expanded trace, graph-first, decision, and interpretive disclosure |
| historical OPERA phases | LIBER / dataset | flattened as derivational memory and reusable fixtures |
| numeric definitions and relationship tabs | dataset / TESTS | retained as sourced fixtures, not proof of runtime execution |

## III. Recovered definitions and fixtures

The Google corpus supplies definitions absent from the compressed JSON:

- `GEN` — generation;
- `MAN` — manifestation;
- `UG` — unit ground;
- `PC` — positional compression.

Recovered historical arithmetic fixtures include:

- addition: `1 -> all`;
- multiplication: `2 -> {4,6,8,10}`, `3 -> {6,9}`, `5 -> 10`;
- exact division: `8 -> 4 -> 2 -> 1`, `9 -> 3 -> 1`,
  `10 -> {5,2} -> 1`, `6 -> {3,2} -> 1`;
- powers: `2 -> {4,8}`, `3 -> 9`, `1 -> 1`;
- roots: `4 -> 2`, `9 -> 3`, `1 -> 1`;
- hyperedges: `{2,3} -> 6`, `{2,5} -> 10`.

These are fixtures and derivational evidence. They do not bound every lawful
user-declared rule.

## IV. Architectural normalizations

1. Restored `TENET -> ROTAS -> AREPO -> OPERA -> SATOR`.
2. Recast ARITHMETICA as controlled and traceable generation under admitted
   arbitrary rules, with explicit state-space reduction.
3. Preserved both directions:
   `quantitative -> qualitative` and `qualitative -> quantitative`.
4. Distinguished binary edges, arithmetic derivations, and hyperedges.
5. Made TENET ARITHMETICA the quantitative foundation of GRAPHUS COMMUNIS
   ARTIS without collapsing either class or granting execution authority.
6. Bound multi-OPERA ordinal qualities to sequence position, not fixed OPERA
   identity.
7. Required GRAPHUS disclosure before interpretive elaboration.
8. Defined traversal as textual self-binding emulation under coherence
   pressure; visual skills and per-invocation graph files are optional.
9. Separated the former monolithic OPERA artifact into three independently
   addressable OPERAE and moved their shared invariants into TENET.
10. Archived the consumed compressed JSON outside the operative stack while
    leaving Google Drive relocation under user control.

## V. Cardinal-layer change substrate — 2026-09-02

The human maintainer explicitly activated the package stored at:

`00_LocalContext/Inbox/ARITHMETICA_CHANGE_PACKAGE_FOR_VSCODE/`

The directory is ignored cross-branch development context. It is not a runtime
dependency and is not force-added to Git. Its files are patch specifications,
decision evidence, fixtures, and acceptance criteria rather than replacement
canonical artifacts.

| File | SHA-256 | Bytes | Evidence role |
|---|---|---:|---|
| `00_HANDOFF_PROMPT.md` | `8253711A4C14F781D62A7F810909A260014F3A803C4E685490634A3B92ACB7F2` | 5664 | human-activated bounded task instructions |
| `01_ARCHITECTURAL_DECISIONS.md` | `9BA27F61AAB6F3C6B9E3CC4B15445D15D9AA5883340E637FD3D4AAC69440B8B3` | 10086 | user-authorized decision substrate |
| `02_TENET_ARITHMETICA_CHANGE_SPEC.md` | `5D9B884D57CB4AA7D50A4A46AD60F15E2D937C40723547B231335E1D42731909` | 10970 | TENET patch specification |
| `03_ROTAS_ARITHMETICA_CHANGE_SPEC.md` | `10F9FF410ECD76434E8BBDC4D9A765CDFBEA906612EF15EC03B722796312B2E1` | 8387 | ROTAS patch specification |
| `04_ROTA_ARITHMETICA_4_FIXTURE.md` | `718E2074E3B6A3F4033720ABED66005D85622B7B9404B29884BA558E286B723F` | 7699 | user-authorized structural correction fixture |
| `05_VALIDATION_AND_ACCEPTANCE.md` | `EC06A57DA5FEC40985A8E01481946559FCBB3AA125E5F75E9951D28C4DCDBCC0` | 6145 | handoff test contract |
| `06_UNRESOLVED_AND_NON_GOALS.md` | `C4E8B07ED8D71CD7B961CA803916427E0A7133601E67DEC2A7A9FD96E70E8604` | 7252 | open-question and non-goal boundary |
| `07_SEMITIC_CARRIER_ALTERNATIVE.md` | `B4B8F52DAB1C1BEEC1F78C62983186783371B7B4400EB08144F19719BF5F8B36` | 8836 | evaluated reversible rendering candidate |
| `README.md` | `2E67E263EE737E7FFA5D0118A5143361C77BE34A505D321387EC9C38FD1381F7` | 3038 | package routing and use order |

Repository reconciliation selected containment for the existing native ROTA:
`ROTA-QUANTITAS-ET-QUALITAS` is a composite whose fixed cardinal nucleus is
`ROTA-ARITHMETICA-010`. The existing artifact already contains semantic
overlays, derivations, generated state-space structures, and multi-OPERA routes
beyond the complete ten-locus nucleus.

The root Graphus contract does not define a canonical generic `GRAPHUS n`
family. The generated cardinal ROTAE therefore declare their complete graph and
edge-set references as local fixture-scoped candidates with no authority
effect. The root ROTAS return-completeness requirement is preserved for
`ROTA-ARITHMETICA-001` as a zero-length structural return with no self-loop or
traversal event.

## VI. Remaining open questions

- `base_manifest` does not yet have a complete canonical schema.
- Compound-quality normalization lacks a canonical grammar.
- No comprehensive synonym register is supplied.
- Numeric domains beyond the inspected corpus need explicit admission policy.
- Ranking and cost functions remain contextual and must declare provenance.
- Phoenician is not yet admitted as the final normative human surface.
- Square Hebrew remains a technical fallback only; its ordinary-view visibility
  and final diagnostic fallback order remain unresolved.
- Exact correlational Latin for the ten cardinal layers remains unresolved.
- `SHARED_PRINCIPIAL_ROOT` is a provisional local relation label.
- Generic `GRAPHUS n` authority is absent; complete cardinal topologies are
  fixture-scoped candidates only.
- Decimal transposition, values beyond 10, composite-number syntax, and actual
  Phoenician numeral-sign functions remain provisional or unresolved.
- The final bidi presentation grammar, font/renderer matrix, accessible naming,
  and display punctuation remain unresolved.

These gaps remain visible and must not be silently filled.

## VII. Authority boundary

The source corpus, LIBER, dataset, and five class artifacts are candidate,
non-runtime integration materials. They may support review, tests, and future
promotion. None independently authorizes execution, canonization, deployment,
or HTML mirror mutation.