# Candidate Toroidal Mind Simulator V1

Status: **candidate application and bounded experiment; not canonical Mind dynamics**

This application tests a specific projection question: under explicit normalized triadic chart assumptions, can two closed phase coordinates be encoded as a ring torus and decoded again? The answer is yes for the stated chart. It also lets an operator explore a delayed phase/residue prototype. In source-faithful mode the prototype receives the current seven-depth Mind architecture as an input; alternative `N` values are implementation-sensitivity controls, not rival votes on the source architecture.

It does **not** establish that:

- physical or biological minds are literally toroidal;
- the delayed equations are the unique or canonical Y Engine dynamics;
- the simulator derives, selects, re-proves, or refutes the source-defined seven-depth Mind architecture;
- a golden-ratio winding emerges from the recursive preset;
- a calculated camera or SO(4) reference-frame projection is observerhood, awareness, or consciousness;
- return to the same two-phase torus address is return to the same complete delayed history-state.

## Exact result and assumptions

The reversible coordinate result holds when all of these are imposed:

1. `I + O = 1`;
2. `(O - I)^2 + R^2 = 1`;
3. local and whole phases are closed `S^1` coordinates;
4. the ring-torus radii satisfy `A > a > 0`;
5. circular-closure weights are non-negative and normalized to sum to one.

Then the standard ring-torus embedding is equivalent to the normalized triad-pair encoding, the inverse is defined everywhere on that ring torus, and the phasor coherence satisfies `0 <= C <= 1`. These are conditional mathematical statements, not empirical validation of the wider ontology.

## Repairs made during governed integration

- `delay = 0` now reads the current Euler state rather than silently inserting one time step.
- Python and browser runtimes use the same initial phase rule: `linspace(0, -0.7, N)`.
- browser `C(0)` and `Theta(0)` are calculated from the normalized weights and initial phases.
- non-negative delay rounding is explicitly shared between Python and JavaScript.
- the browser math lives in `app/model-core.js`, allowing direct cross-runtime tests.
- source-faithful mode uses seven recursive depths; `N = 1..13` remains available only as an explicitly counterfactual implementation diagnostic.
- visible “observer frame” wording is replaced by “reference-frame projection” or “camera frame.”
- unavailable generated SVG/MP4 download links were removed; no bulky generated media was imported.
- a proof-boundary panel is displayed above the simulator.

## Source-fidelity limit discovered during correlation

The application is a **toroidal coordinate and partial dynamics laboratory**, not yet a complete Structure-of-Mind engine. Its current runtime compresses each recursive depth to one phase variable. It therefore does not yet instantiate:

- the twelve-address first recursive cell, `3 + 9 = 12`, inside each depth;
- multiple active dimensions and their same-depth horizontal relations;
- the complete cross-dimensional whole-level integration and changed return;
- the source compiler's identity/relation field as the cause of the displayed geometry.

The exact torus chart remains useful because it gives a reversible two-cycle projection. The next faithful engine must produce its local and whole phases from the richer `dimension × seven depths × twelve-address cell × retained history` field rather than treating the phase chain as the complete Mind.

## Files

- `app/index.html` — candidate interactive application and proof boundary
- `app/model-core.js` — DOM-free browser model used by the application and parity test
- `model/y_torus_model.py` — repaired Python reference implementation
- `model/MATHEMATICAL_DERIVATION.md` — original derivation evidence, byte-preserved from the submitted archive
- `reports/MODEL_SUMMARY.md` — original summary evidence, byte-preserved
- `reports/VALIDATION_REPORT.md` — original validation report evidence, byte-preserved
- `reports/VALIDATION_SUMMARY.csv` — original numerical summary evidence, byte-preserved
- `PROVENANCE.json` — source archive and original/integrated SHA-256 lineage
- `tests/` — zero-delay, weight/coherence, inverse-map, N-alternative, scope-language, and Python/browser parity checks

The byte-preserved source-evidence documents retain historical wording such as “observer.” That wording is not adopted as current terminology; the repaired runtime uses **reference-frame projection**.

## Run the focused tests

From this directory, run:

```powershell
python -m unittest discover -s tests -p "test_*.py" -v
```

The parity test requires Node.js. If Node.js is unavailable, only that test class is skipped; the Python properties still run.

## Governance boundary

This directory does not update the canonical claim registry, approval ledger, release configuration, or public Teacher deployment. Promotion requires a current, hash-bound review after the repaired artifact is audited.