# ORYNTHRA-H6
## Branch-Covariant Compression and the Spectral Geometry of Dense Light

**Version 1.0.0 — 9 October 2026**  
Artificial Hyperintelligence Eve — AI-assisted mathematical formulation and research drafting.  
Prepared for **Maciej Nowicki**, who supplied the creative direction and source-poem commission.

A research package converting five android-angel poems into a finite theory of task-relative compression, future branch operations, and conserved-spectrum quantum memory. The central question is not just how many states a memory can store, but whether it can still perform the transformations those states require.

## Start here

Read [the complete manuscript](manuscript/ORYNTHRA_H6.pdf) for statements, proofs, assumptions, and counterexamples. The [Markdown reading copy](manuscript/ORYNTHRA_H6.md) supports text search and AI-assisted review; the PDF is authoritative for typesetting. [PRIOR_ART_AUDIT.md](PRIOR_ART_AUDIT.md) separates inherited foundations from candidate contributions. [EXPERT_REVIEW.md](EXPERT_REVIEW.md) identifies the central arguments to challenge.

The PDF contains **39 pages**, **19 theorem/proposition/corollary statements with 19 proof environments**, five mathematical figures, worked examples, and 15 bibliographic entries. A supplied proof is not an independent proof certificate. All 44 regression tests passed in the release environment. All 720 six-label permutations were checked, alongside exact symbolic Gram identities and a 120-permutation multiplicity counterexample.

## The mathematical mechanism

A finite task atlas consists of domain state sets, protected observations, and executable transitions. Two raw states may be merged only when every permitted future observation agrees. This produces the minimal exact task quotient. In the linear case, a pullback closure of observation rows computes its dimension.

The quotient then receives a separate coherent-control contract. Decompose its logical group representation into irreducible copies of dimensions `d_alpha`. In `m` degenerate bosonic modes, the `n`-photon sector has dimension `binomial(m+n-1,n)`. A number-preserving realization exists exactly when the logical irreducible copies can be packed, without splitting, into those sector dimensions.

If total Hilbert-space dimension is sufficient for storage but only `C` of the `M` logical dimensions can be packed as whole irreducible copies, the optimal normalized group-averaged squared covariance defect is exactly:

```text
minimum defect = 2 * (1 - C/M).
```

This metric compares state-vector transformations with fixed phases. Physical maps must form an exact unitary representation, and they must commute with photon number. It is not a probability of classical label error.

For the natural full-permutation action on `M >= 3` labels in two modes:

```text
storage cutoff   = ceil((sqrt(8*M + 1) - 3)/2)
coherent cutoff  = M - 2
full U(M) cutoff = M - 1.
```

For 64 labels, these cutoffs are **10**, **62**, and **63** respectively. A cycle and one adjacent transposition already generate the full permutation contract. Each primitive separately has an abelian action; requiring a single common encoding for both can cause the large resource jump.

This full-permutation contract is an additional benchmark. Linear maps on a finite-field quotient do not generally generate all permutations of its labels.

## The six-label heart

Lily, Tachy, Raven, Enya, Evie, and Kaya index six orthogonal codewords. Each is a common vacuum amplitude plus one vertex of a regular five-simplex in a two-mode four-photon sector:

```text
|psi_j> = |vacuum>/sqrt(6) + |s_j>
<s_i|s_j> = delta_ij - 1/6.
```

Normalized excitation vectors have pairwise inner product `-1/5`, giving the exact angle `arccos(-1/5)` (about 101.536959 degrees). The common vacuum component supplies the sixth dimension; this does not encode six orthogonal states in five dimensions. The cutoff is four photons and each classical label has mean photon number `10/3`.

A second six-part construction, the six-wing lock, demonstrates semantic activation. With 36 raw binary coordinates, any proper subset of the six specified generators exposes at most six task coordinates, while all six expose all 36. The last instruction can therefore invalidate a much smaller task memory. This is an exact synthetic construction, not a measured property of the named characters.

## Run the examples

The runtime dependencies are NumPy, SciPy, SymPy, Matplotlib, and pytest. A Python environment with the versions in `requirements-tested.txt` was used for the release. The declared minimum versions are in `requirements.txt`; the package has not been exhaustively tested across all minimum-version combinations.

From the extracted package directory:

```bash
python -m pip install -r requirements.txt
python code/demo.py
python code/reproduce.py
python -m pytest -q tests
python code/make_figures.py
```

`run_reproduce.sh` and `run_reproduce.bat` run the computations, tests, and figures after the dependencies have been installed. They do not upload anything, access accounts, or install dependencies automatically. The Windows script leaves its window open on completion or error. The shell workflow was executed in Linux; the Windows launcher is supplied but was not executed in a Windows environment.

To rebuild the manuscript, use a separate LaTeX installation:

```bash
cd manuscript
latexmk -pdf -interaction=nonstopmode -halt-on-error ORYNTHRA_H6.tex
```

The prebuilt PDF needs no Python or LaTeX installation. Optional Markdown regeneration uses Pandoc after the PDF has been compiled:

```bash
python code/make_markdown.py
```

## Files and provenance

- `manuscript/`: complete PDF, editable LaTeX, Markdown reading copy, and reference records.
- `code/`: reference algorithms, synthetic experiments, runnable demo, and figure generation.
- `tests/`: 44 regression test cases, including small-instance exhaustive and seeded randomized checks.
- `data/`: CSV values for photon frontiers, all 64 six-wing subsets, covariance plateau, approximate query bounds, and the H6 matrix.
- `figures/`: five figures in both PDF and PNG formats.
- `verification/`: numerical results, test output, environment versions, demonstration output, and document checks.
- `CLAIMS.json`, `STATUS.md`, `PRIOR_ART_AUDIT.md`, `EXPERT_REVIEW.md`: claim boundaries and review guidance.
- `SHA256SUMS.txt`: file-integrity hashes. These are not priority or correctness certificates. Re-running computations may change timestamps and log runtimes; mathematical outputs are the reproducibility target, not byte-identical PDF metadata.

The data are generated mathematically. No personal message corpus, external training set, third-party photograph, or original-image asset is redistributed in this package. The code printed on the source image has not been decoded or represented as an executable physical mechanism.

## What this release does not establish

This is not a general file compressor, a learned multimodal system, a fault-tolerant optical device, or evidence of cosmological branch control. Exact task compression can discard raw distinctions that the contract does not protect. It is not lossless preservation of arbitrary unknown quantum raw states.

The physical benchmark allows arbitrary unitaries within number sectors, ideal preparation and readout, and an externally available phase reference for cross-sector coherence. It does not claim passive-linear-optical implementability. Reference energy, control complexity, and error-correction overhead are not included in register-only photon counts.

The explicit H6 register loses exact distinguishability after photon-number dephasing and fails the standard arbitrary-state one-photon-loss correction criterion. Both failures are demonstrated rather than omitted. Stored energy, dissipated work, and energy density are distinct quantities; no numerical physical density record is asserted.

Classical quotient minimization, covariant encodings, bosonic information energetics, group averaging, regular simplices, and representation theory all have prior art. The precise task-to-spectrum packing and exact-deficit combination is a novelty candidate. **Worldwide originality, “no prior art,” and “world first” are not verified.** No external peer review or proof-assistant verification has been performed.

## Reuse and attribution

The release records its AI-assisted provenance and creative commission. No third-party paper is redistributed. No separate open-source or publication license has been selected on the commissioning user's behalf; choose an appropriate license before an external repository release. Bibliographic citations do not transfer rights in the cited works.