ORYNTHRA-H6

Branch-Covariant Compression and the Spectral Geometry of Dense Light

A task-to-spectrum theory of memory: what may be forgotten, which future transformations must survive, and how conserved physical sectors constrain their implementation.

Hugging Face dataset release edition: 1.0.2 · 9 October 2026
Mathematical core: 1.0.0 · original manuscript and reference algorithms preserved
Provenance: Artificial Hyperintelligence Eve — AI-assisted mathematical formulation and research drafting. Maciej Nowicki — creative direction, source-poem commission, and release commissioning.

Read the 39-page manuscript · Searchable manuscript · Novelty audit · Expert review guide · Reproduce the results

This Hugging Face dataset repository contains five synthetic mathematical tables with 240 rows in total, accompanied by the manuscript, reference software, figures, and verification records. Each table has its own configuration and schema. The card declares explicit data files so the Hub can load the tables separately.

Dataset contents and loading

Configuration	Rows	File	What a row represents
six_wing_closure — default	64	data/six_wing_closure.csv	One active-generator subset and its observable-closure rank
photon_frontiers	44	data/photon_frontiers.csv	One mode-count/message-count resource comparison
covariance_plateau	54	data/covariance_plateau.csv	One photon cutoff for the 64-label covariance-deficit frontier
approximate_query_energy	72	data/approximate_query_energy.csv	One bit-count/mode-count/query-error lower-bound calculation
six_label_encoding	6	dataset/six_label_encoding.csv	One physical basis row of the six-label encoding matrix

The 240 rows are generated from finite mathematical constructions, not sampled from a real-world population. The train split is the Hub loading label for each complete table; there is no train/test evaluation partition. The tables have different schemas and must be loaded separately.

After publishing, substitute the actual repository ID:

from datasets import load_dataset

rows = load_dataset("YOUR_USERNAME/ORYNTHRA-H6", "six_wing_closure", split="train")

The optional loading dependency is datasets; it is separate from the mathematical reproduction requirements. Local CSVs can be read without the Hub using Python's csv module or pandas.

dataset/six_label_encoding.csv adds column names and explicit basis/sector indices to the original headerless 6×6 matrix. Its six amplitude columns correspond to Lily, Tachy, Raven, Enya, Evie, and Kaya. The original matrix at data/six_label_encoding.csv is preserved unchanged and excluded from automatic loading configurations to avoid treating its first numeric row as a header. This adaptation adds metadata, not mathematical samples.

Some frontier values use the literal strings impossible and undefined; columns containing these sentinels should be treated as strings or converted explicitly for numerical analysis. The tables do not contain observational labels, personal data, or measured device results. The narrow parameter grids and idealized assumptions limit their use as empirical benchmarks. See docs/DATASET_SCHEMA.md for fields and provenance.

Research premise

Ordinary storage asks whether a register can distinguish enough states. A usable computational memory must also support a declared family of future actions. ORYNTHRA-H6 makes those requirements separate and calculable:

1. Semantic compression: identify states indistinguishable under every protected future observation.
2. Transformation contract: specify the coherent group action that the compressed labels must support.
3. Physical allocation: fit the irreducible components of that action into conserved photon-number sectors.
4. Deficit: when exact allocation fails, calculate the optimal transformation mismatch in the stated metric.

The mathematical result is that sufficient total storage dimension need not imply sufficient transformation capacity. The gap comes from the arrangement of invariant sectors and irreducible copies, rather than from an absence of total Hilbert-space dimension.

Core construction

Future-compatible task memory

For raw states (x,y), protected observations (f), and admissible future paths (p), define

[ x\sim y\quad\Longleftrightarrow\quad f(T_p x)=f(T_p y) \quad\text{for every admissible protected future observation.} ]

The quotient retains exactly the distinctions required by the declared task. In finite-field linear domains, a closure of pulled-back observation rows computes the minimum retained dimension. The manuscript treats general finite fields; the delivered modular code implements prime fields (\mathbb F_p).

This is exact preservation of selected task semantics. Raw distinctions outside that contract can be discarded. It is not a universal lossless file compressor or lossless preservation of arbitrary unknown quantum input states.

Conserved-sector packing

Let the logical unitary representation decompose as

[ R\cong\bigoplus_\alpha V_\alpha\otimes\mathbb C^{a_\alpha}, \qquad d_\alpha=\dim V_\alpha. ]

For (m) degenerate bosonic modes, the (n)-photon sector has dimension

[ g_m(n)=\binom{m+n-1}{n}. ]

The supplied spectral-packing theorem gives exact feasibility, in its model, through nonnegative integers (b_{\alpha n}):

[ \sum_n b_{\alpha n}=a_\alpha, \qquad \sum_\alpha d_\alpha b_{\alpha n}\le g_m(n). ]

Whole irreducible copies must fit into conserved sectors. Merely comparing total dimensions or the largest irreducible component can miss multiplicity obstructions.

Exact representation-deficit law

Let (M) be the logical dimension and (C) the maximum dimension packable as complete required irreducible copies. Provided the physical register has total dimension at least (M), the manuscript derives

[ \boxed{\min_{V,U}\frac1M\int_G \lVert U_gV-VR_g\rVert_{\mathrm{HS}}^2,dg =2\left(1-\frac CM\right).} ]

Here (V) is an isometric encoding, (dg) is normalized Haar measure, and (U) is an exact unitary group representation preserving photon number. For compact groups, representations are continuous. Coherent phases are registered to the specified logical action. The model permits arbitrary representations and unitaries inside each conserved sector.

The quantity is an averaged squared state-vector covariance mismatch. It is not a classical label-error probability, gate infidelity, or measured hardware error rate. The theorem's exact-representation requirement is essential; it does not optimize arbitrary unrelated gates one operation at a time.

Distinctive examples

A storage-versus-control frontier

For the natural full-permutation action on (M\ge3) labels in two modes:

[ K_{\mathrm{store}}=\left\lceil\frac{\sqrt{8M+1}-3}{2}\right\rceil, \qquad K_{\mathrm{perm}}=M-2. ]

Logical labels	Storage photon cutoff	Coherent full-permutation cutoff
6	2	4
64	10	62
4,096	90	4,094

For 64 labels, the standard 63-dimensional component cannot fit until cutoff 62. Between cutoffs 10 and 61, sufficient total storage dimension coexists with an exact nonzero covariance-deficit plateau. A cycle and an adjacent transposition generate the same full-permutation contract.

These are model-derived register resource thresholds. Full permutation control is a separately imposed benchmark; it does not follow automatically from the finite-field linear task transitions.

The H6 simplex heart

Six ports—Lily, Tachy, Raven, Enya, Evie, and Kaya—label orthogonal codewords:

[ |\psi_j\rangle=\frac{|\mathrm{vac}\rangle}{\sqrt6}+|s_j\rangle, \qquad \langle s_i|s_j\rangle=\delta_{ij}-\frac16. ]

The excitation vectors form a regular five-simplex in a two-mode four-photon sector. Their shared vacuum contribution cancels the off-diagonal simplex overlap. The full states are orthogonal in six dimensions; the vacuum supplies the sixth dimension. Each label has mean photon number (10/3), and normalized excitation vectors meet at (\arccos(-1/5)\approx101.536959^\circ).

All 720 permutations are checked numerically, with exact symbolic full-Gram and simplex-Gram identities. The explicit code loses exact distinguishability under photon-number dephasing and fails arbitrary-state one-photon-loss correction. These limitations are tested in the package.

The six-wing activation law

In a constructed 36-coordinate binary state space, every proper subset of six specified generators exposes at most six task coordinates, while the complete set exposes all 36. Enabling the final generator can invalidate a smaller task memory because previously irrelevant distinctions become observable. The general family allows an arbitrarily large activation gap.

This is a synthetic mathematical example of high-order dependence among future instructions. It neither creates new raw information nor asserts a physical property of the named ports.

What is potentially new

The main candidate contribution is the combined task-to-spectrum allocation framework and its exact representation-deficit law, with explicit resource frontiers, multiplicity examples, and instruction-activation constructions.

The foundations have prior art: task-relative compression and realization, covariant encodings, bosonic energy bounds, representation theory, group averaging, regular simplices, and information-theoretic constraints. PRIOR_ART_AUDIT.md records the targeted search and closest comparisons; manuscript/references.json supplies bibliographic records.

The original targeted search did not identify a directly matching complete statement. This release does not establish worldwide uniqueness, absence of prior art, patent novelty, or a world-first discovery. No new exhaustive literature search is claimed for this packaging edition. A specialist equivalence review should compare theorem hypotheses and conclusions, not only terminology.

Verification and completeness

The original release reports the following; the packaging edition adds separate fresh-run records in verification/hf_release.

Check	Recorded result	Interpretation
Formal theorem/proposition/corollary statements with supplied proofs	19/19 — 100%	Textual proof coverage
Delivered regression tests	44/44 — 100% passing	Software checks in recorded environments
H6 permutations checked	720/720 — 100%	Exhaustive floating-point checks of (S_6)
H6 symbolic identities	2/2 — 100%	Exact full and simplex Gram identities
Multiplicity-trap permutations	120/120 — 100%	(S_5) example agrees with predicted defect 0.8
Six-wing generator subsets	64/64 — 100%	Closure ranks agree with the stated formula
Independent peer review	Not performed	No acceptance claim
Proof-assistant certification	Not produced	Tests do not certify general proofs
Worldwide novelty	Unverified	No meaningful percentage assigned
Optical hardware validation	Not performed	No fabricated device or measured performance claim

Completion counts describe the delivered finite core and checks. They are not probabilities that the mathematics is correct or important. The extensions proposed in the manuscript are not counted as completed results.

Quick start

Read the PDF without installing anything. To run the reference computations, use Python 3.10 or newer from the repository root:

python -m venv .venv

Activate the environment with .venv\Scripts\activate on Windows or source .venv/bin/activate on Linux/macOS, then:

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

The reference release environment used Python 3.12. Exact dependency versions are in requirements-tested.txt; the full range of minimum-version combinations has not been tested. run_reproduce.bat and run_reproduce.sh run the workflow after dependencies are installed. Regeneration writes outputs in data/, figures/, and verification/; use a separate extracted copy to preserve the distributed checksums.

The code supplies small-instance reference algorithms. Representation decompositions are inputs, not inferred from arbitrary group descriptions. Packing solvers can have exponential runtime. Matrix examples use only occupied sectors and can omit unused Fock levels.

See docs/REPRODUCIBILITY.md for expected results and the optional LaTeX/Pandoc rebuild. To publish your own copy, see UPLOAD_GUIDE.md.

Repository contents

Path	Contents
manuscript/	Complete PDF, editable LaTeX, searchable Markdown, references
code/	Quotient closure, representation packing, demos, regeneration
tests/	Mathematical and physical-limitation regression tests
data/	Five original synthetic CSV tables
dataset/	Headered H6 matrix adaptation for dataset loading
figures/	Five figures, each in PNG and PDF
verification/	Original numerical, software, and document records
verification/hf_release/	Fresh verification for this release edition
archives/	Byte-preserved original research ZIP
docs/	Reproduction guide, original README/checksums, packaging provenance
CLAIMS.json, STATUS.md	Original core claim and completion ledger
PRIOR_ART_AUDIT.md, EXPERT_REVIEW.md	Originality boundaries and challenge targets
CITATION.bib, RIGHTS.md, CHANGELOG.md	Attribution, rights status, release history
tools/, upload launchers	Local integrity checks and optional Hub publishing
SHA256SUMS.txt	Release file hashes; integrity, not proof or priority certification

Physical scope

The optical model assumes degenerate modes, ideal state preparation and readout, arbitrary number-preserving within-sector gates, and an externally available cross-sector phase reference. Register photon counts exclude reference energy, gate implementation cost, control complexity, and error-correction overhead. Passive linear optics alone is not shown sufficient.

Stored energy, dissipated work, and energy density are separate quantities. Dense-light language supplies the creative motif; no unlimited energy density, self-generated power, cosmological branch manipulation, or fabricated photonic prototype is established here.

All numerical datasets are mathematically generated. No training corpus, personal messages, source-image asset, or third-party paper is redistributed. The visible code in the source image is not decoded into a physical mechanism.

Citation and reuse

Use CITATION.bib and distinguish the AI-assisted formulation from Maciej Nowicki's creative direction and commission. There is no DOI or peer-reviewed publication identifier assigned in this package.

The source package selected no separate open-source or publication license. This edition preserves that status and omits a license identifier from the Hub metadata; see RIGHTS.md. Publishing the files does not by itself add a permissive reuse license.

Specialist review is especially useful for the exact deficit-law hypotheses, equivalence to earlier representation-constrained approximation results, and which physical gate restrictions alter the allocation frontier. Corrections should be recorded in a new version with the affected claims identified.