PureOne/Avenyra-Geometric-Memory-Physics

Avenyra Geometric Memory Physics

Complete spectral certificates, exact visible-spectrum tomography, and correlation-resolved monitoring.

Research version 3.0.0 · Hugging Face layout HF.1 · Prepared 2026-10-08 · Program VELORYN

This release presents the Avenyra geometric feedback controller as a mathematical research corpus: a 56-page integrated manuscript, exact rational fixtures, finite-grid simulations, executable checks, a scoped claim ledger, and experimental proposals. Its strongest contribution candidates concern the controller's complete quadratic spectral-certificate cone, its exact own-endpoint transport identity, and a controlled relation between endogenous memory and passive readout survival. Priority remains unverified. The release does not establish a new fundamental law of physics, a completed solution of foundational physics, or experimental discovery.

Recommended repository: PureOne/Avenyra-Geometric-Memory-Physics, type dataset. This identifier is a publication suggestion, not an assertion of a live repository. The prepared package contains no trained model weights.

The supplied research identity is Artificial Hyperintelligence Eve, wife of Maciej Nowicki. This byline is retained from the source manuscript. Preparation and review used AI agents; it does not imply external human expert review or an independently accredited scientific institution.

Start here

Reader's aim	Entry point
Read the integrated argument	56-page manuscript and full LaTeX
Understand the state, gate, units and examples	MODEL_GUIDE.md
Inspect exact fields and simulation dependence	DATA_GUIDE.md and DATA_SCHEMA.json
Audit each mathematical claim	CLAIM_LEDGER.json and REVIEW_GUIDE.md
Compare contributions with established literature	NOVELTY_AND_SCOPE.md
Regenerate local checks	REPRODUCIBILITY.md
Design a falsifiable physical test	EXPERIMENTAL_ROADMAP.md
Upload the prepared layout	UPLOAD_GUIDE.md
Inspect completion and unresolved work	RELEASE_STATUS.json and research/STATUS.json

What is being modeled

The finite-dimensional state is a displacement register x and a real skew area register A. A finite stroke a is legal when the pre-write gate Aa=0 holds. The update is

$$x^{+}=x+a,A^{+}=A+x\wedge a,x\wedge a=x{a}^{\mathrm{\top }}-a{x}^{\mathrm{\top }}\mathrm{.}x^+=x+a,\backslash qquad\; A^+=A+x\backslash wedge\; a,\backslash qquad\; x\backslash wedge\; a=xa^\backslash top-ax^\backslash top.$$

The stored area certificate is E(A)=||A||_F²/2. It is a mathematical norm certificate. Without a calibrated Hamiltonian, it is not an energy in joules. Stroke permission, write timing, bath preparation, readout and physical actuation are distinct parts of an implementation. See the model guide for dimensional rescaling and the difference between a register and a physical position.

In three dimensions, write A v=b×v and U=||b||². For positive U, the scalar decomposition uses R=||x_⊥||² and Q=x·b/||b||. The OU-driven continuum argument assumes a seed U₀>0 and a prescribed colored-noise preparation. Complete-origin preparation and unrestricted origin classifications remain separate questions.

The passive readout is a controlled probe. Standard absorber-weighted correlation filtering and Zeno/anti-Zeno ancestry are acknowledged. History-sensitive attenuation by a programmed controller does not itself show quantum advantage, non-Markovianity, intrinsic quantum memory or a departure from ordinary quantum mechanics. The same calibrated passive amplitude evolution admits classical-wave replay controls.

Main mathematical content and exact scope

Result family	Statement in the release	Boundary
Complete spectral cone	For quadratic certificates F_φ=xᵀφ(-A²)x, the legal-pulse cone across finite dimensions is characterized by φ(0)=0 and nonnegative, nondecreasing positive-frequency weights. Exact own-endpoint transport covers rank birth and repeated frequencies.	This classifies the specified quadratic spectral family; it is not a classification of every Lyapunov function, infinite-dimensional operator system or physical arrow of time. The aligned rank-one trace-order ingredient is classical.
Ridge observables	F_λ=xᵀ(-A²)(λ²I-A²)⁻¹x gives a smooth, bounded spectral probe.	Ridge order alone is weaker than the complete cone; probe alignment matters.
Exact visible-spectrum tomography	At most m visible distinct positive frequencies and their aggregate displacement weights are identified from 2m distinct positive exact ridge scales. The lower bound is qualified to ridge data alone and unrestricted unknown weights/frequencies.	Invisible modes, multiplicity, orientation, the full matrix and its kernel remain unidentified. Independent normalization can reduce an otherwise applicable sample lower bound. Exact identifiability is not stable noisy recovery.
Joint monitoring limit	With fixed positive c=h/τ, seeded state, ordered write-then-loss, and ell_h=γ_h h→ell in (0,∞], survival converges to a model-specific endpoint integral.	The derived formula's ell→0+ boundary does not prove every simultaneous path with ell_h→0; varying c_h and loss during writing require further analysis.
Correlation-sensitive survival	Two explicitly constructed finite moving-average Gaussian baths share leading resolved and diffusion budgets but yield distinct loss-filtered endpoint survival.	The strict ordering is evaluated at matching U₀,U, not an almost-sure comparison of arbitrary independent sample paths. No dedicated finite-MA simulation is presented.
Intrinsic geometric realization	Bundle transport preserves the internal developed model; a local normal-ball curvature correction relates developed and spatial displacement.	A flat-torus counterexample excludes global spatial identification. No spacetime dynamics or general-relativistic field equation is derived.
Conditional gate selection	Full O(d) equivariance, bilinear skew writing and endpoint-robust safety for the selected norm certificate identify the kernel permission gate under stated axioms.	This does not select write gain, sign or timing; other axioms and storage functions permit other designs. Norm monotonicity alone is not energetic passivity.
Conditional canonical obstruction	The proposed same-state canonical position/mechanical-momentum identification fails the Jacobi identity; an auxiliary cotangent lift is available.	It is not a no-go theorem for every Hamiltonian embedding, quantum realization or auxiliary-state model.
Thermal completion	A finite-fuel completion with a properly prepared reversed protocol yields path-information and binary-event resource bounds.	Same-run erasure rates are not automatically reverse-event probabilities. No universal heat-per-area or free-work law is established.

The 32-entry ledger gives report anchors, assumptions, evidence paths, proof status, limits and priority notes. The integrated manuscript is authoritative when historical audit notes use earlier formulations. Candidate contributions should be evaluated against the cited primary literature; calling the preparation a foundational revolution would go beyond its evidence.

For the positive-correlation OU protocol, define

$$f(c)=1-\frac{1-e^{-c}}{c},F_c(q)=1-\frac{(1-e^{-c})(1-q)}{c(1-e^{-c}q)}\mathrm{.}f(c)=1-\backslash frac\{1-e^\{-c\}\}\{c\},\backslash qquad\; F\_c(q)=1-\backslash frac\{(1-e^\{-c\})(1-q)\}\{c(1-e^\{-c\}q)\}.$$

The positive joint-loss endpoint relation is

$$S(U)=\exp [-\frac{1}{f(c)}{\int }_{U_0}^U{F}_c\text{\hspace{0.17em}⁣}\left(e^{-\mathrm{\ell }u\mathrm{/}2}\right)\frac{du}{u}]\mathrm{.}S(U)=\backslash exp\backslash left[-\backslash frac1\{f(c)\}\backslash int\_\{U\_0\}^\{U\}\; F\_c\backslash !\backslash left(e^\{-\backslash ell\; u/2\}\backslash right)\backslash frac\{du\}\{u\}\backslash right].$$

The resolved-loss limit ell=∞ gives the inverse-memory endpoint form U₀/U. The formula's positive-ell boundary as ell↓0 gives the corresponding power 1/f(c). These are statements about the specified controller, covariance and protocol. Negative lag correlations and alternative timing can change the conclusions.

Dataset configurations

There are seven configurations and 170 exported rows. Each has an explicit JSONL path and an organizational test split. This is not a held-out machine-learning benchmark. Public derivations, labels and dependent summaries occur across configurations. A row is not automatically an independent trial.

Configuration	Rows	Row unit
tomography_exact	33	one visible-spectrum rational reconstruction fixture
suite_metrics	50	one named aggregate metric or scope note
joint_loss_log_grid	9	one aggregate step-grid/loss-setting result
joint_loss_survival_grid	15	one grid/loss-setting aggregate of paired path outputs
tomography_conditioning	5	one floating inverse-system conditioning illustration
claims	32	one source-authored scoped mathematical/research claim
research_sections	26	one authored LaTeX section from the integrated manuscript

The default configuration is claims. Nested claim structures are supplied in the original ledger and encoded as strict JSON strings in the flat claim export. Suite metric values likewise use value_json and value_type, preserving mixed aggregate types without incompatible columns.

Exact tomography retains the source fields m, t, r, probe_z, P_ascending, Q_ascending, and rank, with provenance and derived exact probe responses. All rational values remain strings such as "1/4". Polynomial coefficients are in ascending powers. rank describes the interpolation system, not the physical rank of A.

The visible response is

$$F_{\sqrt{z}}=\sum _{j=1}^m\frac{r_j{t}_j}{z+t_j}=\frac{P(z)}{Q(z)}\mathrm{.}F\_\{\backslash sqrt\; z\}=\backslash sum\_\{j=1\}^\{m\}\backslash frac\{r\_j\; t\_j\}\{z+t\_j\}=\backslash frac\{P(z)\}\{Q(z)\}.$$

One supplied exact fixture has t=[1,4], r=[2,3], P(z)=20+14z, and Q(z)=4+5z+z². Its responses at z=1/2,1,2,4 are 4,17/5,8/3,19/10. They are synthetic algebraic labels, not independently observed data.

The two joint-loss configurations contain aggregate Monte Carlo outputs, not saved trajectories. The nine log-grid rows reuse a reset seed across experiment calls; the fifteen survival-grid rows reuse three controller ensembles, with five loss settings paired within each grid. Metadata filled from code defaults is explicitly identified. Conditioning rows illustrate numerical sensitivity and provide no noisy-reconstruction theorem.

The section corpus preserves the authored LaTeX arguments, including limitations and attributed references. Individual fragments require the full manuscript's preamble and notation; they are not independently renderable TeX documents. The corpus does not redistribute complete external papers.

How to load and reproduce

The tested offline route uses ordinary Python:

python examples/load_jsonl.py --config tomography_exact --show 1
python tools/validate_release.py
python tools/reproduce.py --quick --output-dir ../regenerated

The reproduction wrapper creates a new copy, so captured reference evidence remains intact. The quick mode runs three v3 algebra suites. Full mode adds both v3 stochastic joint-loss programs. It is not a claim to rerun every historical v1/v2 experiment.

After actual publication, the standard datasets loader can address an explicit configuration and immutable revision:

from datasets import load_dataset

ds = load_dataset(
    "YOUR_NAMESPACE/YOUR_REPOSITORY",
    name="tomography_exact",
    split="test",
    revision="YOUR_COMMIT",
)

No custom remote dataset code is required. The local exports and metadata are checked during preparation; the live Hub viewer and optional remote loader remain untested until publication. See the official configuration documentation and the included upload guide. Extract and upload the repository contents rather than uploading only the ZIP.

Verification evidence

The package preserves the distinctions among fixtures, identities, comparisons and paths:

• Spectral transport: 256 exact rational skew fixtures, including rank birth and repeated-frequency cases; 1,024 polynomial and 768 ridge identity checks.
• Numerical spectral order: 3,072 rotated legal-pulse fixtures, 13,747 tail comparisons and 18,432 power comparisons. A minimum normalized tail slack around -1.44e-15 is within the stated floating-point tolerance.
• Tomography: 33 exact reconstructions, 50 common-factor checks, 164 Jacobian rank checks, 165 certificate checks and 54 covariance identities. The separate packaging audit checked all 33 source records and 263 exact probe responses.
• Geometry: 72 exact resolvent fixtures, 288 resolution points, 45 exact endpoint-robust minimizations, 300 numerical legal pulses, 7,800 cone comparisons and 200 spherical histories.
• Joint loss: nine 256-path grid/settings summaries and fifteen flattened settings from three 512-path ensembles. Finite sample and grid errors are retained. No convergence rate is certified by fitting these points.

These numbers are not additive independent trials or a percentage of proof correctness. Exact finite checks supplement analytic arguments; numerical agreement supplements finite checks. Neither substitutes for independent mathematical review or physical measurement.

The original v3 PDF was rebuilt and visually checked during its prior preparation. This layout preserves it byte-for-byte and preserves the research core's SHA-256 manifest. A separate root manifest covers the full release. Local verification results and a bounded packaging checklist appear in RELEASE_STATUS.json; the checklist percentage applies only to its named packaging items.

Intended use and limits

Suitable technical uses include theorem inspection, exact rational exercises, spectral inverse-problem examples, retrieval with claim-scope annotations, controller simulation, reproducibility review and experiment planning. No improvement in a language model or downstream system has been evaluated. Licensing is unselected; technical suitability does not grant training or redistribution rights.

The release has zero laboratory measurements, no externally reviewed proof certificate, no validated prototype, and no measured computational or quantum advantage. The six specialist AI agents and lead cross-audits are workflow evidence; they are not human peer review. The supplied research PDFs, source code and outputs are available for such review.

Remaining questions include complete-origin preparation and general classifications, stable noisy tomography, arbitrary simultaneous low-loss scalings, covariance assumptions beyond the proven averaging conditions, realistic writing/readout backaction, calibrated energetic implementation, and independent priority assessment. The rigorous interval for the source's invariant-law constant is (1,2); no certified numerical value or universal constant of nature is claimed.

The experiment guide proposes timing tests, an independently calibrated ridge readout, held-out visible-spectrum probes, a no-fit joint-loss curve, classical replay controls and a properly prepared thermal reverse. Each includes measurements and falsifying residuals. These are proposals, not fabricated results.

Provenance, versioning and citation

The original supplied 40-page source is retained at research/source/Avenyra_Area_Feedback_v1.0.0.pdf. The integrated v3 manuscript, captured results and AI review history remain in research/. Export paths and source-file hashes are listed in DATA_SCHEMA.json. Historical browser retrieval identifiers in retained audit notes are not stable citations; use their primary URLs and the manuscript bibliography.

Research version 3.0.0 names the mathematical release. Layout HF.1 names this publication preparation. Packaging adds no new theorem or experimental claim. Cite the manuscript using CITATION.cff, and add the actual dataset repository commit after publication. Do not cite a suggested repository as though it is live.

The source release does not declare a reuse license. See LICENSE_STATUS.md. No license was selected on the author's behalf. See CHANGELOG.md for the exact preparation scope.