# Independent review guide

This release presents mathematical claims for a specified geometric-memory controller and proposed conventional thermal/optical readouts. Its proofs and cross-audits were produced by AI agents. It has **no external human or peer review, proof-assistant certification, laboratory measurements or fabricated prototype**. No established fundamental physics breakthrough is claimed. Independent review is invited before treating the analytic arguments as verified research.

Start with the [56-page report](research/Avenyra_Geometric_Memory_Physics.pdf), its [LaTeX source](research/Avenyra_Geometric_Memory_Physics.tex), [STATUS](research/STATUS.json) and [claim ledger](CLAIM_LEDGER.json). The ledger has 32 scoped entries with stable IDs, theorem/equation anchors, hypotheses, evidence paths, limitations and priority status. Review notes in `research/reviews/` preserve the chronology; some earlier conditional formulations were subsequently resolved. The integrated v3 report states the current claims.

## Highest-value mathematical checks

1. **Exact spectral transport and complete cone** — Section 17, Theorems 17.1–17.3; `AVGMP-C001`–`C003`. Check the own-area alignment in the rank-one update, repeated frequencies, rank birth and discontinuous monotone scalar weights. The complete cone concerns finite-dimensional quadratic scalar spectral certificates. It does not classify every Lyapunov function or every reachable state. Separate the established generalized Klein/order argument from its model-specific endpoint specialization.

2. **Visible-spectrum tomography** — Section 17.5, Theorem 17.4; `AVGMP-C004`. Check both the rational-interpolation sufficiency and the local Jacobian obstruction. The $2m$ lower bound is for **ridge samples alone, with unrestricted positive weights and distinct frequencies**. Independent normalization, known weights or other observations can reduce the count. Invisible modes, multiplicities and orientation are not reconstructed. Exact identifiability supplies no stable noisy inverse.

3. **Joint write/loss limits and finite-MA separation** — Section 18, Theorem 18.1 and Corollary 18.2; `AVGMP-Q002`–`Q004`. Check the write-then-held-loss indexing, the $q^k$ bright-lag filter, Gaussian Poisson equation, uniform parameter derivatives and endogenous bounded-variation weighting. The OU theorem uses seeded memory and positive limiting loss per dwell; taking positive $\ell\downarrow0$ afterward does not settle arbitrary sequences $\ell_h\to0$. The two MA baths share their controller diffusion and sequential exponents. Compare their different joint survival curves at the **same initial and final memory values $U_0,U$**. No dedicated finite-MA path simulation is bundled; its claim rests on the analytic finite-state extension.

4. **Singular entrances** — Section 14; `AVGMP-E001`–`E004`. Check the Volterra estimates and selection of the immediate-writing boundary class before the circular-phase reduction. Nonzero-anchor joint weak uniqueness and absence of a strong solution concern the specified Brownian innovation. They do not exclude all Brownian generating filtrations. The origin result selects a positive selfsimilar scalar entrance and constructs vector weak existence; general origin classification and full origin-vector uniqueness remain open.

5. **Constitutive axioms and geometry** — Section 19; `AVGMP-G001`–`G004`. Check full $O(d)$, rather than only oriented $SO(d)$, equivariance, bilinearity and the endpoint-independent permission quantifier. The norm-passivity axiom selects the kernel gate but not the write gain, timing or physical energetic supply. The spatial estimate requires a normal ball and stated curvature/injectivity conditions. The Jacobi obstruction applies to the declared canonical variable identification; an auxiliary cotangent Hamiltonian remains possible.

6. **Thermal reversal and resources** — Section 20; `AVGMP-F001`–`F003`. Check the full resolved state, boundary preparation, fuel budget and reversal of odd controls. The binary entropy bound uses the correctly prepared reverse-event probability $q_R$. Same-run transient erasure counts cannot generally replace it. The stronger three-bin formula has an additional compatibility hypothesis. There is no universal heat per geometric area.

## Reproduce finite evidence

Use the dependencies in [requirements.txt](research/requirements.txt). From the `research/` directory, the main algebraic checks are:

```bash
python3 v3/spectral_order_check.py
python3 v3/tomography_check.py
python3 v3/foundational_geometry_checks.py
```

The heavier stochastic checks are `python3 v3/joint_loss_check.py --paths 256` and `python3 v3/joint_loss_simulation.py`. Earlier scripts and recorded results remain in the bundle; the [research README](research/README.md) describes their scope. `sha256sum -c SHA256SUMS.txt`, run inside `research/`, checks the supplied bundle manifest.

Exact rational fixtures test specific identities and counterexamples; they are not proof-assistant checks. Floating-point fixtures and finite-grid simulations have numerical, sampling and discretization limits. Passing them does not establish a universal theorem, priority or a physical effect.

## Physics and priority review

A useful experimental challenge is independently calibrated agreement of the legal gate, spectral response and joint monitoring curve, with complete controller work and proper forward/reverse preparation. Compare classical-wave readout and conventional hidden-state/controller models under matched protocols. State-memory geometry alone does not distinguish a new fundamental principle from a powered controller.

Generic trace order, rational interpolation, covariance-filtered optical attenuation, eternal circular Brownian motion, geometric connection estimates, cotangent lifts and path-information bounds have established antecedents cited in the report. Priority remains unverified; proposed contributions are the narrower model-specific combinations and endpoint laws.

For a correction, identify the ledger ID and report label, quote the disputed statement with its hypotheses, and supply the smallest counterexample or missing estimate. For executable failures, include command, package versions, seed and unexpected output. A physical challenge should specify the preparation, clock, probe, work account and measured observable.