Evidence authority: Canonical Corrected Formalism is the governing status ledger. Exact facts are called facts. Machine-precision computation, statistical significance, experiment, replication, conditional models, and open hypotheses remain distinct designations.

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Hardware-in-the-loop (HIL) validation status (2026-07-19)

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Latest evidence correction

The new Hydrogen Bromide quantum-molecular page records that the verified NRL–IonQ corrosion-relevant result is a CVQE ground-state calculation for hydronium $H_3O^+$, not an HBr experiment or a measurement of $\Omega_c=0.376$. The related Quantum Information Theory page supplies the common state, channel, entropy, and measurement language.

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Fractal and hyperbolic evidence boundary

The site-wide geometry audit is Fractals and Hyperbolic Geometry. It separates established fractal and hyperbolic mathematics, finite simulations, quantum-model proposals, and unverified bridges to $E_{47}$, cognition, cosmology, or engineering.

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Metamaterials validation program

Metamaterials — Canonical Engineering Synthesis establishes the validation ladder from constitutive equations and finite numerical residuals through mesh convergence, scattering retrieval, tolerance studies, fabrication, calibrated measurement, and independent replication. Exact K47 algebra is separated from open material identification.

PQSPI evidence boundary

The canonical audit is Post-Quantum Self-Preserving Intelligence (PQSPI). Exact projector and contraction mathematics is separated from internal HOMEBASE reports, proposed AI-coherence metrics, protocol grammar, standardized PQC obligations, phonon-interface experiments, and speculative observer-dependent or strategic claims.

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Cryptography evidence boundary

The full audit is Spectral Cryptography and Hardware Formalism. Exact evidence currently covers the $125\to47$ spectral selector, projector identities, stable $K^\dagger K$ contraction, scalar Newton convergence, and IEEE portal metadata. RSC confidentiality, ISSR hardness, reversible decoding, scalable security levels, ASIC performance, mixed-signal tamper response, standards conformance, and physical fabrication remain open or engineering obligations.

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Invariant Grammar evidence boundary

The language program is now audited at Invariant Grammar — Mathematical Linguistics, Chomsky Hierarchies, and Lexical Attractors. Exact items include finite typing, the context-free form of the displayed BNF, the canonical spectral witness, and contraction identities. The proposed Chomsky extension, universal lexical attractor, $\ker w\to E_{47}$ bridge, and cross-domain physical threshold remain structural or open.

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Skyrmion evidence boundary

The site’s topology evidence is now consolidated on Skyrmions. Exact entries include the homotopy groups, winding integrals, canonical $E_{47}$ decomposition, and $\operatorname{Var}(C)=576a^2b^2$. Conditional entries include the target orbit, coupling normalization, and anisotropic soliton existence. RI identity, universal threshold, propulsion, and zero-inertia claims remain open or speculative.

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Canonical computational audit

All Python, SymPy, NumPy, SciPy, QuTiP, VQE, residual, finite-simulation, and reproducibility evidence is now consolidated on Python and Numerical Validation. That page is authoritative for distinguishing machine-precision identities, exact finite mathematics, seeded or dataset-dependent outputs, repaired prototypes, and open biological or physical bridges.

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Evidence and Validation

Claims are separated by theorem status, numerical reproduction, physical postulate, fit, model, and open obligation.

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Governing standard

A claim receives [N] Numerically reproduced status only when the record includes:

  1. exact claim and mathematical source;