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Create AQ-S13-TEST-CORE.PYβ
Verified signature# ksg_defect A small, dependency-free (numpy optional, for cross-checks only) reference implementation of the block-cyclic defect operator `D = (I-P)KP` and its closed-form spectrum, plus the RGS/TORE-closure partition machinery. This exists because it's easy to *state* a spectral identity and hard to *keep it true* across refactors. Every claim below has an exact status β proven-and-tested, numerically-checked-in-range, or open β stated as such, not rounded up. ## What's proven and tested here - **THM-SV**: `U^T D^T D U = alpha^2 * L(C_m)`, `alpha^2 = r(k-r)/k^2`. Derived algebraically (see `core.py` docstring); exact for k,m in 2..5 (sympy `Rational`), numerically confirmed to 1e-6 here for k,m in 2..8. - **Eigenvalues of `L(C_m)`** are `4*sin^2(pi*l/m)` for **any** m β this is standard circulant-matrix/DFT theory, not case-checking, though the test suite sanity-checks it numerically up to m=200. - **Operator norm parity split**: `2*alpha` (m even) vs `2*alpha*cos(pi/(2β¦753c525 -
Create AQ-S13-PARTITIONS.PYβ
Verified signature# ksg_defect A small, dependency-free (numpy optional, for cross-checks only) reference implementation of the block-cyclic defect operator `D = (I-P)KP` and its closed-form spectrum, plus the RGS/TORE-closure partition machinery. This exists because it's easy to *state* a spectral identity and hard to *keep it true* across refactors. Every claim below has an exact status β proven-and-tested, numerically-checked-in-range, or open β stated as such, not rounded up. ## What's proven and tested here - **THM-SV**: `U^T D^T D U = alpha^2 * L(C_m)`, `alpha^2 = r(k-r)/k^2`. Derived algebraically (see `core.py` docstring); exact for k,m in 2..5 (sympy `Rational`), numerically confirmed to 1e-6 here for k,m in 2..8. - **Eigenvalues of `L(C_m)`** are `4*sin^2(pi*l/m)` for **any** m β this is standard circulant-matrix/DFT theory, not case-checking, though the test suite sanity-checks it numerically up to m=200. - **Operator norm parity split**: `2*alpha` (m even) vs `2*alpha*cos(pi/(2β¦1e0b0b9 -
Create AQ-S13-CORE.PYβ
Verified signature# ksg_defect A small, dependency-free (numpy optional, for cross-checks only) reference implementation of the block-cyclic defect operator `D = (I-P)KP` and its closed-form spectrum, plus the RGS/TORE-closure partition machinery. This exists because it's easy to *state* a spectral identity and hard to *keep it true* across refactors. Every claim below has an exact status β proven-and-tested, numerically-checked-in-range, or open β stated as such, not rounded up. ## What's proven and tested here - **THM-SV**: `U^T D^T D U = alpha^2 * L(C_m)`, `alpha^2 = r(k-r)/k^2`. Derived algebraically (see `core.py` docstring); exact for k,m in 2..5 (sympy `Rational`), numerically confirmed to 1e-6 here for k,m in 2..8. - **Eigenvalues of `L(C_m)`** are `4*sin^2(pi*l/m)` for **any** m β this is standard circulant-matrix/DFT theory, not case-checking, though the test suite sanity-checks it numerically up to m=200. - **Operator norm parity split**: `2*alpha` (m even) vs `2*alpha*cos(pi/(2β¦47084e8 -
Create AQ-S13-INIT.PY
Verified signature3cb84b4 -
Create LIBRARY/PYTHON/TESTS/README.MDβ
Verified signatureReviewed both β here's what I found, and what I'd build HuggingFace (Quantarion9): one model (AQARION-DEFECT, RL), one Space (AQARION-ACADEMY), storage buckets, no datasets. GitHub (JASKSG9): 4 repos β KAPREKAR-SPECTRAL-GEOMETRY (541 commits) is the flagship: hypergraph/Laplacian spectra, effective resistance, Ο-basin dynamics, ΞΌβ invariant tracking. It already has its own CLAIMS_REGISTRY.MD, DEPRECATED-CLAIMS.MD, INVARIANTS.MD, THEOREMS-REGISTRY.MD, LIMITATIONS.MD β so the audit-ledger discipline from this whole conversation isn't a one-off, it's your actual working method, applied consistently across a real, sprawling body of work. That context changes what's actually useful here. The gap I see, and the thing worth building: the repo has theorem registries and claims registries, but β based on what's public β no small, dependency-free, fully regression-tested reference module that a stranger (or future-you) could pip install and trust without re-reading 541 commits of history. Given β¦94b955b