Verification report — final v2.0.0
Date: 1 October 2026. All ten release certificate programs passed. The conditional-risk certificate was strengthened to compute the full rare-event distribution and rerun successfully after the suite. Editorial hypothesis/notation changes do not change any certificate computation.
| Check | Method and actual coverage | Outcome |
|---|---|---|
| Canonical seven-ray design | All 15 degree-four coefficients; exact algebraic arithmetic; sign matrix and characteristic polynomial | PASS |
| Independent obstruction audit | Rational/algebraic identities, orthogonal eigenvectors, all seven conference residuals, scalar optimizer polynomial | PASS |
| Rational realization | All 15 fourth moments; positive weights; nonzero dots; exact switching/permutation equivalence | PASS |
| Polar transport | 1284 real/complex numerical comparisons plus 8 finite construction examples | PASS |
| Constrained circulation | 6 real/complex constrained opening examples | PASS |
| Continuous family | Formal rational polynomial identities, harmonic cancellation, involution, 9 rational phase specializations, exact conference identities | PASS |
| Compatible masks | E5, K4, C5, C7, W5; every independent-set dual inequality; exact rational primal/dual equality; exhaustive coloring/robust subset masses; concrete state-mask and boundary examples | PASS |
| Weighted masks/hierarchy | 4 mixed-mask real/complex constructions; 27 three-stage paths; exact inverse order and endpoint amplification identities checked numerically | PASS |
| Robust scalar prefix example | 4368 exact states at depths 4,8,12; 21840 closed-noise test points; conditional entropy, two-bit overhead, precision compensation | PASS |
| Conditional risk/control | Exact rational 16-atom non-Gaussian law; sharp two-atom example; full three-atom rare-posterior distribution | PASS |
Recorded numerical errors
Polar comparison minimum lower-bound margin: -2.22e-16 (roundoff-scale negative); maximum Parseval residual: 1.439e-14. The comparisons use explicit numerical tolerances; roundoff is not represented as exact proof.
Hierarchy maximum correctly ordered inverse residual: 6.239e-16; maximum endpoint noise-amplification equality error: 2.665e-15. Largest observed exact three-stage amplification: 4.89224685416, below the proved product bound 5.19615242271.
Environment
Python 3.12.14; NumPy 2.3.5; SciPy 1.17.0. Exact programs use Fraction and finite polynomial arithmetic; frame programs use NumPy/SciPy. Final manuscript is built with pdfLaTeX. PDF content and visual-layout verification are recorded in PDF_QA.md.
Interpretation
The scripts certify finite algebraic identities and test representative numerical mechanisms. Universal results, asymptotic limits, relative openness, and optimality come from the written proofs. The tests do not numerically prove a universal theorem, formalize proofs in a proof assistant, or certify publication priority. Four separate final derivation audits passed. Required explicit local hypotheses from the finite-metadata audit were incorporated before freeze.