# Verification of the neutral Jordan criteria

The accepted mathematical scope is the complete classification in Theorems 1.1 and 3.1 of the manuscript, including strict equality cases and the construction of invariant open domains. The general AIM source question is not closed.

## Analytic proof audit

The base-coordinate proof constructs a finite Fatou correction, sums its normally convergent defect and inverts the resulting coordinate on right half-strips. The critical drift in z_n^t is a/(2t n), independent of the petal sign. Summable errors give a limiting constant in the matrix logarithm. Commutativity follows from the polynomial-in-B hypothesis. The highest nonzero nilpotent coefficient gives the exact power at each Jordan height and a positive limiting norm at each equality. Block projections prevent cancellation. A weighted shear and a Lyapunov Hermitian norm construct genuinely open, connected, forward-invariant domains; pointwise convergence alone is not used as a substitute for that construction. Open vertical slices contain maximal-height vectors, proving necessity.

The base-coordinate change check includes its induced non-scalar second fiber coefficient; it does not apply the theorem outside its stated scalar-coefficient class. First-order tangency is kept distinct from all-orders formal-curve contact.

## Exact algebra regressions

Both normal Python and Python with optimization enabled pass the same 5,567 checks and produce byte-identical JSON. Explicit exception checks, rather than Python assertions, enforce failures.

| Check family | Cases |
| --- | ---: |
| Matrix logarithm | 6 |
| Weighted shear | 36 |
| Nilpotent height | 21 |
| Base clock | 8 |
| Finite Fatou jet | 32 |
| Critical drift balance | 16 |
| Coordinate residue | 36 |
| Scalar norm expansion | 12 |
| Strict threshold boundaries | 5,400 |

Run `python3 reproducibility/verify_exact.py --output NEW_NORMAL.json` and `python3 -O reproducibility/verify_exact.py --output NEW_OPTIMIZED.json` with SymPy installed. These are finite algebra checks, not formal verification of the infinite analytic proof.

## Numerical diagnostics and PDF

Five long-orbit diagnostic experiments are retained in the research dossier, including two critical cases. They show slow finite-time transients and are not rigorous interval certificates or evidence that a boundary is crossed. The manuscript's boundary conclusions follow from the analytic limiting constants.

The saved source compiled successfully with the built-in LaTeX compiler and Tectonic. All six final PDF pages were visually inspected; title, author footnote, equations, page numbers and references were readable without clipping or unresolved references. Artifact hashes and the visual-review receipt accompany the local publication package.

## Review status

AI-assisted, self-audited, unrefereed. No independent review, proof-assistant verification, exhaustive novelty certificate or general source closure is claimed. Third-party literature is cited but not redistributed in the source archive.