# Verification report

Manuscript: A Diagonal-Jet Criterion for Normalized Gaussian Analytic Covariances

Author: Alper Ferudun, Mercury Software GmbH.
Date: 29 September 2026.

## Accepted mathematical scope

For a connected plane domain and a C2 Hermitian PSD unit-diagonal complex
kernel R, normalized centered proper GAF realization with positive
variance is equivalent to zero diagonal antiholomorphic residual and an
exact real amplitude one-form. On a simply connected domain the latter
is a local closedness condition. Reconstruction is unique up to positive
scale. The proof handles arbitrary off-diagonal zeros.

The sharp residual inequality, every-base-section-has-zeros example, and
annular period obstruction are proved in the manuscript. The ordinary
Gaussian series and zero-intensity formula are attributed classical
ingredients. The entire ambiguous AIM source record remains unresolved.

## Exact diagnostics

Run `python3 -I reproducibility/checks/check_diagonal_jets.py` from the
extracted source archive. No third-party Python dependency is required.

Each of the isolated Python 3.9.6 and 3.13.5 runs passed 13,295 assertions:
1,381 diagonal cases across six kernel families, 3,072 Gram configurations,
and additional algebra, degeneracy, sharpness, section-zero and mutation
checks. Arithmetic is exact rational complex arithmetic in a truncated
second-order Taylor ring; no tolerances or floating point are used.
Reports match except the Python version.

The checker tests finite diagnostics, not universal PSD, analytic series
convergence or the general theorem. The period coefficient is checked
algebraically, while the integral itself has an analytic proof. Two
runtimes do not constitute independent mathematical review.

## Audit boundaries

The originating researcher checked derivative-feature regularity,
Wirtinger signs, zero divisions, positive real versus complex gauges,
periods versus phase winding, simultaneous a.s. convergence, diagonal
chain rules and the factor in the zero intensity. A mistaken extra term
in an early explanatory diagonal chain rule was corrected before release;
the rejected term and exact Fock witness are preserved.

Bounded primary-source searches do not establish novelty or absolute
priority. No external mathematical review, peer review or proof-assistant
verification is represented as completed. Publication is not evidence of
correctness, priority or resolution of another interpretation of the source.

The final build and all-page visual-review receipt, source/checker hashes,
and originating-researcher acceptance are included in the source package.