# Verification report

Manuscript: A Gaussian Obstruction to Uniform Mesh Bounds for Differential Operators

Author: Alper Ferudun, Mercury Software GmbH

Version 1.0, 10 October 2026. Five-page English preprint.

## Mathematical scope

The accepted classification concerns nonzero finite real polynomial-coefficient
hyperbolicity preservers acting on the whole Laguerre-Polya class: only nonzero
scalar multiplication retains a positive uniform fraction of additive mesh.
For every nonscalar operator, three-simple-zero inputs of any prescribed
positive mesh make the output mesh tend to zero. The local theorem proves
the Hermite cluster and its explicit common drift and second-order dilation
at a nonsingular center, for arbitrary fixed real polynomial coefficients.
The broad AIM-ANALYSIS-0146 question is not claimed resolved.

The written self-audit checks all quantifiers, LP approximation, normalization,
simple real root branches, Taylor coefficients, error order, nonzero output,
order-zero operators and exclusions. There are no known gaps in the stated
scope. This is originating-researcher self-audit, not independent review or
proof-assistant verification. No exhaustive novelty or absolute-priority
certification is claimed.

## Reproducibility

The supplied standard-library Python checker passes in ordinary and -O
modes with byte-identical output: 450 operator/parameter cases, 9,505 exact
conditions and six negative controls. Each enumerated case includes rational
endpoint estimates valid throughout a certified interval of Gaussian
parameters. These finite regressions supplement the written arbitrary-order
proof; they are not themselves a proof for every operator.

Checker SHA-256:
517abfe3bf83670f29a6a94f35d6ae9bdd41b7cc2ab7b0fc706affdd93282bc0

Both recorded-output SHA-256 values:
90d97e8adfa771ed74b3dde8754c4bbda01b09afa04d89cc255699736855976c

Run `python3 reproducibility/check_gaussian_clusters.py` and
`python3 -O reproducibility/check_gaussian_clusters.py` from this package.
The research-check receipt preserves the originating runs; fresh package
runs reproduce the accepted output exactly.

## Manuscript checks

The final source compiled successfully with the desktop LaTeX compiler and
Tectonic. The exported PDF has five pages, searchable text, resolved citations
and labels, and no overfull/underfull boxes, undefined commands or compiler
warnings. All five final pages were visually checked: the first four are
pixel-identical to inspected draft pages; the fifth was inspected after
the final bibliography adjustment. No clipping or overlapping text was found.
The author line contains only the name; affiliation and contact details are
in a footnote. AI assistance is disclosed in ordinary body prose.

Final PDF SHA-256:
18de16b5ae9535aca5c61810f6c704500a74806bf1df3d49a5a233c471074a7a

Final LaTeX SHA-256:
eb8886669dbe3e3023b4cbc19f4a6338750795cdde2bcc331de22de84120ae3a

## Source and novelty boundaries

The inherited cubic-Gaussian construction for D^r is credited, as are
older first-derivative failures and classical polynomial-domain mesh results.
The proposed extension is the coefficient-general classification and common
correction formula. The precise AIMPL page could not be freshly retrieved
with valid TLS; its wording and item identity are taken from the frozen
v1.6.0 corpus, not represented as independently verified live source status.
See source_and_novelty_review.md and source-provenance.json.

This package is an AI-assisted, unrefereed preprint. Publication, DOI
registration, indexing, independent endorsement and mathematical correctness
are distinct matters. No external publication is certified by this report.