# Verification report

The five-page English preprint proves polynomial-presentation
independence of the ambient adjoint Cartier algebra for every integral
finite-type algebra over a perfect field of characteristic p > 0.
It also proves pair-lift independence, localization and gluing. Its
characteristic-zero comparison is credited to existing theorems and
has the fixed-pair, sufficiently-general-reduction quantifier.

The original researcher accepted the written argument after a detailed
self-audit. No independent human review or proof-assistant verification
occurred. Acceptance does not certify novelty or whole-source closure.

## Mathematical checks

- Compatibility follows from the c-parameter pigeonhole inclusion
  m^{c(q-1)+1} contained in m^[q] at the prime kernel.
- The dummy-variable trace leaves only h_{q-1}; ideal-power containment
  gives one inclusion and z^{q-1}a gives the reverse inclusion.
- Graph presentations compare arbitrary embeddings while transporting
  the full Hom module, not an assumed invariant chosen trace generator.
- Composition uses a^(p^f)b for the outer degree-e and inner degree-f
  maps. The coefficient exponent and ceiling inequality are explicit.
- Compatible maps kill differences of pair lifts on the quotient.
  The localized graph su-1 compares a localization with its polynomial
  presentation, after which standard test-ideal localization applies.
- The comparison uses the regular ambient ring, not a Q-Gorenstein
  assumption on the quotient. The correction is Khat-J, not just Khat.

## Exact computations

The unchanged standard-library sparse-polynomial checker passed 10,069
assertions on Python 3.13.5 and 3.12.14, counted once. The suite covers
finite traces and graph changes for (p,e) = (2,1), (2,2), (2,3), (3,1),
(3,2), (5,1), (7,1); compatibility, reverse witnesses, unequal-degree
composition order, and exact rational ceiling inequalities. It also
retains a separate monomial-curve differential example in eight prime
characteristics. That example is not used as an unproved equality of
the ambient test ideal with a normalization-defined ideal.

Most assertions check elementary exponent inequalities; the count does
not measure proof strength. Finite tests do not establish the general
theorem, whose proof is in the manuscript and accompanying notes.

## Artifact checks and limits

The standalone source compiled with the native document compiler and
was exported with the installed cached TeX runtime. All five rendered
pages were visually inspected, including formulas, references, author
footnote and prose AI disclosure. The final package manifest records
source, PDF, archive and evidence hashes. Third-party PDFs are excluded
from the public source archive.

The source AIM record is an open-ended construction request, not a
single uniquely quantified conjecture. It is not counted as fully
resolved. Novelty remains undetermined after bounded literature search.
This is an AI-assisted, self-audited, unrefereed mathematical note.