# Verification report

## Result and limits

The manuscript proves geometric and arithmetic independence criteria for normalized Chebyshev maps with nonconstant affine targets over function fields. The endpoint-graph classification includes repeated endpoint pairs, exact subfamily intersections, and full geometric towers. The finite arithmetic formula assumes globally pairwise coprime degrees. The arithmetic tower theorem characterizes finite index for every degree list and bounds a finite index by the number-field degree. Finite polynomial statements require degrees at least three; cofinal levels include towers generated by degree-two maps.

The original AIM independence question remains unresolved in general. These theorems do not specialize to arbitrary constant targets over number fields, and they do not classify arbitrary rational maps or rational targets.

## Written proof audit

The proof audit checks the faithful dihedral root action; isolation of edge-derived subgroups by endpoint commutators; the odd/even quadratic-rank formula; repeated-pair least-common-multiple and greatest-common-divisor covers; intersection degrees; and the finite-level to inverse-limit argument. Auxiliary degree-one and degree-two radical covers are distinguished from polynomial splitting fields.

The arithmetic audit separately verifies regularity over the cyclotomic constant field, square relations including affine slopes, compatible semilinear lifts, the central root-action kernel, the full constant-field formula, and the index divisibility argument. A shared prime yields common real cyclotomic constants of unbounded degree, supplying the converse for towers. No inference from agreement of numerical examples substitutes for these written arguments.

## Exact finite regressions

The geometric checker passes 22,061 conditions on 841 configurations. The arithmetic checker passes 646,484 conditions, including 16 explicit group models with 87,576 enumerated elements, 42 quadratic models, 818 subgroup models, and six negative controls. Normal and optimized Python runs are byte-identical. Both scripts and the saved outputs are distributed under `reproducibility/`.

These are exact finite regressions, not a formal verification system or a universal proof of the field-theoretic claims. The scripts require only the Python standard library.

## Document checks and review status

The saved source compiles with the desktop LaTeX compiler and Tectonic. The final nine-page PDF was visually inspected; references, formulas, author information and disclosure were checked. Source and payload hashes are recorded in the manifests.

This is project-level self-audit of AI-assisted work. Independent human peer review and formal proof-assistant verification have not been completed and are not implied. The source-and-novelty review is bounded; no absolute priority claim is made.