# Verification report

This report is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

## Mathematical verdict

`ACCEPT_COMPLETE`.

The proof has three independent logical gates:

1. finite cyclic-order partial maps extend to Thompson's group T by matching
   dyadic subdivisions;
2. every non-diagonal orbital graph on k-subsets contains two-step replacements
   for the edges of a connected local-move graph;
3. the stabilizer kernel is F^k, its cyclic quotient splits, and finite-subgroup
   orders distinguish different k.

Each quantifier and boundary case, including k = 1 and the single-gap case
k = 2, was checked explicitly. The theorem concerns dyadic finite sets only.

## Exact finite check

`reproducibility/verify_circular_orbitals.py` enumerates all directed cyclic
A/B/X orbit words for k = 1,...,7 and independently verifies connectedness of
finite local-move graphs for k = 1,...,5. It reports 1, 4, 13, 50, 201, 898,
and 4117 directed types, respectively, and all tested move graphs are
connected. These checks support but do not replace the all-k symbolic proof.

The check passes identically under the system and bundled Python runtimes.

## Literature and source gate

The official archived AIMPL wording, official workshop report, standard T
definition, six closest published/preprint sources, current bibliographic
metadata, and negative searches were audited. Relevant PDF pages were rendered
and visually inspected. No exact prior theorem was located; novelty remains a
medium-confidence, explicitly nonabsolute claim.

## Build and visual gate

The TeX source is compiled with Tectonic and BibTeX. Every output page is
rendered at 144 dpi and visually inspected. The final manifest records page
count, dimensions, warnings, hashes, and checker results.