# Verification of the corner resonance factor

Alper Ferudun. Version 1.0, 5 October 2026.

The manuscript proves a complete arbitrary-n theorem: a specified corner
membership indicator in the ASM poset returns after 3n-2 superpromotion
steps; its binary itinerary intertwines superpromotion and rotation;
rotation on the image has effective order 3n-2 for n>=3. The n=2 exception
has period 2. This is not full-action periodicity or a static noncrossing
model, and the full original source record is not counted as closed.

The originating researcher checked the source/operator translation, every
cover type, the induction proving face transfer, the inverse stratum map,
the mixed-time ideal inequalities, the sequential recurrence alignment,
the noncircular proof of R^4=S^(n-2), the four corner identities, the rank
descent and the faithful two-zero word. No mathematical gap is currently
identified in this exact theorem. This is self-audit, not independent
peer review or proof-assistant verification.

Principal finite regressions use exact integer arithmetic:

- Published ASM orbit census reproduced for n=1 through 7, including
  all 218,348 states at n=7 and its length-57 orbits.
- All four corner identities checked on all ideals for n=2 through 7:
  905,056 assertions, zero failures.
- Face transfer checked on all face-stratum ideals through n=8:
  226,264 cases, zero failures.
- Recombination checked on all states through n=5 and 150 deterministic
  nonuniform samples at each n=6 through 10: 1,230 cases.
- Rank-ideal descent checked 435 times and the full-ideal word checked
  in 29 dimensions, n=2 through 30.

These are regression checks, not proofs in arbitrary dimension. The
supplement retains an n=6 failure of the raw boundary projection and a
genuine interior n=3 failure of the naive PL extension. Neither is a
counterexample to the original AIM question. Whole-boundary return is
not promoted from an experiment to a theorem.

The final source passed the desktop LaTeX compiler. Its six-page PDF was
exported using the already-installed Tectonic with cached resources,
without TeX warnings, and all six pages were inspected visually. The
source package includes executable checkers and integrity manifests.

The ASM poset, superpromotion, empty/full-ideal orbit and general resonance
framework are credited prior work. Bounded primary-source searching found
no matching corner proof; novelty and absolute priority remain undetermined.
AI assistance is disclosed in the manuscript. Repository publication does
not constitute independent mathematical endorsement.