An Exhaustive Five-by-Five Classification for an Induced Ordered Binary Pattern

For the induced ordered binary pattern H=001/010/111, this limited computer-assisted study compares the minimum number tau_H of cells meeting every existing occurrence with the minimum flip distance D_H to an H-free matrix. Exhaustive enumeration of all 33,554,432 binary 5-by-5 matrices records exactly 153 with D_H>tau_H, all with (tau_H,D_H)=(1,2). Exhaustive verification through square order four shows that five is the smallest separating square order. The principal contribution is the exact finite classification for this particular 3-by-3 pattern. The direct-sum consequence is elementary and is not claimed as new or as a nonpolynomial removal lower bound. Wang, arXiv:2610.15370, gives a stronger prior separation for another pattern. The complete proof of OpenAI Math #190 was not independently audited here. No minimality claim is made for all rectangles. Author: Ryutaro Yonezu — Independent Researcher. No.51. Version 1.0. Date: 2026-11-03. Preprint; not human peer-reviewed. Novelty: INCONCLUSIVE. Rights: All rights reserved. Prior independent AI audit: MODEL / PROOF / COMPUTATION PASS; MINIMALITY PASS for square order only. AI auditing is not a substitute for human peer review. The accompanying reproducibility ZIP preserves frozen_v0.3/ unchanged, including its historical HOLD wording. It contains the enumerator, the complete 153-code list, recorded counts, proofs, bibliographic notes, SHA256 hashes, and Python checkers. The 153-witness checker alone does not establish completeness. Run the full C enumerator in a separate working copy, since it overwrites separating_5x5.txt. GitHub Release v1.0: https://github.com/yonezaemon1-hub/no51-five-by-five-ordered-binary-pattern/releases/tag/v1.0 SHA256 — PDF: e7ecb7ed79737d2b9499d54e31f26daff4bac10bd959d8492899b8ae9c981ae7SHA256 — reproducibility ZIP: 9a5d227b36fc6a9e099f8fe5b874acfbc75afe957e377175145161add1070cfe