Proposed computer-assisted proof: Z(12,17,3,3)=103

[yousofy]

This draft pull request submits a proposed computer-assisted proof of

$$ Z(12,17,3,3)=103. $$

I could not open a GitHub issue, so I am submitting the complete reproducibility
bundle as a draft pull request for review and integration guidance.

Lower bound

The bundle includes an explicit 12 by 17 Boolean matrix with 103 ones.

The verifier checks all 220 row triples and obtains the histogram

• multiplicity 0: 14 triples;
• multiplicity 1: 57 triples;
• multiplicity 2: 149 triples.

Thus no row triple occurs in three columns, so the matrix contains no all-one
3 by 3 submatrix.

Proposed upper bound

The proposed upper bound excludes every 104-one matrix through:

• independent enumeration of 303 possible column-size patterns;
• symmetry-reduced canonical orbit branching;
• exact aggregate inequalities;
• exact nonnegative rational certificates;
• exhaustive integer splits;
• 303 compressed certificate parts.

The verifier reconstructs the constraints itself and uses Python integer and
rational arithmetic. The optional generator is not part of the trusted proof.

Local reproduction

I ran:

python verify.py certificates --jobs 4 --report reproduced_report.json

from proposals/z12_17_103.

Environment:

• OS: Windows
• Python: 3.14.5
• Date: 7/26/2026

The run ended with:

verified 303/303 patterns
VERIFIED: every 104-one candidate is impossible; Z(12,17,3,3)=103

Integrity

Original proof-bundle SHA-256:

6b7bb29a935780a481bb3e012142cbcaf1411d95deaeaeaccc1b09638818115d

The included SHA256SUMS file binds the original proof files and all 303
certificate parts.

Provenance and review status

This material was produced during a ChatGPT-assisted investigation. The full
provenance is recorded in proposals/z12_17_103/SUBMISSION.md.

This is submitted as a proposed proof for independent scrutiny, not as a
peer-reviewed or already accepted result.

I intentionally have not modified the root README,
analysis/result_status.json, propagated-bound tables, or other established
publication-boundary files. Those should be changed only after review and in
the structure preferred by the maintainer.

@dfield — I would appreciate review of the proof bundle and guidance on how
you would prefer it integrated into the repository.