Add C13 covering research artifact

[jkolantree]

Summary

• Add a standalone finite-combinatorics artifact under research/C13_6_3_covering/, outside the BSC claim and fixture namespaces.
• Record an explicit 20-block family on 13 points covering exactly 284 of 286 triples, with leave {2,5,7} and {5,7,10}.
• Compare it with the attributed La Jolla 21-cover through an exact three-block-for-two-block exchange and a complete one-block-deletion histogram.
• Prove the conditional rigidity result that any hypothetical complete 20-cover has one of three point-degree forms and some block with at least ten private triples.
• Retain deterministic construction/provenance identities, a verification receipt, a dependency-free checker, and positive and fail-closed mutation tests.
• Attribute the La Jolla Coverings Repository v1.2 source and preserve its CC BY 4.0 license boundary.

Evidence and scope boundary

This is an independent reconstruction and hand-checked mathematical argument with mechanically replayed finite arithmetic. It does not:

• construct or exclude a complete 20-cover;
• establish C(13,6,3)=21;
• prove that 284 is optimal or best known;
• claim historical novelty or priority;
• claim kernel verification or formal proof;
• create a BSC claim, fixture, roadmap item, paper result, or release result.

The checked public record remains 20 <= C(13,6,3) <= 21. The artifact records only “no matching public record located,” with explicit warning that this does not establish priority.

Verification actually executed

• C13 deterministic verifier: PASS.
• C13 targeted unit tests: 11/11 PASS.
• Complete unit discovery: 247 tests PASS, 1 Windows symlink-privilege test SKIPPED.
• Manifest regeneration and verification: PASS, 120 files.
• Normal checkout, linked worktree, and fresh Git archive inventory agreement: PASS, 120 files.
• Markdown-math checker: PASS.
• Retained fixture checks F8, F10, F11, F12, and F13: PASS.
• git diff --check: PASS.
• Exact ten-path publication allowlist: PASS.
• Independent mathematical and repository reviews: no remaining defect found after correcting theorem wording, proof exposition, and source licensing.

PDF build verification was not run because this environment has no latexmk or tectonic; no paper, synopsis, or PDF file changes in this PR.

Unchanged authority

No ROADMAP, claim ledger, fixture, workflow, paper, PDF, release metadata, tag, release, DOI, Zenodo record, ruleset, or repository setting is changed.