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Proof assumptions: status interpretation and exact-target evidence #4881

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@williamjblair

Updated 11 September 2026.

The annotations are already implemented: Erdős 427, 750 and 1141 name their assumptions with conditional formal_proof … assuming. Credit #4884, #4885 and #4886. The extractor already exposes proof conditions.

Remaining responsibility Delivery
Keep conditional proofs distinct from unconditional proof status; preserve primary/variant semantics #4828
Check proof-link reachability from published formalProofs #4828, incorporating former #4749; Lychee handles HTTP
Verify an exact submitted target and retain assumptions, revisions and typed outcomes #5387
Show provenance and historical applicability without changing maintainer status #5388
Correct specific file/commit proof locators Independent #4895

The earlier proposal to scan linked text for sorry or axiom is withdrawn. Text scanning misses imported assumptions and cannot establish statement equivalence. A reachable link is only a reachability result. Verification uses the qualified tools and typed result; infrastructure errors remain unevaluated, not rejected proofs.

The original August counts were a dated, linked-file-only survey. They are not the current corpus inventory. The #4884 verification account is corrected in #4394 using the board's retained typed invocation-error record.

Keep this issue open until status interpretation is accepted and exact-target verification/evidence is available with the distinctions above. Mathematical assumptions and maintainer acceptance remain separate from toolkit execution.

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