Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
The completeness test does not reduce indexed limits to conical ones
Remark
Enriched completeness is cotensors plus small conical limits is a test for when all enriched limits exist. It is not a claim that the notion of weighted limit can be discarded in favor of conical ones. The warning from Conical weights are a proper special case of enriched weights remains in force: weights carry genuine information, and the completeness theorem only says that cotensors plus conical limits are enough to reconstruct that information when they are all available.
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Sources
- G. M. Kelly, Basic Concepts of Enriched Category Theory, closing remark after Theorem 3.73 (standard reference, not scraped)