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.
Closedness is local, exactness is global, and a domain hypothesis cannot be omitted
By Every exact C1 vector field is closed, exact fields are closed on every open domain. The converse proved in On a star-shaped open domain, closed, exact, conservative, path-independent, and zero-loop are equivalent requires a star-shaped open domain. A merely connected open domain is not enough: closedness is a local equality of partial derivatives, whereas exactness requires one potential valid throughout the domain.
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Used by
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Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 20 results over 7 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- J.-B. Campesato, Poincare Lemma, sections 1 and 2 (standard reference, not scraped)