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.
Choice strength used in the extremal proof of the Riemann mapping theorem
The displayed extremal proof assumes the Axiom of Choice. Its nonconstructive step is concentrated in the choice of a maximizing sequence and the successive subsequence extraction used in Montel's theorem. That is exactly the step isolated in A maximizing sequence has a locally uniform limit with extremal derivative and in the proof of Montel's theorem: every locally bounded holomorphic family is normal; once the limiting extremizer exists, the remaining univalence and surjectivity arguments are explicit.
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Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
13 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Matthias Weber, Complex Analysis, §5.2 (standard reference, not scraped)