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.
FALSE: little Picard needs a boundedness hypothesis
Statement
Little Picard's theorem needs an additional boundedness assumption on the entire function.
Facts & Assumptions
Given: Little Picard's theorem.
A nonconstant entire function omits at most one finite value (Little Picard theorem).
Refutation
Fact [L1] already states the omitted-value conclusion for every nonconstant entire function, with no boundedness hypothesis.
Therefore the asserted extra boundedness assumption is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 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
- Aleksander Simonic, The Ahlfors lemma and Picard's theorems, §6.2 (standard reference, not scraped)