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: every holomorphic function on a domain continues past its boundary
Statement
False claim. Every holomorphic function on a domain continues past its boundary.
Facts & Assumptions
Given: The factorial-gap counterexample.
The factorial-gap series is holomorphic on the unit disc and has no analytic continuation through any boundary point (The factorial-gap series shows that a holomorphic function need not continue past its boundary).
Refutation
Fact [L1] gives a holomorphic function on a domain whose boundary admits no continuation.
Hence the universal claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
2 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
- Henry Wilton, Riemann Surfaces lecture notes, Example 2.7 (standard reference, not scraped)