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 factorial-gap series shows that a holomorphic function need not continue past its boundary
Statement refuted
Refuted claim. Every holomorphic function on a domain analytically continues past each boundary point.
The witness is
which is holomorphic on the unit disc and has the whole unit circle as a natural boundary.
Facts & Assumptions
Given: The factorial-gap series witness.
The factorial-gap series has radius and the whole unit circle as a natural boundary (The factorial-gap series has the unit circle as a natural boundary).
Counterexample
Fact [L1] gives a holomorphic function on the unit disc that cannot be continued through any boundary point of that disc.
Therefore the universal claim is false.
Depends on
Used by
Dependency tree · two levels
5 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)