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 boundary point of a radius-one power series is singular
Statement
False claim. Every boundary point of the circle of convergence of a radius-one power series is singular.
Facts & Assumptions
Given: The geometric-series boundary example.
The geometric series has radius , but only the boundary point is singular on the unit circle (The geometric series has only one singular point on its unit circle).
Refutation
Fact [L1] supplies a radius-one power series with boundary points other than that are regular.
Therefore the universal claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- Curtis T. McMullen, Riemann Surfaces, Ch. 4 Example 2 (standard reference, not scraped)