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 bounded plane domain solves the Dirichlet problem for every continuous boundary datum
Statement refuted
Every bounded plane domain solves the Dirichlet problem for every continuous boundary datum.
Facts & Assumptions
Given: The universal claim in the Statement refuted.
The punctured unit disc with boundary values on the outer circle and at the puncture has no harmonic solution (The punctured disc has an irregular boundary point and a continuous boundary datum with no harmonic solution).
Refutation
The punctured unit disc is a bounded plane domain, and [L1] supplies a continuous boundary datum on it that is not attained by any harmonic function.
That single bounded counterexample contradicts the universal claim, so the statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- Boris Khoruzhenko, Potential Theory lecture notes (standard reference, not scraped)