Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-27
How 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: a nonconstant subharmonic function can attain a finite interior maximum

Statement refuted

A nonconstant subharmonic function can attain a finite interior maximum.

Facts & Assumptions

Given: The claim in the Statement refuted.

[L1]

A subharmonic function with a finite interior maximum is constant on its connected component (A plane subharmonic function with an interior maximum is constant on its component).

Refutation

technique · direct
1.1

If the claim were true, some nonconstant subharmonic function would attain a finite interior maximum.

assume-contra
2.1

But [L1] says that any subharmonic function with a finite interior maximum must be constant on the connected component where that maximum occurs. This contradicts step 1.1.

L1step 1.1discharge-contradiction∎

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