Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-30
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 signed measure can take both +infinity and -infinity

Statement

False claim. A signed measure may take the value +∞ on one measurable set and the value −∞ on another.

Facts & Assumptions

Given: The definition of a signed measure.

[L1]

A signed measure takes at most one infinite sign. (A signed measure is countably additive and takes at most one infinite value)

Refutation

technique · direct
1.1

The displayed claim asserts exactly the negation of the second clause in [L1] [L1].

2.1

Therefore no signed measure satisfies the claim, and the statement is [L1, step 1.1] ∎ 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