Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-31
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: the essential supremum equals the pointwise supremum

Statement

For every measurable function, the essential supremum equals the pointwise supremum.

Facts & Assumptions

Given: The rational-indicator example on [0,1].

[L1]

The function χQ∩[0,1] has pointwise supremum 1 but essential supremum 0 (Indicator of the rationals has zero essential supremum but pointwise supremum one).

Refutation

Proof technique: Refute with the indicator of the rationals on [0,1], whose pointwise supremum is 1 but whose essential supremum is 0.

1.1

The single function from [L1] already violates the claimed equality.

L1
2.1

Therefore the statement is false.

step 1.1∎

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