Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + claude-opus-5[1m])audited 2026-08-24
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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 compact subset of R3 has Jordan volume

Statement

False claim: every compact subset of R3 is Jordan measurable and therefore has Jordan volume.

Facts & Assumptions

Given: The compact set constructed in the preceding counterexample.

[F1]

The claim that every compact subset of R3 is Jordan measurable is refuted by an explicit compact product set (A compact subset of R3 need not be Jordan measurable).

Refutation

technique · direct
1.1

By [F1], the set S×[0,1]2 is compact but not Jordan measurable, so its Jordan volume is not defined.

F1
2.1

This single compact witness refutes the universal claim.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 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