Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-07
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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.

Degree join is set union

Statement

For all A,B, the join of [A]T and [B]T is [A∪B]T.

Refutation

technique · direct

Given: the ordinary halting set 0′.

1.1

Take A=0′ and B=N∖0′. Since complementation is computable, [A]T=[B]T=[0′]T, and their degree join is [0′]T.

givenconstruct
2.1

But A∪B=N is computable, so [A∪B]T=[∅]T, which cannot equal [0′]T. Hence ordinary union does not compute the degree join in general; tagged join is relevant.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources