Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-12
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 valid many-one reduction may reverse yes-instances and no-instances

Statement

A valid computable many-one reduction may reverse yes-instances and no-instances.

Facts & Assumptions

Given: Languages A and B.

[L1]

A computable many-one reduction satisfies x∈A  ⟺  f(x)∈B for every input x, by Computable many-one reductions between languages.

Refutation

technique · direct
1.1

If f is a many-one reduction from A to B, then [L1] says that x∈A and f(x)∈B always have the same truth value. Equivalently, x∉A  ⟺  f(x)∉B as well.

L1given
2.1

So a valid reduction preserves both yes-answers and no-answers relative to the chosen target language B; it does not reverse them. Reversal would mean reducing to the complement language B‾ instead. Therefore the statement is false.

L1step 1.1∎

Depends on

Used by

Dependency tree · two levels

3 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