Alphabeta MathHow 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.
An immediate-accept machine gives an easy yes-instance inside an undecidable language
Statement refuted
The claim "undecidable means no individual instance can be answered" is false. An explicit yes-instance already appears inside .
Facts & Assumptions
Given: The machine that immediately accepts every input.
A coded pair lies in exactly when the decoded machine accepts the decoded input, by The Turing-machine acceptance problem .
The false statement being refuted is the one recorded in FALSE: undecidable means no individual instance can be answered.
Counterexample
The machine accepts the one-symbol input word on its first step. Therefore [L1] gives .
This specific membership question has a completely transparent yes-answer, so it contradicts the slogan named in [L2]. Hence the slogan is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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
- EECS 376 Course Notes, Part 6: Computability (standard reference, not scraped)