Alphabeta Math
PropositionStatement: AI-adaptedProof: AI-generatedprecheck passaudited 2026-09-01
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.

Well-formed deterministic one-tape Turing machine descriptions form a decidable language

Statement

Under the chosen encoding of A fixed effective binary encoding of deterministic one-tape Turing machines, the set of binary words that decode to well-formed deterministic one-tape Turing machines is a decidable language.

Facts & Assumptions

Given: The chosen machine encoding.

[L1]

By The chosen machine coding is injective and has a total decoder, the chosen code has a total decoder that either reconstructs the unique coded machine or reports malformed input.

[L2]

By Decidable and recognizable languages, a language is decidable exactly when some Turing machine halts on every input and accepts exactly its members.

Proof

technique · direct
1.1

On input a binary word w, run the total decoder from [L1]. If it reports malformed input, reject; if it returns a coded machine, accept. Because the decoder is total, this procedure halts on every input.

L1given
2.1

The procedure accepts exactly those binary words that decode to well-formed deterministic one-tape Turing machine descriptions. Therefore [L2] shows that the description language is decidable.

L2step 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