Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: 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.

Counting the constant-size extended alphabet for a fixed nondeterministic machine

Example

Take a machine with tape alphabet Γ={0,1,⊔} and state set Q={q0,q1,qacc,qrej}.

Facts & Assumptions

Given: The fixed machine above.

[L1]

For a fixed machine, the extended alphabet of one tableau cell is Γ∪(Q×Γ), by For a fixed machine, each tableau cell ranges over a constant-size extended alphabet.

Verification

technique · direct
1.1

The bare tape-symbol options contribute the three symbols 0,1,⊔. The state-tagged options contribute one pair (q,a) for each q∈Q and a∈Γ, so there are 4⋅3=12 such tagged symbols.

givenalgebra
2.1

By [L1], the total extended alphabet size is therefore 3+12=15, independent of the input length. This is the concrete constant hidden in the general lemma.

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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