Alphabeta Math
ExampleConstruction: AI-generatedVerification: 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.

A branching configuration graph with one accepting path and one looping path

Example

Use the nondeterministic machine from FALSE: nondeterministic acceptance requires every branch to halt on input w=1. Its initial configuration C0 has two outgoing arcs:

  • one to the accepting configuration Cacc reached by the move (qacc,1,R),
  • one to the looping configuration CL reached by the move (qL,1,L).

From CL there is an arc back to CL again, because the machine stays in state qL, rewrites 1 by 1, and the left-boundary rule keeps the head at cell 0.

Facts & Assumptions

Given: The machine and input just described, with vertices C0,Cacc,CL in its configuration graph.

[L1]

A machine accepts an input if and only if some accepting configuration is reachable from the initial configuration in its configuration graph, by Acceptance is reachability of an accepting configuration.

Verification

technique · direct
1.1

The arc C0→Cacc is a directed path of length 1 from the initial configuration to an accepting configuration.

given
1.2

The arc C0→CL followed by the loop CL→CL shows that the graph also contains a nonhalting branch.

given
2.1

By [L1] and step 1.1, the existence of the length-1 path already proves acceptance of the input, regardless of the looping branch from step 1.2.

L1step 1.1step 1.2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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