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.

Testing a few short binary strings for machine-code well-formedness

Example

Under the chosen code of A fixed effective binary encoding of deterministic one-tape Turing machines, compare the short words 0,10,111111011011100101101100101.

Facts & Assumptions

Given: The three displayed binary words.

[L1]

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

[L2]

By Well-formed deterministic one-tape Turing machine descriptions form a decidable language, this decoder test decides well-formed machine descriptions.

Verification

technique · direct
1.1

The words 0 and 10 are malformed. The first never even begins the required positive-arity tuple code, and the second announces arity 1 but provides no self-delimiting payload block. Therefore the decoder of [L1] rejects both.

L1given
1.2

The word 111111011011100101101100101 is the code of the tuple (11,0,1,1,0,1), so it decodes to the normalized machine with m=3, s=0, n=1, and the unique transition (0,0)↦(1,0,1). In particular 0≤s<n, and the tuple has the required 3+3(m−2)n=6 entries. Thus [L1] accepts it as a well-formed machine description, and [L2] classifies the three sample words exactly as claimed.

L1L2given
2.1

This makes the decidability test concrete: two malformed inputs are rejected and one genuine machine code is accepted.

step 1.1step 1.2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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