Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedjudge pass (gpt-5.6-terra)audited 2026-09-07
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.

An effective-dimension calculation from prefix complexity

Example

If K(X↾n)=n/2+o(n) along every sufficiently large n, then dim⁡(X)=1/2.

Verification

Given: the displayed asymptotic equality.

1.1

Dividing by n gives K(X↾n)/n=1/2+o(1).

given
2.1

Its liminf is 1/2, and Effective dimension is the liminf prefix-complexity rate identifies this with dim⁡(X).

step 1.1algebra∎

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