Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-27
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.

The Cantor measure is concentrated on the Cantor set

Example

The Cantor measure μc is a probability measure with

μc(C)=1,μc(R∖C)=0.

So it is entirely supported on the Cantor set even though the Cantor set has Lebesgue measure 0.

Facts & Assumptions

Given: The Cantor measure μc and the Cantor set C.

[L1]

The Cantor measure is a singular atomless probability measure concentrated on the Cantor set. (The Cantor measure is a singular atomless probability measure concentrated on the Cantor set)

Verification

technique · direct
1.1

By [L1], μc(R∖C)=0.

L1
2.1

The same fact [L1] says μc([0,1])=1, hence [step 1.1, L1] μc(C)=1−μc([0,1]∖C)=1. This is exactly what concentration on C means.

step 1.1L1∎

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