Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17
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 Borel sigma-algebra of the Cantor set is the trace of the real Borel sigma-algebra

Example

For the Cantor middle-thirds set C⊆R with its subspace topology,

B(C)={B∩C:B∈B(R)}.

Facts & Assumptions

Given: The Cantor middle-thirds set C with the subspace topology inherited from R.

[L1]

The Cantor middle-thirds set is C=⋂n∈NCn⊆[0,1] (The Cantor middle-thirds set as the intersection of the sets Cn obtained by removing open middle thirds).

[L2]

The Borel sigma-algebra of a subspace is the trace of the ambient Borel sigma-algebra (The Borel sigma-algebra of a subspace is the trace of the ambient Borel sigma-algebra).

Verification

technique · direct
1.1

The description in [L1] makes C a specified subset of R, equipped here with the subspace topology.

L1
2.1

The subspace theorem [L2] applies to this inclusion C⊆R.

step 1.1L2
3.1

Therefore [L2] gives B(C)={B∩C:B∈B(R)}, as claimed.

step 2.1L2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 40 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources