Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passaudited 2026-08-31
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.

Every star-shaped plane domain is simply connected

Example

Every star-shaped complex domain is simply connected.

Facts & Assumptions

Given: A star-shaped complex domain Ω⊆C.

[L1]

Every star-shaped plane domain is homologically simply connected (Star-shaped plane domains are homologically simply connected).

[L2]

Homological simple connectivity is equivalent to simple connectivity for plane domains (For a plane domain, the complement, homology, primitive, logarithm, conjugate, conformal, homotopy, and contractibility conditions are equivalent).

Verification

technique · direct
1.1

Fact [L1] makes the given domain Ω homologically simply connected.

givenL1
2.1

By [L2], step 1.1 implies that Ω is simply connected.

step 1.1L2∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

32 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