Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-28
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.

Hurwitz preserves a simple zero under local uniform convergence

Example

Define

fn(z)=z+z2n+1.

Then fn→z locally uniformly, and on a small disc around 0 each sufficiently large fn has exactly one zero counted with multiplicity.

Facts & Assumptions

Given: The sequence fn(z)=z+z2/(n+1) and the limit function f(z)=z.

[L1]

Locally uniform convergence preserves the total multiplicity near an isolated zero (Locally uniform convergence preserves the total multiplicity near an isolated zero).

Verification

technique · direct
1.1

On every compact set, ∣z2/(n+1)∣→0, so fn→f locally uniformly. The limit function f(z)=z has a simple zero at 0.

givenalgebra
2.1

Apply [L1] to the isolated zero at 0. It follows that on some disc D(0,r), every sufficiently large fn has exactly one zero counted with multiplicity.

step 1.1L1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources