Alphabeta Math
CorollaryStatement: Literature-sourcedProof: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16
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 complex analytic function has a primitive on a neighbourhood of each point

Statement

If f is analytic at a, then some neighbourhood of a admits a primitive of f.

Facts & Assumptions

Given: A function f analytic at a.

[L1]

Analyticity supplies f(z)=∑cn(z−a)n on a positive-radius disc (Complex analytic functions as locally representable by convergent power series).

[L2]

The zero-constant-term formal antiderivative has the same radius as the original series (A complex power series, its formal derivative, and its zero-constant-term formal antiderivative have the same radius).

[L3]

A complex power series may be differentiated term by term inside its radius (Inside its disc of convergence a complex power series is holomorphic and may be differentiated term by term).

Proof

technique · constructive
1.1

Choose a local representation from [L1] and define F(z)=∑n≥0cn(z−a)n+1/(n+1) on the same disc.

L1L2construct
2.1

By [L3], F′(z)=∑cn(z−a)n=f(z) throughout the disc, so F is a local primitive.

step 1.1L3discharge-construct∎

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: 28 results over 6 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