Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-02
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 five fifth roots of unity and their sum

Example

The fifth roots of unity are exp⁡ ⁣(i2πιR(k)ιR(5))\exp\!\left(i\frac{2\pi\iota_{\mathbb R}(k)}{\iota_{\mathbb R}(5)}\right) for k∈Nk\in\mathbb N with 0≤k<50\le k<5, and their sum is 00. The conventions and prerequisite facts used below are recorded in The nn-th roots of a complex number and the nn distinct roots of unity for every n≥1n\ge1, For n≥2n\ge2, the sum of all nn-th roots of unity is zero.

Facts & Assumptions

Given: n=5n=5.

Verification

1.1

The root classification lists the five values exp⁡ ⁣(i2πιR(k)ιR(5))\exp\!\left(i\frac{2\pi\iota_{\mathbb R}(k)}{\iota_{\mathbb R}(5)}\right) for k∈Nk\in\mathbb N with 0≤k<50\le k<5.

given
2.1

The root-sum corollary gives that their sum is 00.

given∎

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: 57 results over 12 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