Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-27
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.

x5−x−1 has a real root

Example

The polynomial

f(x)=x5−x−1

has a real root.

Facts & Assumptions

Given: The polynomial f(x)=x5−x−1.

[L1]

Every odd-degree real polynomial has a real root (Every odd-degree real polynomial has a real root).

Verification

technique · direct
1.1

Direct evaluation gives f(1)=1−1−1=−1andf(2)=32−2−1=29.

givenalgebra
2.1

The sign change in step 1.1 is exactly the kind of endpoint behaviour used in the proof of [L1]. Since f has odd degree, [L1] gives a real root.

step 1.1L1
3.1

Thus x5−x−1 is a concrete odd-degree polynomial with a real zero.

step 2.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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