Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-12
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.

A concrete majority-vote error estimate from Chebyshev's inequality

Example

If 25 independent trials are each correct with probability 3/4, then the majority vote is wrong with probability at most 9/25.

Facts & Assumptions

Given: 25 independent Bernoulli trials, each correct with probability 3/4.

[L1]

The Chebyshev majority bound gives P(S≤k/2)≤9/k whenever each trial has success probability at least 2/3 (Chebyshev bounds the majority error of repeated Bernoulli trials).

Verification

technique · direct
1.1

The hypotheses of [L1] hold with k=25 because 3/4≥2/3.

L1given
2.1

Therefore the majority error probability is at most 9/25. This is a concrete instance of the general O(1/k) estimate.

L1step 1.1algebra∎

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