Alphabeta Math
LemmaStatement: Literature-sourcedProof: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-31
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 maximal layout has at most ϵ−1 blocks

Statement

Let ϵ∈(0,12) and d≥1. In the counterexample layout construction used for Theorem 6.1 of the cited source, the chosen maximal layout has fewer than ϵ−1 blocks; otherwise its blocks already contain the blockade required by that theorem.

Facts & Assumptions

Given: The maximal layout and counterexample hypotheses in the proof of Theorem 6.1 of the cited source.

[L1]

Claim 6.1.1 of the cited source proves that a chosen layout with at least ϵ−1 blocks already satisfies the target blockade conclusion.

Proof

technique · direct from the cited source claim
1.1L1given

If the chosen layout had at least ϵ−1 blocks, [L1] would make its blocks a blockade satisfying the conclusion of the surrounding theorem.

2.1step 1.1∎

The enclosing counterexample excludes that conclusion, so the layout has fewer than ϵ−1 blocks.

Depends on

Used by

Dependency tree · two levels

7 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