Alphabeta Math
LemmaStatement: Literature-sourcedProof: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-06
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 read-only-workspace diagonal machine halts

Statement

Let s be work-space constructible with log⁡(n+2)=O(s(n)). The local read-only-workspace diagonal simulator can stop every deterministic computation after its finite configuration bound while using O(s(n)) work space.

Facts & Assumptions

Given: the stated constructible bound and a read-only machine capped at s(n) work cells.

Proof

technique · direct
1.1

Compute the cap s(n). The input is fixed and read-only, while finite control, work contents, and all head positions have only exponentially many configurations in s(n)+log⁡n=O(s(n)).

givenconstruct
2.1

Use the universal simulator and a binary counter of O(s(n)) bits to count through that bound, stopping at expiry. A deterministic nonhalting computation repeats a configuration beforehand, so the forced answer makes the simulation total without exceeding O(s(n)) work space.

step 1.1algebra∎

Depends on

Used by

Dependency tree · two levels

4 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