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False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-07
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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.

An oracle machine reads the infinite oracle at once

Statement

An oracle machine can inspect all infinitely many bits of its oracle in one halting computation.

Refutation

technique · direct

Given: a halting oracle-machine computation.

1.1

A halting oracle-machine run has finitely many transitions and therefore only finitely many query instructions.

givenconstruct
2.1

More precisely, An oracle computation has a finite query witness supplies a finite set of queried bits which fixes the whole run and output. Thus no halting computation reads the entire infinite oracle.

step 1.1∎

Depends on

Used by

Dependency tree · two levels

3 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