Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-12
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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.

FALSE: every total computable function is primitive recursive

Statement

False claim: every total computable function on a finite power of N is primitive recursive.

Facts & Assumptions

Given: The false claim above.

[A1]

Every total computable function on a finite power of N is primitive recursive.

[L1]

The Ackermann function is total computable but not primitive recursive, by The Ackermann function is total computable but not primitive recursive.

Refutation

technique · direct
1.1

By [L1], the Ackermann function A is a total computable function on N2, so it is directly an instance of the universal claim [A1].

L1given
2.1

The same fact [L1] states that A is not primitive recursive. This contradicts [A1].

A1L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

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