Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-30
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.

FALSE: a DFA transition diagram may omit a sink without changing totality

Statement

False claim: once a transition diagram has all of its "interesting" edges, one may omit a sink transition and still regard the picture as specifying a DFA.

Facts & Assumptions

Given: The alphabet Σ={0,1} and a one-state picture with state q, start state q, and only one drawn edge, a loop q→0q.

[A1]

The statement refuted is: omitting a sink transition from a DFA diagram does not affect whether the diagram defines a total DFA.

[L1]

A DFA requires a total transition function δ:Q×Σ→Q, by Deterministic finite automata.

Refutation

technique · direct
1.1

In the displayed picture, the input pair (q,0) has a specified next state, namely q. But the input pair (q,1) has no specified next state at all.

given
2.1

Therefore the picture does not determine a total function on Q×Σ, so by [L1] it does not yet define a DFA.

L1step 1.1
3.1

This contradicts the conclusion of [A1]. The omitted transition really matters: one must add a sink or some other specified 1-transition to obtain a DFA.

A1step 2.1∎

Depends on

Used by

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