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Hallucination, abstention, and computable inseparability

math.LO · 2026-04-30 · accept · novelty 7.0 · 2 refs

Abstaining AI systems cannot guarantee both large coverage of correct answers and zero hallucination in sufficiently expressive domains, as shown by the existence of inseparable pairs in the arithmetical hierarchy.

Experiments, Computability, and the Existence of Physical Functions

physics.hist-ph · 2026-04-23 · unverdicted · novelty 5.0

Reproducible experiments compute physical functions via a Church-Turing bridge, compatible with finite precision through computable analysis, while separating existence, computability, and protocol-independence questions.

Turing or Cantor: That is the Question

cs.CL · 2026-04-12 · unverdicted · novelty 3.0

Turing's work relies on Cantor's contributions; a new undecidability measure and U-complete, D-complete, H-complete classes are defined, with a negative answer to a P-vs-NP analog for undecidable problems.

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  • Hallucination, abstention, and computable inseparability math.LO · 2026-04-30 · accept · none · ref 6 · 2 links

    Abstaining AI systems cannot guarantee both large coverage of correct answers and zero hallucination in sufficiently expressive domains, as shown by the existence of inseparable pairs in the arithmetical hierarchy.