Ontological free will as incompressible information adjunction: A noncomputability boundary beyond P versus NP

We study a conditional model of ontological free will in which a pre-act state structures several coherent global continuations without intrinsically distinguishing one as the future actualisation. The topos-theoretic component is formalised by a choice sheaf and by the action of automorphisms preserving the pre-act data: the absence of a fixed point rules out any natural equivariant selection. An act changes an unpointed object into a pointed one and reduces its symmetry group to a stabiliser. Independently, a causal algorithmic incompressibility axiom imposes nearly maximal online description complexity on the actual choices. Uniformly observable post-act traces then allow their reconstruction. We prove a conditional transfer result: such traces must carry asymptotically all the singularisation information unavailable in the pre-act regime, and no uniform Turing predictor computes the choices from causal histories alone. The formalism proves neither that human beings satisfy the model nor a separation of P from NP; it identifies a boundary at which prediction concerns the existence of a computable function rather than its time complexity.

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Publication Details

Journal
HAL (Le Centre pour la Communication Scientifique Directe)
Published
2026-09-14
DOI
https://doi.org/10.48550/arxiv.2609.15464
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

Ontological free will as incompressible information adjunction: A noncomputability boundary beyond P versus NP

J{é}rome Clech
HAL (Le Centre pour la Communication Scientifique Directe)
Computability, Logic, AI Algorithms
preprint

Ontological free will as incompressible information adjunction: A noncomputability boundary beyond P versus NP

J{é}rome Clech
preprint en

Abstract

We study a conditional model of ontological free will in which a pre-act state structures several coherent global continuations without intrinsically distinguishing one as the future actualisation. The topos-theoretic component is formalised by a choice sheaf and by the action of automorphisms preserving the pre-act data: the absence of a fixed point rules out any natural equivariant selection. An act changes an unpointed object into a pointed one and reduces its symmetry group to a stabiliser. Independently, a causal algorithmic incompressibility axiom imposes nearly maximal online description complexity on the actual choices. Uniformly observable post-act traces then allow their reconstruction. We prove a conditional transfer result: such traces must carry asymptotically all the singularisation information unavailable in the pre-act regime, and no uniform Turing predictor computes the choices from causal histories alone. The formalism proves neither that human beings satisfy the model nor a separation of P from NP; it identifies a boundary at which prediction concerns the existence of a computable function rather than its time complexity.

HAL (Le Centre pour la Communication Scientifique Directe)
Institut d'Etudes Politiques de Paris (FR)
Reduced inequalities
Computability, Logic, AI Algorithms
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Ontological free will as incompressible information adjunction: A noncomputability boundary beyond P versus NP — J{é}rome Clech · HAL (Le Centre pour la Communication Scientifique Directe) (2026) | TGRS Research Map | TGRS