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arXiv · 2609.15464

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

J{é}rome Clech
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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.

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J{é}rome Clech. 2026-09-14. Ontological free will as incompressible information adjunction: A noncomputability boundary beyond P versus NP. https://arxiv.org/abs/2609.15464

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