Substantive agency characterization links key complexity classes conditionally

Substantive Agency and Computational Non-Anticipability: An Axiomatic Route to a Conditional Separation of P and N P

Logic in Computer Science

Summary

This paper explores a formal way to describe decision-making called substantive agency and connects it to a major question in computer science about whether all problems whose solutions can be checked quickly can also be solved quickly (the P vs NP problem). The authors show that under specific conditions involving how decisions can be chosen or predicted, this leads to an important conclusion about P and NP being equal. However, their result depends on assumptions and does not prove that human decisions meet these criteria. Instead, it provides a conditional theoretical bridge between concepts in agency and computational complexity.

What this means in practice

  • For complexity theorists: Clarify conditional relations between complexity classes P and NP under agency assumptions, refining theoretical understanding.
  • For algorithm designers: Assess algorithm feasibility with respect to decision-making models linked to substantive agency constraints and polynomial-time selectors.

A theory result. No direct application yet.

Authors

Jérome Clech

Abstract

This paper characterises substantive agency and identifies the additional bridges under which it has a standard complexity-theoretic consequence: conditionally, P __ = N P . The constitutive core separates coherent plurality, causal openness, anticipatory non-pointing, act-level singularisation, and endogenous sourcehood. Its temporal claim yields a two-sided modal result: exact passive pre-act selection is incompatible with jointly retaining singularising priority and invariance under causally inert informational extension. If every standard polynomial procedure is deployable in that passive form, the actualisation map $α$ has no polynomial-time selector. On an effective presentation, $α$ is therefore either computable outside FP or noncomputable. A separate certifiedactualisation protocol supplies polynomially bounded, polynomially verifiable traces with extensional unique projection. This is the constructive interface that turns historical actualisation into a total standard search relation; combined with the modal result, it places that relation in TFNP search \ FP search , from which a self-contained search argument yields P __ = N P . The result is a domain-relative conditional transfer theorem: it neither assumes polynomial non-anticipability in the definition of agency nor proves that human decision-making satisfies the bridge and certification premises.
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