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The study aims to formally prove the impossibility of zero-drift self-maintenance in self-referentially self-maintaining systems.

May 22, 2026Open Access

THE IMPOSSIBILITY OF ZERO-DRIFT SELF-MAINTENANCE: A Formal Proof of the IRM Theorem and Its Place in the Gödel–Turing–Lawvere Family

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Formal proof demonstrates zero-drift self-maintenance failure in self-referential systems, indicating mathematical necessity.

The study aims to formally prove the impossibility of zero-drift self-maintenance in self-referentially self-maintaining systems.
Proved the IRM impossibility theorem using a stochastic-operator framework on a Hilbert space.
Established the theorem's connection to Lawvere's fixed-point theorem in a categorical framework.
IRM impossibility theorem is validated, showing that finite-fidelity maintenance leads to positive expected target drift.
Derived time-to-threshold formula T ≈ ε*·R/η as a corollary of the IRM theorem.
Identified the IRM theorem as a dynamical member of the Gödel–Turing–Lawvere family.

José Caetano de Mattos Neto (2026) studied this question.

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May 22, 2026Open Access

View Full Paper

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Authors

Formal proof demonstrates zero-drift self-maintenance failure in self-referential systems, indicating mathematical necessity.

The study aims to formally prove the impossibility of zero-drift self-maintenance in self-referentially self-maintaining systems.
Proved the IRM impossibility theorem using a stochastic-operator framework on a Hilbert space.
Established the theorem's connection to Lawvere's fixed-point theorem in a categorical framework.
IRM impossibility theorem is validated, showing that finite-fidelity maintenance leads to positive expected target drift.
Derived time-to-threshold formula T ≈ ε*·R/η as a corollary of the IRM theorem.
Identified the IRM theorem as a dynamical member of the Gödel–Turing–Lawvere family.

José Caetano de Mattos Neto (2026) studied this question.

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