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May 29, 2026Open Access

WHY SELF-REFERENTIAL MAINTENANCE NECESSARILY PRODUCES THRESHOLD DYNAMICS: A Categorical Derivation of IGT Dynamics from the Theory of Polynomial Functor Coalgebras (IGCDT)

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Authors

JMJosé Caetano de Mattos

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Overview

Categorical derivation shows self-referential maintenance produces threshold dynamics in self-referential systems, indicating a structural necessity.

Key Points

  • The study aims to establish why self-referential systems exhibit threshold dynamics independent of noise modeling.
  • Demonstrated that SRSM systems are terminal coalgebras of polynomial functors in state space categories.
  • Developed core arguments through two formal lemmas and proof sketches for additional machinery.
  • The IGT Categorical Derivation Theorem states no natural transformations are stable under self-modification in terminal coalgebras.
  • Three corollaries that unify major theories and dictate IGT transitions categorically are established.
  • Characterization of internal precursors as domain-specific measures of GAMMA morphism variance in coalgebra sequences.

Cite This Study

José Caetano de Mattos (2026) studied this question.

synapsesocial.com/papers/6a192e68fab5b468c4417695https://doi.org/10.5281/zenodo.20407541
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