Zenodo · May 27, 2026
The Architecture of Self-Referential Failure: A Unified Theory of SRSM Systems. Bayesian Self-Reference · Immune Ageing as SRSM
By de Mattos JC
Unified Abstract Article 1: The Bayesian IRM: Self-Referential Belief Updating and the Fifth Member of the Gödel–Turing–Lawvere–IRM Family Article 2: Immune Ageing as Quality-Control Feedback Degradation: The SRSM Account of Immunosenescence Hallmark Coupling and TCR Repertoire Diversity as Internal Precursor Abstract This monograph establishes the Unified Theory of Self-Referentially Self-Maintaining (SRSM) Systems, proving that systemic failures in both cognitive and biological sciences stem from a single mathematical law: categorical diagonalization on self-referential structures. Governed by the Internally-Referenced Maintaining (IRM) Impossibility Theorem, any system that relies on its own internal state to maintain itself will inevitably drift toward a self-confirming, degraded fixed state unless it receives an independent external calibration. We deploy this framework across two isomorphic domains: -The Epistemic Domain: We formalize Self-Referential Bayesian (SRB) updating, mathematically unifying algorithmic echo chambers, AI generative model collapse, and Goodhart’s Law under a single structural law of belief drift. -The Biological Domain: We reframe immunosenescence as a coupled Quality-Control Feedback Degradation (QCD). When central thymic input fades, the peripheral immune system falls into a recursive loop, making T-cell receptor diversity ($\Gamma_{immune}$) the definitive geometric precursor to immune collapse. Finally, we move from diagnostics to engineering by deriving the formula for the Minimum External Calibration Frequency ($f_{min}$), providing the exact operational thresholds required to structurally halt both AI value drift and biological immune aging. Keywords: Self-Referentially Self-Maintaining (SRSM) Systems; IRM Impossibility Theorem; Categorical Diagonalization; Self-Referential Bayesian Updating; Credence Drift; AI Model Collapse; Echo Chambers; Goodhart’s Law; Immunosenescence; Quality-Control Feedback Degradation (QCD); T-Cell Receptor (TCR) Repertoire Diversity; Minimum External Calibration Frequency. Method ALGUILAS-AI Dialectical Engine