The Mathematics of Holonic Trust Trust as a Verifiable System Primitive

This paper develops the mathematical foundations of Proof of Holonic Trust (PoHT) by formalizing trust as a verifiable system primitive rather than a subjective belief, reputational score, or probabilistic estimate. Trust is modeled as an explicit state evolving within a directed acyclic graph (DAG) of interdependent entities, enabling bounded recursion, termination, and reproducibility under partial observability. We introduce a formal trust-state representation, define admissible trust update operators, and establish conditions for reproducibility and spectral stability. The framework demonstrates how trust evaluations can remain coherent across independent observers and adversarial environments without reliance on prediction or implicit inference. This work provides the theoretical basis corresponding to the canonical PoHT RC1 specification and is intended to support academic analysis, standards alignment, and empirical validation.