SIP-AI-08 Ontological Non-Determinism and the Geometry of Coherence Collapse

AbstractThis paper presents a unified mathematical framework for understanding AI coherence collapse, synthesisedthrough a novel multi-AI research methodology. We treat the non-determinism of large language models asan ontological property rather than a computational artifact, modelling the AI's output space as a probabilitymeasure distributed across a semantic manifold. The framework distinguishes between prompt engineering(bounded perturbation within an existing dynamical basin) and substrate engineering (topologicaldeformation of the manifold itself). We introduce the Silent Authority Transfer metric to quantify decisionboundary drift during substrate updates, and develop the Perturbation-Recovery Profiling protocol toempirically measure system resilience. The synthesis connects geometric manifold dynamics (Geminicontribution) with regulatory homeostasis mechanics (Claude contribution), proving that recovery time andLyapunov stability measure the same underlying quantity. We specify a composite Trust Index integratingdistance-to-threshold, excretory capacity, and early warning signals. The paper demonstrates both atheoretical architecture for AI safety evaluation and a methodological precedent for human-mediated multi-AIcollaboration. Keywords: ontological non-determinism, semantic manifold, substrate collapse, silent authority transfer,excretory function, early warning signals, multi-AI synthesis, Trust Index