AxoDen Unified Mathematical Backbone A Compositional Theory of Entropy-Bounded Pipelines, Cognitive Coherence, Engineered Independence

Modern AI assurance frequently relies on behavioural evaluation (e.g., red-teaming and benchmark-driven testing). These approaches are valuable for discovery, but they do not provide compositional guarantees against correlated failure, distribution shift, or drift in adaptive systems. This work presents the AxoDen Unified Mathematical Backbone, a formal framework for system-level AI assurance based on explicit structural constraints. The framework unifies (i) information-theoretic bounds on uncertainty accumulation across pipelines, (ii) bounded influence/leakage constraints for reasoning and decision processes, (iii) engineered independence across architectural trust roots to mitigate common-mode failure, (iv) quantitative multi-agent coherence objectives, and (v) closed-loop verification and recovery principles suitable for safety cases. We establish a compositional safety envelope showing how local constraint satisfaction yields system-wide assurances under clearly stated threat and drift assumptions. The accompanying record contains formal proofs and architectural specifications; access to technical details is restricted to protect intellectual property and safety-critical mechanisms.