SIS‑10: Safety Intelligence System: Formal Core v1.2

Abstract

Abstract The SIS‑10 framework establishes a typed, invariant preserving safety calculus for cyber physical systems. It unifies temporal semantics, schedulability, semantic preservation, ML admissibility, cryptographic verification, and risk bounded control into a single mathematically coherent architecture. All domains and operators are fully explicit, enabling formal reasoning over system trajectories and safety envelopes. The temporal layer defines an ordered metric structure with drift aware bounded causality, interval set operators, and jitter robust event semantics. The QoS layer enforces schedulability and feasible actuation, ensuring that all control actions remain within admissible timing and load bounds. Semantic compression provides a safety preserving homomorphism that guarantees invariants survive dimensionality reduction. Multi‑modal fusion introduces cross sensor falsifiability, enabling fault detection through probabilistic disagreement. The ML layer is input validated and logic embedded, ensuring that all model outputs entail the SIS‑10 invariant set. The cryptographic layer supplies zero knowledge execution trace proofs, allowing runtime verification of transition correctness without revealing internal state. Predictive shutdown optimization is constrained by a formally defined safety envelope, ensuring that operational objectives never violate admissible safety bounds. Cyber physical risk evolves through a bounded monotone propagation model with explicit mitigation operators, while the Safety Twin provides deterministic and stochastic discrete time system dynamics. The inductive proof layer establishes global invariant preservation for all admissible executions, and the event→action mapping connects the formal calculus to real SIS triggers. SIS‑10 therefore constitutes a unified, verifiable, and implementation ready safety architecture, suitable for runtime assurance, cyber‑physical certification, and next generation functional safety systems. Further enhancements include graphical formalization, parameterized system tuning, implementation DSLs, and automated verification scripts, none of which alter the core mathematical model..