The SignalRupture Causal Axiomatic Framework (SR‑CAF) establishes the mathematical substrate of the SignalRupture discipline. It defines a falsifiable causal measurement architecture for diagnosing instability, drift, and harm propagation within complex sociotechnical systems. SR‑CAF formalizes four interacting primitives — Drift (D), Visibility Lag (ΔV), Harm (H), and Drift Transfer (Φ) — as a substrate‑level state representation (S (t) =D (t), V (t), H (t), (t) ). Through these primitives, the framework models how instability emerges, propagates, and becomes observable across coupled human‑machine infrastructures. The manuscript introduces a sparse stochastic generative model, identifiability conditions, and a finite‑sample recovery theorem that together enable empirical reconstruction of drift‑transfer topologies under dependent stochastic processes. It also defines the SR‑SYNTH‑1 benchmark system for synthetic simulation, a continuous regime manifold for hybrid sociotechnical classification, and nonlinear operator‑level extensions using RKHS and Neural ODEs. SR‑CAF’s architecture is explicitly falsifiable: if its primitives cannot be operationalized or its causal relationships fail empirical validation, the framework collapses within that domain — preserving epistemic integrity and testability.
Signal Rupture (Fri,) studied this question.