The Domain Projection Paradigm: A Unified Computational Spine for Autonomous Systems

Autonomous systems deployed across high-consequence substrates frequently experience critical state divergence when probabilistic control models (neural networks, large language models, heuristic solvers) interface with asynchronous, physical, or distributed environments. Engineering practice has historically addressed these failure modes through ad-hoc wrappers, application-level timeout heuristics, and post-incident exception handlers. This monograph formalizes the alternative established by the Arcstone Computational Spine (ACS): the Domain Projection Paradigm. The foundational thesis posits that host-level execution safety is governed by a minimal Layer-0 Universal Kernel (I1–I3) enforcing bare-metal admission contracts on the reference monitor's own transition relation and dispatch path. To address diverse operating physics without kernel modification, we define a formal projection operator, Π_domain, synthesizing specialized child invariants (I4–I11) and composite cross-domain tensor invariants (I12–I13). We establish a containment priority hierarchy for composed state spaces (Ω_A ∩ Ω_B), specify crash-consistent non-volatile journaling protocols across host restarts, present mechanized Coq proofs of joint financial and kinematic inductive trace safety for the abstract transition system under zero admitted axioms, and document the boundary closure derived from an iterative automated adversarial scoping dialogue conducted with Grok.