A Unified Safe-Critical Embodied AI Architecture: Bridging Non-Smooth Continuum Dynamics and Deterministic Embedded Control via Topological Invariance

Modern end-to-end Embodied AI (e.g., Vision-Language-Action models) inherently suffers from catastrophic phase-space divergence and Material Constitutive Inadmissibility when interacting with discontinuous contact boundaries and friction bifurcations. This capstone whitepaper (Paper 16) formally establishes the Unified Safe-Critical Embodied AI Architecture (USC-EAI), synthesizing the complete mathematical, physical, and control-theoretic foundations established across the preceding 15 foundational research monographs. Key Highlights of USC-EAI: Continuum Dynamics & Constitutive Inadmissibility: Formulates finite-deformation hyperelastic strain energy boundaries, proving that continuous autoregressive sampling provably induces non-physical manifold intersections under Signorini-Moreau complementarity conditions. Three-Tier Hierarchical Defense: Decouples asynchronous high-level semantic intent generation (Tier 1: 10–50 Hz) from algebraic topological invariance gates (Tier 2: 200–1000 Hz) and a microsecond deterministic safety kernel (Tier 3: 10–50 kHz). Deterministic C99 Execution Core: Fully implements a zero-heap, statically-allocated, WCET-bounded state estimator and momentum projection algorithm in pure C99, featuring explicit torque derivative slew-rate protection (FAULT_CONSTITUTIVE_INADMISSIBLE) and bounded momentum hard saturation. Formal Lyapunov Invariant: Formally proves that discrete system kinetic energy remains strictly bounded within a compact convex set under arbitrary adversarial policy inputs. Empirical Hardware-in-the-Loop (HIL) Benchmark: Demonstrates 0.0% contact divergence and an exact WCET of 11.82 microseconds on an ARM Cortex-M7 microcontroller under rigid impact conditions. Code & Open Reproduction: The audited C99 core kernel and adversarial benchmark fixtures are open-sourced on GitHub: c99-fault-tolerant-estimator (Release tag: v2.0-usc-eai).