A Cyber-Physical Sovereign Architecture for Autonomous Swarms: Formal Verification, Post-Quantum Consensus, and Immutable Zero-Trust Sandboxing (Phase IV)

This paper formally establishes the mathematical foundations and deployment architecture of the ZARQA Cognitive Swarm Core (Version 33.18.0), an unprivileged, zero-trust, hardware-abstracted operating matrix for decentralized grid-inspection humanoids. By fusing Robust Discrete-Time Control Barrier Functions (R-DTCBF) with finite-difference Hamilton-Jacobi-Bellman (HJB) optimal solvers, I guarantee kinematic safety under stochastically bounded physical disturbances. I extend this physical sovereignty into the computational and network domains via a Byzantine-resilient ZeroMQ consensus fabric, hardened by Hybrid Post-Quantum Cryptography (Kyber768/X25519) and strict Extended Berkeley Packet Filter (eBPF) kernel-level rootkit suppression. Furthermore, I formalize the execution dynamics of Proof-Carrying Code (PCC) using the Lean 4 theorem prover within a socket-activated Linux daemon. I explicitly map and resolve POSIX Discretionary Access Control (DAC) recursions and dynamic linker (ld.so) security paradigms, guaranteeing continuous, deadlock-free mathematical liveness.