A Cyber-Physical Sovereign Architecture for Autonomous Grid-Inspection Humanoids: Variational Bayesian Cubature Kalman Filtering, Sobolev-Orthogonalized MoE-CLIP Anomaly Detection, and Tamper-Evident Spatial Memory (Phase III)

Abstract

Autonomous humanoid robotics deployed in high-voltage transmission grid inspection require spatial cognition engines that are simultaneously resilient against physical sensor drift, adversarial false data injection, and runtime memory corruption. Most existing spatial perception stacks decouple state estimation and computer vision from cryptographic integrity, leaving robotic platforms vulnerable to localization spoofing and adversarial visual camouflage. This paper establishes the formal mathematical foundation and systems architecture for Phase III of the ZARQA Grid Inspection Humanoid Core (zarqa_gih_spatial_cognition_core.py). We present formal proofs of asymptotic stability, covariance positive-definiteness, cryptographic invariance, and anomaly separation bounds for a multi-modal spatial cognition engine deployed on high-voltage transmission towers. Specifically, we prove: 1. Hurwitz Stability & Left-Half Plane (LHP) Invariance: Continuous-to-discrete bilinear (Tustin) state-space discretization remains strictly Hurwitz stable under dynamic skew-symmetric perturbations (). 2. Covariance Positive-Definiteness: Bures-Wasserstein trace regularization combined with Ledoit-Wolf shrinkage guarantees strict positive-definiteness and bounded condition numbers for Variational Bayesian Gaussian-Sum Cubature Kalman Filtering (GSCKF). 3. Tamper-Evident Spatial Memory: Log-odds Bayesian occupancy mapping coupled to an SHA-256 cryptographic hash chain guarantees collision-resistant detection of unauthorized spatial memory modification under the Random Oracle Model. 4. Sobolev-Orthogonalized Anomaly Detection: Fréchet Inception Distance (FID) gating on Sobolev-projected CLIP embeddings guarantees deterministic separation between benign structural features and adversarial visual anomalies. The cognition core executes within an immutable, zero-trust Blue-Green Linux POSIX sandbox featuring TPM 2.0 / PBKDF2 hardware attestation, GCM-mode AEAD timestamp encryption, and automated orphan process management, achieving full compliance with IEC 63439 and IEC 62443 industrial automation standards.