Validated Symmetry Projection: A Trust-Regulated Information Architecture

Modern autonomous robots operate under increasingly demanding real-time constraints where the physical cost of delayed decisions frequently exceeds the cost of managing bounded structural uncertainty. Conventional dimensionality-reduction techniques, including Principal Component Analysis (PCA), optimize geometric data representation but provide little guidance regarding which information should be trusted sufficiently to participate in safety-critical computation. Consequently, redundant sensing, recursive state estimation, and repeated uncertainty evaluation introduce unnecessary computational latency (Δ_c) despite excellent offline reconstruction performance. This paper develops a mathematically rigorous Validated Information Architecture (VIA) in which candidate physical symmetries are modeled as operational hypotheses, statistically sieved on independent calibration data under explicit multiple-comparison control, and only subsequently admitted into the lower-dimensional computational representation. The resulting processing pipeline combines validated symmetry projection with optimal PCA while preserving the mathematical optimality of PCA itself. Experimental evaluation on a physically motivated quadruped telemetry benchmark demonstrates substantial reconstruction improvements, modest increases in subspace stability, and, equally importantly, establishes that the observed tension with compressed-domain fault localization is not an empirical curiosity but an exact conservation identity — reported here as a proved theorem rather than a qualitative trend. The framework is subsequently generalized beyond dimensional reduction by introducing trust-regulated information flow, in which operational trust emerges from the simultaneous satisfaction of validated local invariants and validated global invariants, formalized correctly as a conjunctive (AND) condition rather than an additive one. Rather than recursively seeking complete statistical certainty before acting, the proposed architecture permits coherent information to flow continuously toward coordinated behavior under bounded uncertainty. This leads naturally to a dual-path architecture separating compression from fault monitoring and suggests a broader methodology applicable to real-time robotics, distributed sensing, and adaptive autonomous systems. The paper concludes with a clearly identified conjectural extension proposing that future robotic systems may evolve toward architectures combining reactive local sensing, predictive global models, and continuously updated trust metrics to maximize coherent information flow rather than recursive certainty. Throughout, experimentally validated results, derived theorems, and open conjecture are carefully and explicitly distinguished.