Observer-Robust Control of Obstruction Diagnostics

Abstract: This paper establishes a formal architecture for the observer-robust control of discrete constraint systems. Shifting from a single-metric view of system error, the work defines a repair-policy layer that operates over a bundle of observer-induced geometries. A control policy (Ctrl) is defined as "observer-robust" if its performance—measured by descent adherence, structural stability, and diagnostic responsiveness—remains bounded across a declared class of admissible observers (𝔒). The core contribution is the operationalization of the Observer-Robust Control Criterion, which evaluates policies based on their ability to stabilize obstruction diagnostics (Φ₁, Γ₂, Rcl, Ξ) without assuming a universally privileged metric. This framework incorporates a committed-state descent law and a piecewise closure-ratio guardrail to prevent "fake repair" through topological tearing. This is a technical contribution to the theory of finite control and discrete geometry; it is not a theory of intelligence, cognition, learning, or consciousness. Experimental results demonstrate that diagnostic channels can activate separately in finite test systems, validating the requirement for multi-channel, diagnostic-responsive repair routing. Key Technical Contributions: Observer-Robust Control Criterion: A formal property for evaluating policy admissibility across varying observer assumptions. Hierarchical Control Model: From primitive observer selection to induced obstruction geometry and state-dependent repair routing. Committed-State Descent Law: Ensures non-increasing quotient residuals (Φ₁) while allowing exploratory operator proposals. Diagnostic-Separation Evidence: Empirical validation that geometric, logical, and relational channels provide separable signals for structural repair.