Boundary Compensation – Compensated Islands V: Weight-Robust Certification and Pareto-Stable Hidden Sections

BC-CI-IV introduced externally anchored hidden sections and a finite-dimensionalcertification-cost functionalJw(Ξ) = wreadJread(Ξ)+wleakJleak(Ξ)+wvarJvar(Ξ)+wresetJreset(Ξ)+wbalJbal(Ξ)+wambJamb(Ξ).That construction solved the selection problem without importing dynamics, but it alsocreated an immediate methodological risk: a hidden section selected by one hand-tuned weightvector may be only a tuning artifact. The present paper develops the fifth CompensatedIslands module as an anti-tuning layer. The scientific object is no longer a single scalarizedminimizer for one declared weight profile, but the stability of selected hidden sections underuncertainty in the certification-policy weights.The paper defines the vector certification costJ(Ξ) = (Jread, Jleak, Jvar, Jreset, Jbal, Jamb)(Ξ) ∈ R6≥0,Pareto domination, the Pareto set of externally anchored hidden sections, admissible weightsimplices, exact weight-selection chambers, epsilon-suboptimality regions, and minimaxcertification. A central technical warning is made explicit: exact optimality on a nonemptyopen set of weights is too strong as a universal robustness criterion, especially for strictlyconvex Pareto fronts. Therefore exact chamber robustness is treated only as a strong specialcase. The primary finite-resolution notions are epsilon-robustness and minimax robustness.The main results are elementary finite-dimensional theorems with high architectural value.Positive-weight scalar minimizers are Pareto-minimal. Under compactness and continuityassumptions, minimax-robust hidden sections exist. If a hidden section remains within anexplicitly declared tolerance of optimality on a positive-measure region of weight space, then itscertification status cannot be attributed to one isolated hand-tuned weight vector. The paperalso introduces a status protocol distinguishing PARETO_STABLE, EXACT_WEIGHT_ROBUST,EPSILON_ROBUST, MINIMAX_ROBUST, WEIGHT_FRAGILE, DOMINATED, TUNING_ARTIFACT, andNONUNIQUE_SELECTION.The module is finite-dimensional and epistemic. It does not claim that nature performsminimax optimization, that the weights are physical constants, or that Pareto-stable sectionsare physical fields, particles, trajectories, spacetime structures, causal cones, or laws ofmotion. Its purpose is narrower and stricter: to prevent BC-CI-IV certification-cost selectionfrom collapsing into hyperparameter engineering.