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

BC-CI-IV introduced externally anchored hidden sections and a finite-dimensional
certification-cost functional
Jw(Ξ) = wreadJread(Ξ)+wleakJleak(Ξ)+wvarJvar(Ξ)+wresetJreset(Ξ)+wbalJbal(Ξ)+wambJamb(Ξ).
That construction solved the selection problem without importing dynamics, but it also
created an immediate methodological risk: a hidden section selected by one hand-tuned weight
vector may be only a tuning artifact. The present paper develops the fifth Compensated
Islands module as an anti-tuning layer. The scientific object is no longer a single scalarized
minimizer for one declared weight profile, but the stability of selected hidden sections under
uncertainty in the certification-policy weights.
The paper defines the vector certification cost
J(Ξ) = (Jread, Jleak, Jvar, Jreset, Jbal, Jamb)(Ξ) ∈ R
6
≥0
,
Pareto domination, the Pareto set of externally anchored hidden sections, admissible weight
simplices, exact weight-selection chambers, epsilon-suboptimality regions, and minimax
certification. A central technical warning is made explicit: exact optimality on a nonempty
open set of weights is too strong as a universal robustness criterion, especially for strictly
convex Pareto fronts. Therefore exact chamber robustness is treated only as a strong special
case. 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 continuity
assumptions, minimax-robust hidden sections exist. If a hidden section remains within an
explicitly declared tolerance of optimality on a positive-measure region of weight space, then its
certification status cannot be attributed to one isolated hand-tuned weight vector. The paper
also introduces a status protocol distinguishing PARETO_STABLE, EXACT_WEIGHT_ROBUST,
EPSILON_ROBUST, MINIMAX_ROBUST, WEIGHT_FRAGILE, DOMINATED, TUNING_ARTIFACT, and
NONUNIQUE_SELECTION.
The module is finite-dimensional and epistemic. It does not claim that nature performs
minimax optimization, that the weights are physical constants, or that Pareto-stable sections
are physical fields, particles, trajectories, spacetime structures, causal cones, or laws of
motion. Its purpose is narrower and stricter: to prevent BC-CI-IV certification-cost selection
from collapsing into hyperparameter engineering.