Observer-Theoretic Integration Capacity Estimation in Nonlinear Capacity-Limited Recursive Systems: Type-Profiles, Adaptive Safety Margins, and the Type Misidentification Adversary

This paper extends the nonlinear integration capacity framework of 2026g by introducing a trajectory-observable estimator for integration capacity and resolving three structural limitations left open in the prior work. First, it constructs an empirical estimator Γ̂ derived from trajectory data and shows that it converges to the global minimum capacity rather than the pointwise state-dependent capacity. The estimator is proven to be conservative by construction and admits a finite-sample error bound consisting of a sampling term and an irreducible error floor induced by structural doubt, which does not vanish with additional data. Second, the paper generalizes the adaptive safety margin to a three-term form that accounts for state-dependent variation in nonlinear systems. This extension ensures that safety guarantees remain valid during expansion phases where local capacity contracts toward its minimum, addressing undercoverage present in the prior state-independent margin. Third, it qualifies the ergodicity assumption underlying recurrence estimation. In multi-attractor systems, recurrence estimates are shown to be basin-local rather than global, and the resulting limitations are formalized without invalidating the operational use of recurrence-based detection. Building on these results, the paper introduces Type-profiles for agents operating across multiple domains and derives a bound on maneuverability degradation under Type miscalibration using a recurrence-geometry distance metric. It further defines the Type Misidentification Adversary (Class 11), which exploits the estimator’s irreducible uncertainty to induce systematic miscalibration without altering system dynamics or violating existing alarm conditions. An operational algorithm is provided that computes Γ̂ and the associated adaptive safety margin using only observed trajectories, with guarantees that decisions taken under the estimated capacity remain safe relative to the true minimum capacity with high probability. The results apply to control-affine nonlinear systems and recover prior linear results as special cases.