Threat-Aware Capillary Branch Shifting: Adversarial Path Detection, Maneuverability Maximization, and Safe Grafting under Structural Doubt

This paper develops a threat-aware extension of capillary branch navigation in contracting linear systems operating under structural emulation limits. Building on prior work establishing integration capacity (Γ) and emulation deficit (δ), we formalize adversarial path detection in recursive hierarchies where uncertainty arises geometrically rather than from additive disturbance models. We prove that adversarially luring trajectories necessarily induce detectable subsystem violations when projected to sufficiently low integration capacity (Lemma 0; Theorem 1), separating adversarial forcing magnitude from emulation deficit (Lemma 3). A constrained lexicographic graft rule—prioritizing safety, maneuverability, and cumulative deficit— is shown to be uniquely admissible within a formally defined strategy class and resistant to manipulation under structural doubt (Theorem 5). A reserve-to-jump policy with Hold Mode is introduced, and we prove a structural dominance result: when recovery is physically reachable, delaying terminal commitment weakly dominates immediate shutdown (Proposition 8). Numerical simulations verify subsystem density, forcing-chain detection, lexicographic branch selection, and energy-reserve invariance. The results are proved in the linear contracting class. Extensions to nonlinear contraction metrics and full minimax equilibria remain future work.