Entropy-Horizon Navigation in Emulation Hierarchies: Inverted Capillary Mapping, High-Γ Proposals, and Low-Γ Pilot Verification under Structural Doubt and Maximum-Entropy Termination

Entropy-Horizon Navigation in Emulation Hierarchies constructs an inverted proposal–verification navigation architecture for contracting recursive systems operating under structural epistemic limits. Building on prior results establishing integration capacity (Γ) and emulation deficit (δ), the framework separates roles: high-capacity actors generate candidate future trajectories, while a strictly lower-capacity pilot (Γ_L < δ) verifies and steers using capacity-separated detection. A proposal becomes certain when its per-path deficit exceeds a computable indistinguishability threshold. We prove that any such certain proposal necessarily induces a velocity-mismatch violation at the verification level and must therefore be emulation-resident. False certainties (“blips”) are identified through ensemble disagreement across admissible verification paths and corrected by grafting the highest-coherence sibling continuation. Grafting preserves the hierarchy depth bound H*(Γ), ensuring that map correction does not consume navigation horizon. Two structural guarantees follow. First, after pruning, surviving trajectories always admit a nontrivial binary fork and retain a strictly positive residual doubt margin δ_res > 0; certainty cannot be reduced to zero within the hierarchy. Second, under sustained forcing, navigation terminates at a finite entropy horizon T_ent bounded explicitly by system parameters. At maximum-entropy disorder, instantaneous re-coherence probability equals (1−τ)^n — strictly positive but super-exponentially small in dimension — while deterministic recovery is guaranteed under zero forcing. All results are proved in the linear contracting class. The framework formalizes navigation under permanent structural doubt: proposals may be generated, certainty is tested and corrected, but irreducible residual doubt remains intrinsic to the system architecture.