Route–Resource Interlock in a Controlled Reaction Network: Finite-Horizon Viability, Observation Failure, and Refinement

This preprint develops a route–resource interlock in a thermodynamically specified controlled reaction network with two non-equivalent finite fuel pools, competing restoration and repair, and evolving coupling. The feasible-current correspondence depends on the support state, while realized routing changes those same support variables and thereby alters later control authority. For systems admitting the route–resource representation used in the paper, the manuscript identifies hidden resource directions generated by effect-equivalent routing and proves that every effect-closed linear resource summary must annihilate those directions. When the feasible-current correspondence varies along such a direction, the summary is blind to a present authority difference. In the specified network, computer-assisted all-control lifetime certificates and complete verified trajectories establish universal exclusion for initial allocation \(\theta\in[0.09,0.49425]\) and constructive finite-horizon feasibility for \(\theta\in[0.49915,0.70]\) at horizon \(H=0.20\). The interval \((0.49425,0.49915)\) remains unclassified by the present certificates and is not asserted to be a transition region or exact viability boundary. The paper further shows that favorable instantaneous margin motion does not determine finite-horizon viability; that pooled peak restoration capacity and thermodynamic free-energy density remain insufficient observations; and that directional and joint restoration–repair readouts provide different sufficient refinements. A separate same-output reorganization trajectory outlasts every trajectory constrained to preserve the original working populations and coupling. This version substantially reframes and extends the original preprint around the route–resource interlock, adds a general hidden-resource-direction result, strengthens the distinction between present control authority and finite-horizon continuation, and includes revised figures and supplementary material. The accompanying reproducibility archive is available at DOI 10.5281/zenodo.22879945.