Observation Sufficiency for Finite-Horizon Viability: Certified Failure and Repair in a Controlled Reaction Network

This preprint studies when a coarse observation of a controlled reaction network is sufficient to determine a finite-horizon viability record. The model contains two non-equivalent finite fuel pools, competing restoration and repair processes, an evolving coupling state, and a shared activity constraint. Initial states can have identical working state, coupling condition, current outputs, total charged inventory, and requirements while differing only in fuel allocation. Computer-assisted certificates establish continuous allocation bands with opposite finite-horizon viability indicators, showing that the aggregate observation is insufficient. A pooled peak-restoration observation retains this ambiguity, whereas task-aligned directional and joint restoration--repair observations restore sufficiency on the declared domain. Separate certified trajectories show that same-output reorganization can outlast preservation of the initial organization and that continuation can be lost while substantial charged stocks remain. The results are established for a fully specified thermodynamically consistent reaction network using analytic arguments and verified numerical certificates.