Focal and Immediate-Support Observations Can Fail to Preserve Finite-Horizon Viability in a Three-Tier Reaction Network

This preprint studies whether observations of a working subsystem and its immediate support are sufficient to determine finite-horizon viability when that support can itself be replenished from a deeper finite reserve. The model is a thermodynamically specified three-tier controlled reaction network with two independent actuator pools: restoration and coupling repair share one activity simplex, while a reversible recharge reaction has a separate bounded activity. Two preparations are constructed with identical working populations, immediate fuel inventories, coupling condition, present outputs, and original restoration–repair effectiveness values; only the deeper charged reserve differs. At horizon H=0.20, an accounting functional Z3=p1+2p2+b+g+z provides an all-policy exclusion certificate for z∈[0,0.003], while a complete interval-verified trajectory establishes viability for z∈[0.79,0.80]. Thus the same upper-two-tier observation can correspond to opposite finite-horizon continuation records. A deeper-support recharge observation O3=max⁡(0,ϕT) repairs the representation on the declared certified domain [0,0.003]∪[0.79,0.80], including a non-singleton record-homogeneous zero fiber. The result is a model-specific certified observation-failure and repair construction.