Adaptive Navigation in Open Fields: Thermodynamic Sinks and Envelope-Robust Viability

The non-scalar viability kernel of NSVK v4 guarantees recursive feasibility only when the external field is unchanged between steps. We treat a moving field. When the admissible transitions of the field are given by a known set-valued map G, we define a family O^G=(O^G_y)_y of state sets indexed by the field value, the greatest fixed point of a monotone operator on a complete lattice, and prove that it is exact: a state lies in O^G_y if and only if some policy that sees the current field value but not the next keeps the node above its existence floors against every disturbance and every admissible field path. No topology and no measurable selection are needed. Feasibility is then recursive with no horizon and no forecast-consistency condition; O^G is antitone in G and monotone in the control set, so a critical radius of the field can be found by bisection. For forecasts not generated by a known map we keep an envelope-robust terminal set and its kernel, prove that both lie inside O^G, and show that the inclusions can be strict, down to an empty envelope set in a field where the node persists. We then add the node's internal entropy and the field's remaining absorption capacity as stocks. Their sum changes independently of the fluxes between them. With exogenous rates, the node can keep both stock floors along a path if and only if two budgets hold, one for the sum and one for the sink alone, and exporting as little as possible at each step attains this; under an export cap and non-degenerate floors, least export remains optimal for every sequence of exogenous rates if and only if the cap is identically zero or its increments are at least those of the sink stock divided by the time step, a condition that in particular lets the whole stock be exported within one step and that a fixed cap stops meeting once the step is fine enough. Finally, the exact revealed-preference test of NSVK v4 is applied to two state-dependent tie-breaks on its deposited instance. The interpretation of the stocks as entropy is a hypothesis, not a derived identity.