Finite Na⁺/K⁺-ATPase Export Capacity as a Proximal Determinant of Conservation-Limited Electrochemical Instability in Excitable Tissue

Electrochemical instability in excitable tissues is conventionally attributed to energetic failure. This manuscript advances a different proximal coordinate: instability is governed by proportional balance between aggregate inward sodium demand and the finite export capacity of the Na⁺/K⁺-ATPase, formalised as the dimensionless stability ratio σ = ΣJᵢₙ / Jₚᵤₘₚ,ₘₐₓ. Five results are established. The causal framing is shifted from energetic sufficiency to conservation-limited feasibility, and a unified constraint space is defined in which mechanistically distinct perturbations are represented relative to a common feasibility boundary. Embedding sodium conservation within a slow-fast dynamical framework shows that loss of equilibrium proceeds generically through a saddle-node fold of the fast ionic subsystem, entailing an inverse square-root divergence of recovery time as the feasibility boundary is approached from below, which constitutes an independently testable prediction. Bayesian synthesis of pump kinetic parameters from Nakao and Gadsby (1986) and Gadsby and Nakao (1989) with ionic trajectory data from Müller and Somjen (2000) constrains σ at threshold crossing to a posterior mean of 1.17 with a 95 per cent credible interval spanning 0.97 to 1.44. Structured synthesis across orthogonal perturbation axes, capacity-dominant and load-dominant, demonstrates convergent threshold shifts consistent with approach to σ = 1 under pump-permitting energetic conditions, establishing an explicit empirical framework for classifier discrimination. The formulation is regime-restricted, explicitly falsifiable, and advances from conceptual proposal to empirical claim within the spreading depolarisation literature.