Phase Structure of Moral Space: The Zero-Instantiation Constraint as Boundary

I develop a formal framework for moral theory under resource constraints. Modeling agents with multi-dimensional basic needs competing for finite environmental resources, I prove a trichotomy theorem: the space of viability-preserving allocations is either positive dimensional (Sufficiency), singleton (Zero-Instantiation Constraint), or empty (Scarcity). I show that classical moral theories (Kantian, utilitarian, Singerian, Rawlsian) implicitly assume Sufficiency and become undefined or degenerate at or below the Zero-Instantiation Constraint (ZIC). The framework explains why demanding prescriptions exhibit systematic non-instantiation and formalizes the boundary conditions implicit in “ought implies can.” Applications include development ethics, healthcare resource allocation, and the demandingness debate.