Mathematical Scaffolding and a Structural Toy Model for Equilibria Field Theory

This paper presents a stand-alone technical formalisation of Equilibria Field Theory(EFT), a substrate-first ontological framework in which the physical universe is grounded inan atemporal, equilibrium-seeking continuum. Spacetime, forces, and dynamics are treatedas emergent structural descriptions rather than as fundamental entities.The purpose of this work is not to propose a completed physical theory, but to providemathematical scaffolding that renders the EFT ontology precise, internally coherent, andempirically vulnerable. A field-theoretic representation based on a purity order parameter is developed, together with a complexity-limited collapse mechanism and a toy modelillustrating steady-state cosmological behaviour without fundamental time or spacetime.