This paper is archived as a speculative research work. We develop a closure-based formulation of interface structure in the Entanglement–Algebraic Spacetime (EAS) framework, in which admissibility is described by a signed scalar field and physical structure arises from constraints on comparability across an ordered family of configurations. Focusing on the rank–3 closure grammar, we introduce a saturation invariant that limits the number of irreducible admissible comparisons at a persistence and define refinement-stable generator sets and their type-profiles. We prove that, under closure irreducibility, canonical equivalence, and refinement stability, only two generator type-profiles are admissible: (1,2) and (3,0). This classification forces a decomposition of admissible comparability into two inequivalent classes, distinguished by whether their associated mismatches are reducible or irreducible under closure. We formalize this as a split between null comparability, which carries no independent invariant content, and residual comparability, which defines irreducible invariants. We show that any gauge-invariant, closure-neutral, and refinement-stable interface functional must, at quadratic order, assign opposite effective signs to these two classes. This yields an intrinsic indefinite quadratic structure on admissible mismatches, from which an effective signature and relativistic dispersion relation emerge under continuum compression. No primitive spacetime, metric, or dynamical law is assumed; the signature structure is forced entirely by rank–3 closure and persistence constraints. Finally, we demonstrate that this closure-based derivation is consistent with the second-order ordering formulation, establishing that both approaches encode the same underlying decomposition of admissibility variation.
Michael Labhard (Mon,) studied this question.