Unavoidable Structure Constraint-Derived Limits on Absolute Nullity, Continuity, and Relational Foundations

This paper presents a constraint-based computational investigation into the lowest possible foundations of coherent structure. Rather than assuming physical laws, particles, spacetime, logic, or evaluative frameworks, the study enforces maximal eliminative constraints and observes whether coherence can persist. Absolute non-initiation, continuous non-localized binding, and purely relational structure without discreteness are each tested under explicit prohibitions. Across all experimental regimes, systems initialized without initiation, localization, or discrete units fail to remain stable. Instead, minimal initiation events, localized binding centers, and irreducible grain emerge as unavoidable consequences of coherence constraints. Attempts to maintain absolute nullity, perfectly continuous binding, or infinitely subdividable relational structure result in instability or collapse. These results establish a foundational no-go theorem: initiation, localization, and grain are not contingent modeling assumptions but structural necessities. The findings place strict lower bounds on eliminative foundational models and suggest that discreteness and initiation precede physical laws rather than emerge from them.