Operational Causality and Closure

Abstract

Operational Causality and Closure (OCF) starts from a deliberately simple question: what must happen for a transition to become a completed, persistent physical fact? Rather than assuming from the outset a spacetime, a global clock, a Hilbert space, or an equation of motion, this foundational paper begins with a finite operational structure: admission, present processing, and restitution. From this minimal starting point, it develops a common chain linking unresolved content, closure defects, retained memory, reciprocal dynamics, persistent identity, local placement, and conditional global time. Several familiar mathematical structures then appear as consequences or reductions of this chain. Bilateral reconstructibility leads naturally to defect completion; positive storage and passivity force reciprocal couplings; eliminating the retained state produces an exact Volterra memory kernel; persistent capture turns an achieved closure into an operational identity. In the explicitly stated class where oriented two-direction incidence must close on its own real carrier, three dimensions are selected, and an additional positive associative completion leads to a quaternionic response structure. Completed closures form a causal event network, while a global time exists only when local temporal increments satisfy an exact path-independence condition. The paper is intentionally careful about the boundary between derivation and assumption. It does not claim to derive spacetime, general relativity, the Standard Model, a universal Born rule, or the numerical values of physical constants. Instead, it proposes a pre-geometric foundational architecture and makes explicit the additional interfaces required to reach downstream results. Companion works explore how this same closure grammar may lead, under further stated conditions, to global spatial reconstruction, a common Lorentzian propagation cone, mass equivalence, Schrödinger dynamics, and quantum measurement weights. The central proposal is therefore not a new equation of motion, but a possible common provenance for structures that physics usually introduces separately.