Spacetime as Conjugate Registration: Generative Space, Maintained Duration, and Ontological Closure in Registration Theory

This foundational research paper presents a comprehensive synthesis of Registration Theory's (RT) proposed ontology of spacetime. It develops the Frontier–Retention Conjugate Consistency Principle (FRCCP), according to which spatial extension and experienced duration are complementary manifestations of one continuing Trinity registration process. Within this framework, space emerges through generative relational expansion, while operational duration arises through maintained distinctions, retained historical consequences, and persistent internal closure. Mass-like organization is interpreted as expansion constrained by retained duration rather than as the cessation of expansion. The paper consolidates mathematical results concerning common-mode expansion cancellation, host-relative stationarity, ACRF-4 current–retention conjugacy, first-kiss opposition and timelike daughter formation, conservative recursive registration, common-frontier propagation, and conditional relativistic clock behavior. It distinguishes exact mathematical identities, model-specific results, conditional theorems, and foundational conjectures. The analysis establishes a coherent conditional spacetime ontology while identifying the remaining requirements for unique physical dynamics, universal causal invariance, and empirical identification. Version 0.2 — October 20, 2026. The accompanying research archive contains supporting mathematical investigations and reproducibility materials.