Dynamic Accessibility and Realized Identity in Registration Theory: Bilateral Constitution, Retained-History Selection, and the Mathematics of Persistent Relational Possibility

Registration Theory (RT) begins from Trinity as an undivided generative ontology, with physical distinctions arising through continuing bilateral registration rather than through independently primitive space, time, energy, or pre-existing particles. This paper develops the Dynamic Accessibility Principle: bilateral registration can constitute multiple persistent relational organizations, retained consequential history can differentiate their accessibility, and continuing reciprocal interaction can maintain realized identities without requiring any particular outcome to be universally inevitable.The investigation establishes exact model-level results in canonical Adaptive Closed Registration Framework (ACRF-4), including the existence of distinct persistent organizational fixed points, bilateral symmetry constraints, and the failure of perfectly undifferentiated deterministic states to select a preferred differentiated organization. Controlled numerical experiments demonstrate that preparations with identical current registration coordinates but different retained reciprocal couplings can converge toward different attracting organizations under the same successor law.The paper further develops history-sensitive conservative daughter-registration constructions, showing how changes in admissible bilateral encounters can reorganize daughter relationships while preserving the model's additive registration ledger. These results distinguish mathematical possibility, consequential accessibility, and dynamically maintained realization.The findings support a constructive, non-deterministic-in-outcome research direction for RT without asserting fundamental randomness or requiring a unique realized universe. The models demonstrate mathematically admissible mechanisms rather than a uniquely derived primitive Trinity successor. The connection to physical particle constitution, confinement, and the Yang–Mills mass-gap problem remains a subject for further derivation and empirical comparison.