Registration Theory and the Mass-Gap Problem II: Retained-History Selection and Reciprocal Host Tuning

This second paper in the Registration Theory (RT) mass-gap investigative series examines whether retained relational history and reciprocal registration between interacting hosts can select, coordinate, and stabilize distinct persistent registration organizations without assuming particles, mass, or physical excitation energy as fundamental primitives.Building upon the attractor classification and transverse-stability findings of Paper I, the investigation first tests the canonical ACRF-4 successor dynamics with identical current registrations but different retained-coupling histories. Across 80 seeded numerical trials, the system converges to ten different attracting configurations spanning three structural families. These results demonstrate that retained relational organization can determine which persistent state is selected even when the current registration configuration is unchanged.A separately specified two-host extension then investigates reciprocal tuning and synchronization. Controlled variation of inter-host coupling produces transitions from initially distinct persistent organizations to shared successor states in three tested initial-state pairs. The resulting transition values depend on the initial organizations and interaction parameters and are not proposed as universal physical constants.The investigation also establishes exact invariance of the concordant-host submanifold under the specified reciprocal interaction law. Together, the analytical and numerical results provide a finite-model mechanism for studying how history-dependent registration and reciprocal host interaction can influence state selection and manifestation.These findings support further investigation of synchronization as mutual compatibility of successor organizations rather than an externally imposed oscillatory mechanism. They also motivate the possibility that persistent physical identities may arise through dynamically selected host–system relationships.The paper distinguishes established results of canonical ACRF-4 from results obtained through the proposed reciprocal-host extension. It does not claim to derive the inter-host interaction law from primitive Trinity organization, establish a physical particle mass spectrum, or solve the Yang–Mills mass-gap problem.The accompanying reproducibility package provides the numerical methods, datasets, source code, and supporting figures. Subsequent investigations will address the derivation of native resonant inter-host registration, the robustness of selected organizations, and the possible emergence of a positive excitation-consequence gap.