Static Self-Configurations and the Emergence of Temporal Continuity from Finite Relational Horizons

This paper develops a conditional mathematical reconstruction of temporal continuity within Horizon Monism, a relational framework founded on a single scale-free relational totality and embedded finite first-person horizons. Unlike configuration-space and shape-dynamical approaches, which investigate time through relational configurations, dynamical constraints, and geometric or complexity-based structures, the present approach begins with non-faithful horizon extraction, irreducible distinctions between ontic relational completeness and finite effective representation, and horizon-relative ultraviolet–infrared resolution ordering. The central proposal is that personal continuity does not require a persisting ontic individual or a fundamental succession of physical states. Instead, an admissible family of structurally corresponding local self-configurations may be represented within the same timeless relational totality. Each configuration contains its own present relational structure, including internal self-models, apparent memories, clock readings, and physical correlations. Memory is therefore treated as a present relational configuration rather than necessarily as information transmitted from an ontically prior state. Building upon the finite-horizon framework and the HM-14 relational projection model, we construct compatible resolution hierarchies, static clock correlations, and cross-scale consistency conditions for effective physical laws. A conditional continuum theorem establishes that uniformly bounded relational coordination energy, with an appropriate refinement-dependent coupling scaling, admits subsequences converging to Hölder-continuous effective configurations. Under a stable self-model readout, this regularity extends to the corresponding family of local self-representations. The resulting framework demonstrates the mathematical compatibility of timeless relational ontology, finite local horizons, structurally continuous effective histories, and clock-like correlations without requiring fundamental temporal transport or an ontically persistent self. These results establish conditional existence and representation theorems rather than a unique derivation of physical time, consciousness, or observed dynamical laws. The emergence of the required coupling scaling and physical clock calibration from the underlying relational structure remains an open problem. Methodological Distinction from Shape Dynamics The methodological distinction lies in the starting point and the role assigned to relational structure. Shape dynamics and related configuration-space approaches formulate physical descriptions through configurations, symmetry reduction, and dynamical or complexity-based principles. Horizon Monism instead begins with one complete relational totality that carries no fundamental temporal parameter, spatial metric, or intrinsic resolution scale. Finite reference horizons generate non-faithful effective representations of this totality. The associated distinction deficit establishes a reference-relative asymmetry, while an additional resolution-time identification assigns operational temporal order to admissible coarse-to-fine refinement families. Temporal continuity is then reconstructed not through the fundamental evolution of configurations but through structural compatibility and relational coupling among local effective self-configurations. The HM-14-type coordination functional supplies a conditional mathematical route from bounded inter-configuration mismatch energy to continuous effective representations. Accordingly, the proposed distinction is not the mere rejection of fundamental time, which is shared with several existing approaches, but the attempt to reconstruct effective temporal order and continuity from finite relational distinguishability, horizon-relative resolution, and static coupling regularity.