A Chronos Change-Clock: Representing Temporal Progression Through Numbers, Shell Geometry, and Ordered State Transitions

Conventional clocks represent time by counting repeated physical processes such as oscillations, rotations, transitions, or pulses. This work develops a reconstructed numerical Chronos change-clock that approaches clock construction from the opposite direction: an ordered numerical progression coordinate generates an evolving geometric state. The clock is represented through optimized shell radii, radial gap profiles, competing shell-family branches, and ordered structural transitions. An initial affine model reproduced a six-shell to seven-shell branch transition but produced insufficient geometric deformation. A subsequent v5 model introduced radial gap-profile and outer-gap response mechanisms. Seed-aware geometry tests, nonlinear transition analysis, ablation, reduced-model certification, parameter sweeps, and corrected boundary searches identified radial gap-profile coupling as the minimal sufficient mechanism. The accepted reduced model preserves the transition from the merged_6_beta branch to the birth_7_gamma. The results establish the numerical engine of a change-clock in which ordered numerical progression produces reproducible geometric deformation and a stable shell-family event. The model is not yet calibrated to seconds and has not yet been physically realized. Continuous interval proof, physical calibration, and experimental validation remain open stages. This deposit includes the manuscript and its complete computational reproducibility package, including simulator code, configurations, run outputs, numerical certificates, logs, documentation, and a SHA-256 manifest.