Temporal Redistribution and Flux Conservation in the Enchan Field: From Finite-Tension Phase Balance to Galactic Rotation

Temporal Redistribution and Flux Conservation in the Enchan Field: From Finite-Tension Phase Balance to Galactic Rotation This work investigates temporal redistribution and flux conservation in the Enchan Field, a nonlinear finite-tension geometric field framework in which the order field S determines both local clock rate and weak-field gravitational response. The paper derives separate field-value and energy ledgers for the effective temporal-spatial split dynamics and organizes the proposal into three nested, falsifiable hypotheses: structural temporal redistribution (H1), global signed scalar balance under symmetric closed conditions (H2), and compact-source temporal sign reversal (H3). The study also documents the theoretical evolution of the Enchan Field. A covariant nonlinear K(X) formulation remains viable in the static spatial sector, while a naive timelike continuation is rejected because of gradient instability. Dynamical evolution is therefore represented by an effective temporal-spatial split while retaining the inherited finite-tension response. In the static gravitational sector, the inherited quadrature branch produces flat-rotation and baryonic Tully-Fisher behavior. A frozen axisymmetric Enchan F0 prediction is evaluated against 2,823 SPARC radii in 163 galaxies, giving a median absolute velocity error of 11.790 km/s. The same frozen excess-acceleration field is integrated to obtain a paired resolved temporal-potential profile, with a median inner-to-outer clock-rate offset of 2.518 seconds per year. The paper explicitly retains observational tension and negative results. Only 22.60% of the admitted SPARC radii fall within the published one-sigma velocity intervals under the frozen F0 realization, and an alternative density-anchor completion does not improve all error metrics. These results are reported without post-hoc refitting. The accompanying reproducibility package contains audits of the finite-tension kinetic vessel, the temporal-spatial energy ledger, the rejected timelike continuation, the Candidate C reconstruction ledger, and the frozen SPARC/F0 observational cross-check. The work is presented as a falsifiable research program rather than as a completed proof of global temporal conservation. Update (Sep 16, 2026 / v1.1): Aligned with the strict non-bundling policy (Policy 310) by removing pre-computed raw/derived observation datasets (f0_sparc_observational_rows.csv) and redundant pre-rendered files from the reproducibility archive. Removed the stale local-path-based ROTMOD C patch and replaced it with a 100% clean-room, patent-safe black-box dynamic compilation and connection approach. Resolved a quantitative discrepancy on page 12 of the manuscript PDF (now compiled to Version 1.1) to state that comparative row-level statistics are dynamically regenerated by the reproducibility pipeline rather than bundled. Added requirements-verified.txt to guide exact environment replication.