Scale-Selective Propagation of Time-Rate Waves Through Fine Structure in the Enchan Field

This work studies how small perturbations of the Enchan local time-rate field propagate through fine spatial structure in the same field. The problem is motivated by the hard-wall boundary used in a previous Enchan two-route interference study: rather than imposing a primitive material opacity or an S=0 wall, the present work asks whether finite structure in the Enchan field itself can generate scale-selective transmission and reflection. Starting from the reduced finite-tension branch S_tt = div[mu(D) grad S] - S with mu(D) = 1/(1 + D^(3/2)), the field is decomposed as a structured background plus a small propagating perturbation. Stage A uses a predeclared one-dimensional frozen structured background and compares it with a matched smooth/homogenized control. The response is banded rather than a monotonic low-pass: long-scale perturbations remain comparatively transmissive while strong reflection bands appear when the perturbation resolves the fine structure. At ka = 2 the mean Stage-A structured transmission is approximately 6.25e-4 while the smooth control remains approximately 0.989; at ka = 4 the structured transmission is approximately 1.07e-14 while the smooth control remains approximately 0.962. Stage B replaces the hand-constructed surrogate with three previously frozen source-free Enchan final states from the published localized-field study. The source files are SHA-256 checked against the original run manifest before analysis. All three source profiles remain within the declared positive longitudinal branch and reproduce a scale-dependent structured-versus-smooth transmission difference. The largest Stage-B mean differences occur near ka = 1.0 and 1.5, where structured transmission is approximately 0.330 and 0.358 while the smooth controls remain approximately 0.994 and 0.988. The maximum Stage-B conservation residual is approximately 1.89e-15. Stage C extends the test to a full three-dimensional propagation study using the same three previously frozen source-free Enchan field configurations. A total of 54 cases were evaluated across structured, smooth, and vacuum controls, three selected spatial scales, and both normal and 30° oblique incidence. The scale-dependent scattering observed in the one-dimensional diagnostics persists in three dimensions. Structured backgrounds show reduced forward transmission together with increased reflection and lateral scattering relative to the matched controls. At ka = 4 under normal incidence, the mean structured transmission is approximately 0.486, compared with approximately 0.527 for the smooth control and 0.532 for vacuum. The maximum three-dimensional energy-accounting residual remains below 1.2% across all 54 cases. The result supports a model-level statement: fine S-field structure can act as a wavelength-selective barrier for small time-rate perturbations within the declared linearized Enchan branch. It does not identify ordinary matter with the tested surrogate or source-free structures, does not claim monotonic high-frequency blocking, and does not claim that a macroscopic material wall has been reconstructed. The Zenodo deposit contains the Version 1.1 manuscript PDF together with the complete reproducibility package for Stages A, B, and C, including the frozen numerical code, Stage-C configuration, archived source states, full numerical results, summary tables, execution manifest, README, LICENSE, and SHA-256 integrity records. The manuscript PDF is generated directly from the final Version 1.1 TeX source and is set as the default Zenodo preview. Version 1.1 update:Version 1.1 adds the completed Stage-C three-dimensional validation, updates the manuscript and reproducibility package accordingly, and preserves the Stage-A and Stage-B results unchanged. License: Enchan Research & Verification License v1.0. Copyright (c) 2026 Mitsuhiro Kobayashi.