WHM-3D: A Three-Dimensional Test of Spatially Structured Wave-History Time-Rate Modulation in the Enchan Field
Year: 2026
Type: preprint
Abstract: Primary result: The previously demonstrated one-dimensional Wave-History Time-Rate Modulation (WHM) effect survives extension to three spatial dimensions and becomes spatially structured. Later probes respond according to position, path, propagation direction, delay, and local history strength. This record contains the Version 1.0 manuscript and reproducibility package for WHM-3D: A Three-Dimensional Test of Spatially Structured Wave-History Time-Rate Modulation in the Enchan Field. The study connects the published true-3D Enchan partial-differential-equation solver to the published proper-time and ray measurement protocol. A one-shot Gaussian velocity kick is applied at the center of a periodic field, after which delayed central, off-axis, far, angular, and reverse true-3D probes measure the residual history. After the source is removed, a finite spatial history remains and decays with time. Probe readout depends strongly on where and how the residual field is traversed: central paths produce substantially larger modulation than off-axis and far paths, while reverse and angular paths expose directional and trajectory-dependent structure. Across the continuum-consistent N = 24, 32, and 48 refinement sequence, using Courant-matched time steps and a shared band-limited continuous seed, the central modulation remains positive and changes monotonically from approximately 2.49e-4 to 3.86e-4 to 4.51e-4. At each tested resolution, the directly measured proper-time modulation agrees with the independent first-order variational metric prediction to approximately 0.02%. An isotropic-background control shows angular symmetry to numerical precision and reverse-direction agreement within 0.67%, supporting the interpretation that the directional differences observed in the primary run arise from the realized spatial history rather than a systematic bias in the probe implementation. As a secondary robustness comparison, nonzero WHM also persists in the tested mu = 1 and no-V' branches, indicating that persistence of the history effect is shared across the tested dynamical descriptions. The principal new result is the transition from a one-dimensional history signal to a three-dimensional spatial readout field carrying positional, path, directional, delay, and strength information. This is a synthetic numerical study. It does not constitute an observational or laboratory confirmation, and no ordinary acoustic coupling to the Enchan field is assumed. The deposit provides the final PDF, README, LICENSE, and a reproducibility archive containing the LaTeX source, code, frozen protocol and provenance records, generated figures, classification outputs, and the continuum-refinement data artifact. The large local intermediate cache results/history_enchan.npz is intentionally excluded; the authoritative unified runner recomputes the experiment without reading prior result files.
Author: Kobayashi, Mitsuhiro
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208787890