WHM-3D: A Three-Dimensional Test of Spatially Structured Wave-History Time-Rate Modulation in the Enchan Field

Version 1.1 correction: Version 1.0 inadvertently combined a native-N=32 baseline result set with a separately generated shared-N=24-seed continuum result set, and some figures used an older probe geometry. Version 1.1 separates these evidence layers, regenerates all tabular and graphical artifacts from provenance-tagged runs, and uses the declared P2 (y = z = 28) and P3 (x = 16, z = 20) geometry. 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. The canonical baseline generates the seed-42 Gaussian initial field directly on the N = 32 grid. Its central P0 modulation at delay 3 is approximately 1.0941e-5. The corrected baseline path table, control table, baseline CSV files, and baseline figures share the canonical baseline run ID and protocol SHA-256. A separately identified continuum-oriented study uses one shared Hermitian strict-low-k seed reconstructed across N = 24, N = 32, and N = 48 with Courant-matched time steps. The observed central amplitudes are approximately 2.5976e-4, 3.8601e-4, and 4.5175e-4. The N = 32 to N = 48 change is 14.55%, so the tested range does not determine a continuum absolute amplitude. The maximum 0.0230% difference from the first-order variational calculation is an implementation-consistency check between two numerical routes using the same field and metric mapping, not independent physical validation. An isotropic-background control shows angular symmetry to numerical precision and reverse-direction agreement within 0.674%. Nonzero WHM also persists in the tested mu = 1 and no-V' branches as a secondary robustness comparison. The evolution is the previously published Enchan nonlinear scalar-field equation, not a classical fluid free-surface model introduced for this experiment. Its mu = 1, no-V' ablation is damped-wave-like, so residual-wave persistence alone is not claimed as Enchan-specific. The time-rate observable follows from the previously published geometric mapping d tau/dt = exp(-S); no additional frequency-modulation rule is introduced. This is a synthetic numerical study. It does not constitute observational or laboratory confirmation, and no ordinary acoustic coupling to the Enchan field is assumed. The deposit provides the Version 1.1 PDF, README, LICENSE, and a reproducibility archive containing the canonical code, Version 1.1 protocol, separate baseline and continuum run manifests, generated CSV/JSON artifacts, generated figures, and generated manuscript results section.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-04
DOI
https://doi.org/10.5281/zenodo.22304422
Primary Topic
High-pressure geophysics and materials
Type
preprint
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preprint

WHM-3D: A Three-Dimensional Test of Spatially Structured Wave-History Time-Rate Modulation in the Enchan Field

Mitsuhiro Kobayashi
Zenodo (CERN European Organization for Nuclear Research)
High-pressure geophysics and materials
preprint

WHM-3D: A Three-Dimensional Test of Spatially Structured Wave-History Time-Rate Modulation in the Enchan Field

Mitsuhiro Kobayashi
preprint en

Abstract

Version 1.1 correction: Version 1.0 inadvertently combined a native-N=32 baseline result set with a separately generated shared-N=24-seed continuum result set, and some figures used an older probe geometry. Version 1.1 separates these evidence layers, regenerates all tabular and graphical artifacts from provenance-tagged runs, and uses the declared P2 (y = z = 28) and P3 (x = 16, z = 20) geometry. 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. The canonical baseline generates the seed-42 Gaussian initial field directly on the N = 32 grid. Its central P0 modulation at delay 3 is approximately 1.0941e-5. The corrected baseline path table, control table, baseline CSV files, and baseline figures share the canonical baseline run ID and protocol SHA-256. A separately identified continuum-oriented study uses one shared Hermitian strict-low-k seed reconstructed across N = 24, N = 32, and N = 48 with Courant-matched time steps. The observed central amplitudes are approximately 2.5976e-4, 3.8601e-4, and 4.5175e-4. The N = 32 to N = 48 change is 14.55%, so the tested range does not determine a continuum absolute amplitude. The maximum 0.0230% difference from the first-order variational calculation is an implementation-consistency check between two numerical routes using the same field and metric mapping, not independent physical validation. An isotropic-background control shows angular symmetry to numerical precision and reverse-direction agreement within 0.674%. Nonzero WHM also persists in the tested mu = 1 and no-V' branches as a secondary robustness comparison. The evolution is the previously published Enchan nonlinear scalar-field equation, not a classical fluid free-surface model introduced for this experiment. Its mu = 1, no-V' ablation is damped-wave-like, so residual-wave persistence alone is not claimed as Enchan-specific. The time-rate observable follows from the previously published geometric mapping d tau/dt = exp(-S); no additional frequency-modulation rule is introduced. This is a synthetic numerical study. It does not constitute observational or laboratory confirmation, and no ordinary acoustic coupling to the Enchan field is assumed. The deposit provides the Version 1.1 PDF, README, LICENSE, and a reproducibility archive containing the canonical code, Version 1.1 protocol, separate baseline and continuum run manifests, generated CSV/JSON artifacts, generated figures, and generated manuscript results section.

Zenodo (CERN European Organization for Nuclear Research)
École Normale Supérieure Paris-Saclay (FR)
High-pressure geophysics and materials
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