| _version_ | 1866901120496959488 |
|---|---|
| author | Tanaka, Yasuo |
| author_facet | Tanaka, Yasuo |
| contents | <p>This technical note reinterprets truncation errors and Gibbs phenomena arising in finite Fourier series as <strong>observable boundary fingerprints</strong>, rather than numerical artifacts to be eliminated.<br>By treating the Fourier band limit, the value of π, and spatial sampling as explicitly finite, boundary oscillations are shown to encode structural information about underlying update rules in discrete space-division models.</p> <p>The note defines a minimal set of boundary observables (overshoot amplitude, ringing energy, and effective boundary shift) and proposes an inversion workflow that classifies update-rule families without invoking continuum limits or infinite sums.<br>Residuals, non-convergent behavior, and finite-precision effects are preserved as first-class scientific records.</p> <p>This document is intended as a methodological and archival technical note, compatible with discrete physics, cellular automaton models, numerical simulation diagnostics, and space-division interpretations of physical laws.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18210405 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Boundary Fingerprints as Observables Tanaka, Yasuo Finite Fourier series Gibbs phenomenon Discrete space models Boundary effects Quantization error Update rule inference Space-division model <p>This technical note reinterprets truncation errors and Gibbs phenomena arising in finite Fourier series as <strong>observable boundary fingerprints</strong>, rather than numerical artifacts to be eliminated.<br>By treating the Fourier band limit, the value of π, and spatial sampling as explicitly finite, boundary oscillations are shown to encode structural information about underlying update rules in discrete space-division models.</p> <p>The note defines a minimal set of boundary observables (overshoot amplitude, ringing energy, and effective boundary shift) and proposes an inversion workflow that classifies update-rule families without invoking continuum limits or infinite sums.<br>Residuals, non-convergent behavior, and finite-precision effects are preserved as first-class scientific records.</p> <p>This document is intended as a methodological and archival technical note, compatible with discrete physics, cellular automaton models, numerical simulation diagnostics, and space-division interpretations of physical laws.</p> |
| title | Boundary Fingerprints as Observables |
| topic | Finite Fourier series Gibbs phenomenon Discrete space models Boundary effects Quantization error Update rule inference Space-division model |
| url | https://doi.org/10.5281/zenodo.18210405 |