article · Zenodo (CERN European Organization for Nuclear Research) · 2025

Numerical Framework and Code Architecture

Stanford, Paul Vincent Raymond

Cited by 0Open access

Abstract

This paper presents the computational and analytical realization of the Sc-Rubs persistence field and examines how threshold resonance governs field coherence and pattern stabilization. Using both symbolic and numerical evaluation, it reconstructs the recursive Laplacian field φ = PF τ(r) and verifies the Law of Persistence through iterative solution of ∇·(|∇φ|^{p−2} ∇φ) − β Δ²φ + ∂Vα/∂φ = 0. Results demonstrate that stable geometric persistence emerges when the activation threshold α ≈ 0.3 is crossed, producing resonance lock between curvature and diffusion modes. The simulations confirm that roughly 70 % of the system’s residual energy forms the root-mean-square equilibrium value, matching analytical expectations from earlier papers. This state defines the coherence plateau — a regime where form, energy, and recursion achieve dynamic stability. Computational modules written in Python reproduce the octahedral–spherical–cubic transitions under controlled parameter sweeps (β ≈ 24, 10 ≤ λ ≤ 80), demonstrating convergence toward scalar-field persistence. These results validate the complete Sc-Rubs framework as a unified scalar-field model of self-organization and geometric emergence. This paper concludes the Sc-Rubs Modelling Series prior to the unified mathematical statement (Paper 8: Unified Scalar-Field Description).For figures, code fragments, and supporting data, visit https://sc-rubs.cloud.Related DOI: 10.5281/zenodo.17443937.

Cite this paper

APA 7

Stanford, P. V. R. (2025). Numerical Framework and Code Architecture. Zenodo (CERN European Organization for Nuclear Research). https://doi.org/10.5281/zenodo.17448055

MLA 9

Stanford, Paul Vincent Raymond. “Numerical Framework and Code Architecture.” Zenodo (CERN European Organization for Nuclear Research), 2025, https://doi.org/10.5281/zenodo.17448055.

Chicago

Stanford, Paul Vincent Raymond. 2025. “Numerical Framework and Code Architecture.” Zenodo (CERN European Organization for Nuclear Research). https://doi.org/10.5281/zenodo.17448055.

Harvard

Stanford, P.V.R. (2025) ‘Numerical Framework and Code Architecture’, Zenodo (CERN European Organization for Nuclear Research). Available at: https://doi.org/10.5281/zenodo.17448055.

BibTeX

@article{stanford2025numerical,
  title = {{Numerical Framework and Code Architecture}},
  author = {Stanford, Paul Vincent Raymond},
  journal = {Zenodo (CERN European Organization for Nuclear Research)},
  year = {2025},
  doi = {10.5281/zenodo.17448055}
}

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