Phantom-Net Technical Appendix V1.3 – Dimensionally Consistent Edition

Abstract: This technical appendix defines the computational, numerical, and analytical procedures for implementing and validating the Phantom-Net (PN) unified physics model. It specifies spectral discretization, symplectic temporal integration, and conservation-preserving algorithms for solving the PN master equation. The implementation achieves second-order convergence (p ≈ 2.0), energy conservation (ΔE/E₀ < 10⁻⁸), and numerical stability across 10⁶ time steps. All codes, parameter sets, and validation protocols are openly archived with cross-referenced DOIs to ensure full reproducibility and transparent verification of PN predictions.Description: Version 1.3 introduces full dimensional consistency with Formula Table V1.9, expanded energy and momentum diagnostics, and an automated unit verification system. It includes comprehensive tables for parameter normalization, conservation metrics, and cross-document linkage to the Formula Table and Validation Testplan. The appendix serves as a computational blueprint for numerical realizations of the Phantom-Net framework, ensuring scientific traceability and open reproducibility within the Phantom-Net Research Community.