QDL/QDC Computational Companion II: Weighted-BCC Soliton Engine for Primitive Trefoil Seeds, Same-Sector Competitors, Hopf Diagnostics, Hessian Tests, and Decay Barriers

QDL/QDC Computational Companion II is an open-source Python reference implementation and preregistered numerical workflow for the soliton-analysis phase of the Quantized Dimensional Ledger and Quantized Dimensional Cell research program. The software implements the weighted two-shell body-centered-cubic contact lattice, including exact second- and fourth-contact-moment checks and exact-versus-infrared dispersion tests. It provides M1 density-orientation and M2 phase-extended QDC energy functionals, algebraic T(2,3) trefoil seeds, axial same-sector competitor seeds, constrained L-BFGS relaxation, Coulomb-gauge Hopf-charge diagnostics, regular-preimage extraction, Alexander-polynomial knot classification, matrix-free Hessian tools, and a reference climbing-image nudged elastic band implementation. The archive also contains preregistered parameter grids, seed and acceptance ledgers, production-resolution templates, automated unit tests, an interactive demonstration notebook, complete documentation, machine-readable run manifests, and small-grid smoke-test outputs. Version 1.0.0 is intended to provide transparent, reproducible numerical infrastructure. It does not report a production-scale stable QDC trefoil and does not claim numerical evidence for a physical soliton. The included smoke test verifies the implementation pathways for the lattice, energy functionals, gradients, optimization, topology diagnostics, serialization, and reporting. A physical stability claim would additionally require production-scale convergence, a sufficiently small Euler–Lagrange residual, virial control, integer-stable Hopf charge, robust tre A physical stability claim would additionally require production-scale convergence, a sufficiently small Euler–Lagrange residual, virial control, integerfoil preimage classification, a positive physical Hessian spectrum, and either same-sector energetic ordering or a positive continuum decay barrier. This software continues QDL/QDC Computational Companion I and supports the numerical investigation of toroidal QDC closure modes and the QDC Completion Theorem.