Boundedness Is Not Stationarity: Proof, Fields, and Reproducibility Archive

This record provides the proof, field data, numerical results, source code, and reproducibility materials supporting the manuscript “Boundedness Is Not Stationarity: Coercive Completion, Degree-Compatible Discretization, and Action-Selection Obstructions in a Rank-Three Tensor–SU(2) Soliton Model.” The archive contains the complete manuscript and bibliography, vector figures, exact algebraic audits, topology-energy validation tables, production and validation scripts, endpoint field arrays for the N = 19, 23, and 27 principal runs, three independent N = 19 seed replications, source-record reports, machine-readable decision tables, cryptographic checksums, and an internal red-team proof and claim audit. The study proves that the original cubic tensor-gradient interaction is unbounded below through a compact, degree-zero ultraviolet bubble. A positive sixth-order completion controls that channel on bounded domains or within fixed compact-support classes, but neither its coefficient nor a unique broader repair operator is selected by the declared symmetries. The archive also implements a normalized tetrahedral discretization in which topological degree and local winding energy are evaluated on the same interpolated field. Multimesh, physical-coordinate, trust-region, wavelength-resolved, same-action coarse-grid, and independent-seed tests preserve bounded degree-one threefold textures while identifying explicit energy-lowering directions at every stored endpoint. The resulting evidence establishes a reproducible finite-dimensional nonstationarity finding for the tested action and discretizations. The archive supports an exact boundedness obstruction, a conditional coercive completion, and a numerical criticality audit. It does not establish a continuum no-critical-point theorem, certify a stable physical soliton, derive a unique stabilizer, or assign any field configuration to a physical particle. The principal reproducibility audit can be run from the reproducibility directory with: python scripts/run_all_checks.py