Reproducibility materials for "Sharp dimension bounds for commutator-constrained finite-time Gramians"

Reproducibility materials accompanying the manuscript “Sharp dimension bounds for commutator-constrained finite-time Gramians”. This record contains Python source code, exact symbolic verification outputs, high-precision numerical CSV/JSON tables, environment metadata, and the code and vector PDF outputs used to generate the manuscript figures. The scripts check the four-state and six-state calculations, path commutator identities, independent Frechet-derivative/kernel identities, and finite-budget convergence of the asymptotic coefficients. Numerical full-Gramian evaluations use 85 decimal digits. No experimental or observational data are used. The analytic proofs are contained in the manuscript; these computations are provided to verify formulas and illustrate asymptotics and are not a substitute for the proofs.