| { |
| "status": "PASS", |
| "arithmetic": "Exact fractions.Fraction; no floating point in feasibility or energy checks.", |
| "scope": "Finite reproducibility checks of an analytic universal packing theorem; not a numerical global-optimization claim.", |
| "normalization": "Each cap has mass 1; pair capacity is 1-max(b_ij,b_ji).", |
| "target_squared_flow": "5/9", |
| "owner_tournaments": 64, |
| "rational_profiles_per_tournament": 5, |
| "structured_arrays": 320, |
| "random_rational_arrays": 500, |
| "random_seed": 20261029, |
| "sharp_star_arrays": 1, |
| "total_arrays": 821, |
| "edge_capacity_checks": 9852, |
| "node_capacity_checks": 3284, |
| "weighted_Hall_subset_checks": 22988, |
| "construction_cases": { |
| "balanced_pair_and_third": 146, |
| "complementary_outlier": 350, |
| "source": 325 |
| }, |
| "minimum_squared_flow_observed": "5/9", |
| "sharp_star": { |
| "construction": { |
| "flows": { |
| "0-1": "2/3", |
| "0-2": "1/3", |
| "0-3": "0", |
| "1-2": "0", |
| "1-3": "0", |
| "2-3": "0" |
| }, |
| "owners": { |
| "0-1": 0, |
| "0-2": 0, |
| "0-3": 0, |
| "1-2": 1, |
| "1-3": 3, |
| "2-3": 2 |
| }, |
| "case": "source" |
| }, |
| "squared_flow": "5/9", |
| "feasible_star_polytope_vertices": 10, |
| "exact_maximum_over_star_vertices": "5/9", |
| "upper_bound_reason": "A convex squared norm attains its maximum over this bounded polytope at a vertex; all vertices were enumerated exactly." |
| }, |
| "errors": [], |
| "seconds": 0.159325, |
| "sha256": { |
| "cap_packing.py": "363f9b2c2382774b1173f3dcf0fa5e1fea278d9ca7b7b7b244136b2f8af629dc", |
| "verify_cap_packing.py": "c610a3a31598a08d2393da1dd235323f8ede0847891b316497f7f810e1eccc2a" |
| } |
| } |
|
|
