| { | |
| "assessment": "verified", | |
| "claim": 3, | |
| "convex_combinations_checked": 570, | |
| "destructive_control": { | |
| "effect": "the middle atom is never active, so the parameterization is not lean", | |
| "minimum_domination_margin_on_129_points": 0.25, | |
| "mutation": "raise only the y=0 intercept of r(y)=y\u00b2 by 1/2" | |
| }, | |
| "exact_witness_inequalities_checked": 14250, | |
| "finite_Y": [ | |
| "-1", | |
| "-1/2", | |
| "0", | |
| "1/2", | |
| "1" | |
| ], | |
| "kernel": "Phi(x,y)=xy", | |
| "lean_parameterizations": 20, | |
| "literal_claim": "Theorem 4 (Section V.C) proves that the lean subset of finitely \u1ef8-convex functions forms a convex parameter space, which is what allows bilevel objectives to be rewritten as single-level problems solvable with standard first-order optimization (Section I).", | |
| "unordered_pairs": 190, | |
| "witness_identity": "at x=2ay_i+b, line_i-line_j=a(y_i-y_j)^2 >= 0" | |
| } | |