| { |
| "status": "PASS", |
| "model": "Retain boundary(rD); add a finite segment network; connected union; convex hull encloses (r+delta)D.", |
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| "proof_file": "tmp/sharp_augmentation_proof.tex" |
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| ], |
| "limitations": [ |
| "The proof is analytic; these double-precision diagnostics do not certify universal optimization over networks.", |
| "The scalar maximization is reduced analytically, but its reported numerical value is not interval certified.", |
| "Integer optimality refers only to equally spaced radial-arm constructions.", |
| "The old circle is retained. Replacement of a component is a different problem; no obstruction to a linear replacement rate is established.", |
| "This is not a solution of the unrestricted shortest opaque barrier problem." |
| ], |
| "elapsed_seconds": 1.6742134209998767 |
| } |
|
|
