{ "study04": { "study": "04", "results_sha256": "b5730fbb49266def11e9b5bb12d6bb1a8351ee341df018cb0fcb7fbe91b32c81", "frozen_utc": "2026-09-09T21:41:14.517422+00:00", "created_utc": "2026-09-09T21:41:14.968195+00:00", "completed_utc": "2026-09-09T21:41:34.635468+00:00", "case_count": 120, "distinct_input_hashes": 120, "workflow_rows": 360, "eligible_workflow_rows": 300, "unique_candidate_paths": 564, "distinct_candidate_svg_hashes": 551, "strata": [ { "stratum": "expand", "denominator": 20, "initial": 20, "counts": { "restart": 20, "nested-sampling": 20, "witness-refinement": 20 } }, { "stratum": "contract", "denominator": 20, "initial": 1, "counts": { "restart": 1, "nested-sampling": 5, "witness-refinement": 14 } }, { "stratum": "near-margin", "denominator": 20, "initial": 0, "counts": { "restart": 0, "nested-sampling": 4, "witness-refinement": 8 } }, { "stratum": "landmarks", "denominator": 20, "initial": 0, "counts": { "restart": 0, "nested-sampling": 3, "witness-refinement": 8 } }, { "stratum": "unknown", "denominator": 20, "initial": 1, "counts": { "restart": 1, "nested-sampling": 3, "witness-refinement": 9 } } ], "aggregates": { "witness-feasible": { "denominator": 80, "initial_certified": 21, "methods": { "restart": { "certified": 21, "failed": 59, "additional_recoveries": 0, "initial_failure_denominator": 59, "cost_seconds": { "median": 0.04304537599091418, "p90": 0.08997087849129458, "max": 0.10336100097629242 }, "iterations": { "median": 103.5, "p90": 144.0, "max": 195.0 }, "function_evaluations": { "median": 104.0, "p90": 144.10000000000002, "max": 196.0 }, "movement_all_cases": { "median": 25.97266368366924, "p90": 50.26114842339698, "max": 70.93330703534781 }, "final_solver_success": 80, "final_max_errors": { "area_error": 7.65e-11, "centroid_error": 9.61767791711897e-11, "anchor_error": 0.0, "max_slope_jump": 1.291866028708134e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.11844325618219634, "failure_checks": { "minimum_gap": 59 }, "decision_budget_certified": { "0.025": 19, "0.05": 21, "0.1": 21 } }, "nested-sampling": { "certified": 32, "failed": 48, "additional_recoveries": 11, "initial_failure_denominator": 59, "cost_seconds": { "median": 0.038000000480678864, "p90": 0.07552755962242373, "max": 0.0892006259819027 }, "iterations": { "median": 34.0, "p90": 59.10000000000001, "max": 99.0 }, "function_evaluations": { "median": 34.0, "p90": 59.10000000000001, "max": 99.0 }, "movement_all_cases": { "median": 25.972838484660663, "p90": 50.26339810253493, "max": 70.93613882374339 }, "final_solver_success": 80, "final_max_errors": { "area_error": 1.2375e-10, "centroid_error": 7.918775714824621e-13, "anchor_error": 0.0, "max_slope_jump": 1.4102564102564104e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.0061873190401966665, "failure_checks": { "minimum_gap": 48 }, "decision_budget_certified": { "0.025": 20, "0.05": 27, "0.1": 32 } }, "witness-refinement": { "certified": 50, "failed": 30, "additional_recoveries": 29, "initial_failure_denominator": 59, "cost_seconds": { "median": 0.03080195951042697, "p90": 0.05439686707977672, "max": 0.06419174998882227 }, "iterations": { "median": 34.0, "p90": 60.20000000000002, "max": 99.0 }, "function_evaluations": { "median": 34.0, "p90": 60.20000000000002, "max": 99.0 }, "movement_all_cases": { "median": 25.97283065893073, "p90": 50.26340846713875, "max": 70.93613882374339 }, "final_solver_success": 80, "final_max_errors": { "area_error": 7.8e-11, "centroid_error": 9.422626287435654e-13, "anchor_error": 0.0, "max_slope_jump": 1.0833333333333333e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.005789379827119657, "failure_checks": { "minimum_gap": 30 }, "decision_budget_certified": { "0.025": 27, "0.05": 44, "0.1": 50 } } } }, "unknown": { "denominator": 20, "initial_certified": 1, "methods": { "restart": { "certified": 1, "failed": 19, "additional_recoveries": 0, "initial_failure_denominator": 19, "cost_seconds": { "median": 0.04521302100329194, "p90": 0.09420287835819181, "max": 0.1004501249990426 }, "iterations": { "median": 104.0, "p90": 137.4, "max": 174.0 }, "function_evaluations": { "median": 104.5, "p90": 140.3, "max": 176.0 }, "movement_all_cases": { "median": 32.5184583753698, "p90": 65.6518015765434, "max": 80.04044178414902 }, "final_solver_success": 20, "final_max_errors": { "area_error": 5.76e-11, "centroid_error": 8.828506736723353e-11, "anchor_error": 0.0, "max_slope_jump": 1.1290322580645162e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.10855624869890505, "failure_checks": { "minimum_gap": 19 }, "decision_budget_certified": { "0.025": 1, "0.05": 1, "0.1": 1 } }, "nested-sampling": { "certified": 3, "failed": 17, "additional_recoveries": 2, "initial_failure_denominator": 19, "cost_seconds": { "median": 0.04000870902382303, "p90": 0.07469958679866978, "max": 0.08647379200556315 }, "iterations": { "median": 33.0, "p90": 58.20000000000002, "max": 69.0 }, "function_evaluations": { "median": 33.0, "p90": 59.100000000000016, "max": 70.0 }, "movement_all_cases": { "median": 32.51977884546149, "p90": 65.65369082101387, "max": 80.04124996251316 }, "final_solver_success": 20, "final_max_errors": { "area_error": 5.205e-11, "centroid_error": 3.8906346545549946e-13, "anchor_error": 0.0, "max_slope_jump": 1.2857142857142857e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.006741907996414474, "failure_checks": { "minimum_gap": 17 }, "decision_budget_certified": { "0.025": 1, "0.05": 2, "0.1": 3 } }, "witness-refinement": { "certified": 9, "failed": 11, "additional_recoveries": 8, "initial_failure_denominator": 19, "cost_seconds": { "median": 0.03241837500536349, "p90": 0.052565837508882406, "max": 0.06244783298461698 }, "iterations": { "median": 33.5, "p90": 54.300000000000004, "max": 67.0 }, "function_evaluations": { "median": 33.5, "p90": 55.300000000000004, "max": 67.0 }, "movement_all_cases": { "median": 32.51993758585706, "p90": 65.65369615937188, "max": 80.04126590915965 }, "final_solver_success": 20, "final_max_errors": { "area_error": 5.655e-11, "centroid_error": 5.262479768033568e-13, "anchor_error": 0.0, "max_slope_jump": 8.387096774193548e-14, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.00674187349802115, "failure_checks": { "minimum_gap": 11 }, "decision_budget_certified": { "0.025": 2, "0.05": 7, "0.1": 9 } } } }, "eligible": { "denominator": 100, "initial_certified": 22, "methods": { "restart": { "certified": 22, "failed": 78, "additional_recoveries": 0, "initial_failure_denominator": 78, "cost_seconds": { "median": 0.04400510451523587, "p90": 0.09040009101154284, "max": 0.10336100097629242 }, "iterations": { "median": 103.5, "p90": 141.3, "max": 195.0 }, "function_evaluations": { "median": 104.0, "p90": 143.10000000000002, "max": 196.0 }, "movement_all_cases": { "median": 29.533748179287965, "p90": 51.74608043222243, "max": 80.04044178414902 }, "final_solver_success": 100, "final_max_errors": { "area_error": 7.65e-11, "centroid_error": 9.61767791711897e-11, "anchor_error": 0.0, "max_slope_jump": 1.291866028708134e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.11844325618219634, "failure_checks": { "minimum_gap": 78 }, "decision_budget_certified": { "0.025": 20, "0.05": 22, "0.1": 22 } }, "nested-sampling": { "certified": 35, "failed": 65, "additional_recoveries": 13, "initial_failure_denominator": 78, "cost_seconds": { "median": 0.03872635500738397, "p90": 0.07552755962242373, "max": 0.0892006259819027 }, "iterations": { "median": 34.0, "p90": 59.10000000000001, "max": 99.0 }, "function_evaluations": { "median": 34.0, "p90": 59.10000000000001, "max": 99.0 }, "movement_all_cases": { "median": 29.53807139653653, "p90": 51.74950925439465, "max": 80.04124996251316 }, "final_solver_success": 100, "final_max_errors": { "area_error": 1.2375e-10, "centroid_error": 7.918775714824621e-13, "anchor_error": 0.0, "max_slope_jump": 1.4102564102564104e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.006741907996414474, "failure_checks": { "minimum_gap": 65 }, "decision_budget_certified": { "0.025": 21, "0.05": 29, "0.1": 35 } }, "witness-refinement": { "certified": 59, "failed": 41, "additional_recoveries": 37, "initial_failure_denominator": 78, "cost_seconds": { "median": 0.031091520984773524, "p90": 0.05439686707977672, "max": 0.06419174998882227 }, "iterations": { "median": 34.0, "p90": 58.20000000000002, "max": 99.0 }, "function_evaluations": { "median": 34.0, "p90": 58.20000000000002, "max": 99.0 }, "movement_all_cases": { "median": 29.53802654820667, "p90": 51.74952135924917, "max": 80.04126590915965 }, "final_solver_success": 100, "final_max_errors": { "area_error": 7.8e-11, "centroid_error": 9.422626287435654e-13, "anchor_error": 0.0, "max_slope_jump": 1.0833333333333333e-13, "landmark_error": 0.0 }, "worst_gap_shortfall": 0.00674187349802115, "failure_checks": { "minimum_gap": 41 }, "decision_budget_certified": { "0.025": 29, "0.05": 51, "0.1": 59 } } } } }, "paired": [ { "left": "witness-refinement", "right": "nested-sampling", "denominator": 80, "left_only": 18, "right_only": 0, "both": 32, "neither": 30 }, { "left": "witness-refinement", "right": "restart", "denominator": 80, "left_only": 29, "right_only": 0, "both": 21, "neither": 30 }, { "left": "nested-sampling", "right": "restart", "denominator": 80, "left_only": 11, "right_only": 0, "both": 21, "neither": 48 } ], "examples": [ "contract-001", "contract-000" ], "example_selection": "Post-run illustrations: lexicographically first witnessed-feasible case where witness refinement alone beats nested sampling, then first case refinement fails. Not additional trials.", "audit": { "status": "passed", "audited_utc": "2026-09-09T21:43:09.394029+00:00", "results_sha256": "b5730fbb49266def11e9b5bb12d6bb1a8351ee341df018cb0fcb7fbe91b32c81", "freeze_sha256": "6cc1588620d21975e04c84da4b51fcb2c5731b69ad00c90813775702b314ab04", "frozen_files_matched": 732, "distinct_paths_rechecked": 764, "path_kinds": { "input": 120, "witness": 80, "candidate": 564 }, "workflow_rows": 360, "history_entries_including_shared_initials": 764, "exact_candidate_moments_matched": 564, "decisive_disagreements": 0, "completeness_differences_in_candidate_checks": 0, "study": "04", "meaning": "Two implementations replay actual exported bytes; shared SVG XML parsing dependency and common authored assumptions remain. No formal proof or external review." }, "environment": { "python": "3.14.3", "numpy": "2.4.2", "scipy": "1.17.0", "platform": "macOS-26.3-arm64-arm-64bit-Mach-O" }, "deviations": [ "No outcome-based protocol changes. Timing scope clarification: input decoding after preflight, preflight JSON writing and per-step record JSON writing are outside timed decision boundaries; aggregate/report writes also excluded. Times are decision-path measurements, not full process end-to-end latency." ], "limits": [ "Synthetic affine-centerline family; asymmetric gaps and varying widths do not cover arbitrary independently curved boundaries.", "Only two repair rounds and a fixed .001 numerical gap buffer were evaluated; feasible failures do not prove non-convergence.", "Single-host subsecond decision times and post hoc deadline truncations are descriptive.", "The oracle is a separate implementation by the same author, shares Python Fraction/XML dependencies and the declared mathematical model; no formal verification or external review." ] }, "snapshot_scope": "Full records for Studies 01\u201303; Study 04 summary and source manifest. Complete Study 04 records are in validation/output/results.json.", "built_utc": "2026-09-09T21:56:35.045444+00:00", "records": [ { "id": "s1-input", "study": "01", "case": "symmetric-area-50-percent", "method": "input", "role": "input", "status": "violated", "infeasible": false, "area_error": 15000.0, "centroid_error": 0.0, "anchor_error": 0.0, "slope_jump": null, "solver_success": null, "seconds": null, "verification_seconds": null, "path": "output/input.svg", "input_path": "output/input.svg", "request_path": "output/request.json", "verification_path": "output/receipt.json", "code_path": "steer.py", "checker_path": "verifier.py", "preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMjAwIDM0MCA0MDAiIHdpZHRoPSI1MTAiIGhlaWdodD0iNjAwIj4KPHBhdGggZmlsbD0iIzI0NzY4YSIgc3Ryb2tlPSJub25lIiBkPSJNIDAgLTUwIEMgMTAwIC01MCAyMDAgLTUwIDMwMCAtNTAgTCAzMDAgNTAgQyAyMDAgNTAgMTAwIDUwIDAgNTAgWiIvPgo8L3N2Zz4K", "input_preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMjAwIDM0MCA0MDAiIHdpZHRoPSI1MTAiIGhlaWdodD0iNjAwIj4KPHBhdGggZmlsbD0iIzI0NzY4YSIgc3Ryb2tlPSJub25lIiBkPSJNIDAgLTUwIEMgMTAwIC01MCAyMDAgLTUwIDMwMCAtNTAgTCAzMDAgNTAgQyAyMDAgNTAgMTAwIDUwIDAgNTAgWiIvPgo8L3N2Zz4K", "raw": { "request": { "target_area": "45000", "area_tolerance": "0.0000001", "centroid": [ "150", "0" ], "centroid_tolerance": "0", "anchors": [ [ "0", "-50" ], [ "300", "-50" ], [ "300", "50" ], [ "0", "50" ] ], "minimum_half_gap": "5" }, "verification": { "accepted": false, "checks": { "anchors": true, "monotone_graphs_and_vertical_caps": true, "curve_separation": true, "simple_closed_outline": true, "target_area": false, "centroid": true }, "scope": "Exact rational geometry of the supported exported SVG path; not pixels, perception, rights, or arbitrary SVG.", "svg_sha256": "b6e4a45ed8c5414856d01cf454d2535a9f4f3b25b631f1776099eac20b29e66e", "area": "30000", "area_decimal": 30000.0, "area_error": "-15000", "centroid": [ "150", "0" ], "separation_bounds": { "top_negative_y": [ { "interval": [ "0", "1" ], "lower_bound": "50", "depth": 0 } ], "bottom_positive_y": [ { "interval": [ "0", "1" ], "lower_bound": "50", "depth": 0 } ] } }, "operation": { "controller": "symmetric cubic area solve", "inner_control": "100", "export_decimal_places": 12 }, "note": "The input is measured against the edited target. Its rejection is expected. No optimizer timing exists for this algebraic solve; anchor error is derived from exported endpoints." } }, { "id": "s1-target-only", "study": "01", "case": "symmetric-area-50-percent", "method": "target-only", "role": "candidate", "status": "violated", "infeasible": false, "area_error": 0.0, "centroid_error": 0.0, "anchor_error": 25.0, "slope_jump": null, "solver_success": null, "seconds": null, "verification_seconds": null, "path": "output/target-only.svg", "input_path": "output/input.svg", "request_path": "output/request.json", "verification_path": "output/receipt.json", "code_path": "steer.py", "checker_path": "verifier.py", "preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMjAwIDM0MCA0MDAiIHdpZHRoPSI1MTAiIGhlaWdodD0iNjAwIj4KPHBhdGggZmlsbD0iIzI0NzY4YSIgc3Ryb2tlPSJub25lIiBkPSJNIDAgLTc1IEMgMTAwIC03NSAyMDAgLTc1IDMwMCAtNzUgTCAzMDAgNzUgQyAyMDAgNzUgMTAwIDc1IDAgNzUgWiIvPgo8L3N2Zz4K", "input_preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMjAwIDM0MCA0MDAiIHdpZHRoPSI1MTAiIGhlaWdodD0iNjAwIj4KPHBhdGggZmlsbD0iIzI0NzY4YSIgc3Ryb2tlPSJub25lIiBkPSJNIDAgLTUwIEMgMTAwIC01MCAyMDAgLTUwIDMwMCAtNTAgTCAzMDAgNTAgQyAyMDAgNTAgMTAwIDUwIDAgNTAgWiIvPgo8L3N2Zz4K", "raw": { "request": { "target_area": "45000", "area_tolerance": "0.0000001", "centroid": [ "150", "0" ], "centroid_tolerance": "0", "anchors": [ [ "0", "-50" ], [ "300", "-50" ], [ "300", "50" ], [ "0", "50" ] ], "minimum_half_gap": "5" }, "verification": { "accepted": false, "checks": { "anchors": false, "monotone_graphs_and_vertical_caps": true, "curve_separation": true, "simple_closed_outline": true, "target_area": true, "centroid": true }, "scope": "Exact rational geometry of the supported exported SVG path; not pixels, perception, rights, or arbitrary SVG.", "svg_sha256": "97e477e2c57d4c6765dfb7a610caedf89acdeb477d0b1688a41e9cbf25900466", "area": "45000", "area_decimal": 45000.0, "area_error": "0", "centroid": [ "150", "0" ], "separation_bounds": { "top_negative_y": [ { "interval": [ "0", "1" ], "lower_bound": "75", "depth": 0 } ], "bottom_positive_y": [ { "interval": [ "0", "1" ], "lower_bound": "75", "depth": 0 } ] } }, "operation": { "controller": "symmetric cubic area solve", "inner_control": "100", "export_decimal_places": 12 }, "note": "The input is measured against the edited target. Its rejection is expected. No optimizer timing exists for this algebraic solve; anchor error is derived from exported endpoints." } }, { "id": "s1-constrained", "study": "01", "case": "symmetric-area-50-percent", "method": "constrained", "role": "candidate", "status": "certified", "infeasible": false, "area_error": 0.0, "centroid_error": 0.0, "anchor_error": 0.0, "slope_jump": null, "solver_success": null, "seconds": null, "verification_seconds": null, "path": "output/constrained.svg", "input_path": "output/input.svg", "request_path": "output/request.json", "verification_path": "output/receipt.json", "code_path": "steer.py", "checker_path": "verifier.py", "preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMjAwIDM0MCA0MDAiIHdpZHRoPSI1MTAiIGhlaWdodD0iNjAwIj4KPHBhdGggZmlsbD0iIzI0NzY4YSIgc3Ryb2tlPSJub25lIiBkPSJNIDAgLTUwIEMgMTAwIC0xMDAgMjAwIC0xMDAgMzAwIC01MCBMIDMwMCA1MCBDIDIwMCAxMDAgMTAwIDEwMCAwIDUwIFoiLz4KPC9zdmc+Cg==", "input_preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMjAwIDM0MCA0MDAiIHdpZHRoPSI1MTAiIGhlaWdodD0iNjAwIj4KPHBhdGggZmlsbD0iIzI0NzY4YSIgc3Ryb2tlPSJub25lIiBkPSJNIDAgLTUwIEMgMTAwIC01MCAyMDAgLTUwIDMwMCAtNTAgTCAzMDAgNTAgQyAyMDAgNTAgMTAwIDUwIDAgNTAgWiIvPgo8L3N2Zz4K", "raw": { "request": { "target_area": "45000", "area_tolerance": "0.0000001", "centroid": [ "150", "0" ], "centroid_tolerance": "0", "anchors": [ [ "0", "-50" ], [ "300", "-50" ], [ "300", "50" ], [ "0", "50" ] ], "minimum_half_gap": "5" }, "verification": { "accepted": true, "checks": { "anchors": true, "monotone_graphs_and_vertical_caps": true, "curve_separation": true, "simple_closed_outline": true, "target_area": true, "centroid": true }, "scope": "Exact rational geometry of the supported exported SVG path; not pixels, perception, rights, or arbitrary SVG.", "svg_sha256": "1f5d7f908b20186bc5491787c7423c69b28a5bda30120edd697d00f9ac344083", "area": "45000", "area_decimal": 45000.0, "area_error": "0", "centroid": [ "150", "0" ], "separation_bounds": { "top_negative_y": [ { "interval": [ "0", "1" ], "lower_bound": "50", "depth": 0 } ], "bottom_positive_y": [ { "interval": [ "0", "1" ], "lower_bound": "50", "depth": 0 } ] } }, "operation": { "controller": "symmetric cubic area solve", "inner_control": "100", "export_decimal_places": 12 }, "note": "The input is measured against the edited target. Its rejection is expected. No optimizer timing exists for this algebraic solve; anchor error is derived from exported endpoints." } }, { "id": "s2-asymmetric-expand-target-only", "study": "02", "case": "asymmetric-expand", "method": "target-only", "role": "candidate", "status": "violated", "infeasible": false, "area_error": 3.3527475e-05, "centroid_error": 0.2222221993615157, "anchor_error": 12.656250037253, "slope_jump": null, "solver_success": true, "seconds": 0.0026276249845977873, "verification_seconds": 0.0006759999960195273, "path": "benchmark/output/asymmetric-expand/target-only.svg", "input_path": "benchmark/output/asymmetric-expand/input.svg", "request_path": "benchmark/output/asymmetric-expand/request.json", "verification_path": "benchmark/output/asymmetric-expand/target-only.verification.json", "code_path": "benchmark/producer.py", "checker_path": "benchmark/checker.py", "preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMTIyLjY1NjI1MDAzNzI1MyAzNDAgMjYwLjMxMjQ5OTk4MTM3NCIgd2lkdGg9IjYwMCIgaGVpZ2h0PSI0MDAiPjxwYXRoIGZpbGw9IiMyNDc2OGEiIHN0cm9rZT0ibm9uZSIgZD0iTSAwIC01Mi42NTYyNTAwMzcyNTMgQyAxMDAgLTkyLjY1NjI1MDAzNzI1MyAyMDAgLTM3LjY1NjI1MDAzNzI1MyAzMDAgLTY3LjY1NjI1MDAzNzI1MyBMIDMwMCA0Ny42NTYyNDk5NDQxMjEgQyAyMDAgMTA3LjY1NjI0OTk0NDEyMSAxMDAgMzcuNjU2MjQ5NTcxNTkyIDAgNjIuNjU2MjQ5OTQ0MTIxIFoiLz48L3N2Zz4K", "input_preview": "data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9Ii0yMCAtMTEwIDM0MCAyMzUiIHdpZHRoPSI2MDAiIGhlaWdodD0iNDAwIj48cGF0aCBmaWxsPSIjMjQ3NjhhIiBzdHJva2U9Im5vbmUiIGQ9Ik0gMCAtNDAgQyAxMDAgLTgwIDIwMCAtMjUgMzAwIC01NSBMIDMwMCAzNSBDIDIwMCA5NSAxMDAgMjUgMCA1MCBaIi8+PC9zdmc+Cg==", "raw": { "case": "asymmetric-expand", "category": "ordinary", "method": "target-only", "width": 300, "input_y": [ -40, -80, -25, -55, 50, 25, 95, 35 ], "output_y_before_serialization": [ -52.6562500372529, -92.6562500372529, -37.6562500372529, -67.6562500372529, 62.656249944120646, 37.656249571591616, 107.65624994412065, 47.656249944120646 ], "request": { "target_area": "151875/4", "area_tolerance": ".001", "centroid": [ "1360/9", "47/63" ], "centroid_tolerance": ".001", "anchors": [ [ "0", "-40" ], [ "300", "-55" ], [ "300", "35" ], [ "0", "50" ] ], "anchor_tolerance": ".001", "minimum_gap": "10", "y_control_bounds": [ "-280", "295" ] }, "solver": { "attempts": [ { "success": true, "message": "Optimization terminated successfully", "iterations": 2, "objective": 1.601806626605438e-08, "normalized_full_request_residual": 0.12656250037252903, "seconds": 0.0015694579924456775 }, { "success": true, "message": "Optimization terminated successfully", "iterations": 1, "objective": 1.9548431398022167e-08, "normalized_full_request_residual": 0.13936507936507936, "seconds": 0.0004336660203989595 }, { "success": true, "message": "Optimization terminated successfully", "iterations": 2, "objective": 3.35611888312944e-08, "normalized_full_request_residual": 0.2002098885140059, "seconds": 0.0006126249791122973 } ], "selected_attempt": 0, "solver_success": true, "seconds": 0.0026276249845977873 }, "verification": { "accepted": false, "status": "violated", "checks": { "anchors": "violated", "minimum_gap": "certified", "positive_graph_order": "certified", "simple_closed_outline": "certified", "control_bounds": "certified", "target_area": "certified", "centroid": "violated" }, "scope": "Exported path geometry only; no pixel, perceptual, authorship or rights claim.", "svg_sha256": "beaaf9e8eeb74e6703a6f44c07669e635c896cd35f155928cf90afa46b01a867", "gap_proof": { "status": "certified", "floor": "10", "strict": false, "max_depth": 12, "witness": null, "leaves": [ { "interval": [ "0", "1" ], "lower_bound": "57656249990687/500000000000", "depth": 0 } ], "unresolved": [] }, "topology_proof": { "status": "certified", "floor": "0", "strict": true, "max_depth": 12, "witness": null, "leaves": [ { "interval": [ "0", "1" ], "lower_bound": "57656249990687/500000000000", "depth": 0 } ], "unresolved": [] }, "area": "1518749998658901/40000000000", "centroid": [ "25462499981373640/168749999850989", "4263280696523551237974559657/5906249994784615000000000000" ], "area_error": 3.3527475e-05, "centroid_error": 0.2222221993615157, "anchor_error": 12.656250037253, "measurement_interpretation": "Region moments" }, "verification_seconds": 0.0006759999960195273, "input_sha256": "24680424810bf1b8032d9d2dd2e399e21c4bb04efd96175be4dbbd6ab116f043", "request_sha256": "00d7e4b55a4f113b31bd0207ba5395eacdce9a0e7170d7966540369cc850d211", "source_accounting": "Synthetic fixture plus declared operation; no training attribution or authorship inference", "feasibility": { "width_lower_bound": "149999/500", "endpoint_gap_sum_lower_bound": "44999/250", "gap_area_lower_bound": "149999/50", "anchor_midpoint_area_lower_bound": "2749931667/250000", "proven_infeasible": false, "assumptions": "Shared linear x; four anchors within stated maximum-norm tolerance; gap >= declared floor everywhere. 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