{
  "board": "Shape Packing",
  "blocked": null,
  "scorer_runs": true,
  "setup": "Ran the public scorer without changes at commit 78a78626f098cd236f3a09bb2cb242f72951599d, cloned into .cache/shape-packing-challenge. Installed NumPy 2.5.4 and Shapely 2.2.0 in .cache/venv; SciPy 1.18.1, Numba 0.68.1 and llvmlite 0.50.0 supported the optimizer, and Matplotlib was used for inspection. Initial clone-to-starter-record elapsed 1.336886735757192 minutes (reconstructed from the two task-file timestamps, including source inspection). A timed clean-target reproduction used .cache/repro-scorer and .cache/repro-runtime: 0.1707779485693512 minutes including fresh clone, runtime install from cached wheels, and starter validation; dependency installation alone 0.13389777810079978 minutes. The original loader plus validate_and_score returned VALID and 3.5 for the shipped starter. Reproduction needs only the official scorer, NumPy/Shapely, and the JSON array in entry; the entry has no optimizer dependencies.\nScorer semantics: x, y and theta are rounded to six decimal places BEFORE validation/scoring. Each semicircle is an inscribed polygon with 4096 arc points for overlap testing. A pair is rejected only when polygon intersection AREA is greater than 1e-6; equality is accepted. This is an area tolerance, not a universal allowed penetration distance. Polygon chord sag is about 7.4e-8. MEC sampling uses 128 boundary points per shape, then up to 20 analytic farthest-point refinement rounds with a 1e-12 add-point threshold; Welzl membership epsilon is 1e-10 and final containment tolerance is 1e-9. Extra input digits beyond six have no effect. Radii here retain the original scorer's raw floats, not its six-place CLI display; printed digits are not a proof of geometric optimality.\nAt least 13882 completed candidate-polish attempts were logged across the search families, plus 47400000 logged annealing proposals; these are NOT all independent random starts or all scorer evaluations. Total elapsed work at this report: 90.540 minutes since clone. The fast search used geometric surrogates; each score reported below for a saved strategy candidate was separately checked with the original six-decimal loader semantics and validator. The final entry was reloaded with the original _load_solution and scored again. A second clean clone at the same commit reproduced the identical final score using only its NumPy/Shapely runtime; git diff confirmed the original scorer source was unmodified. Live server scoring was neither requested nor verified. Final maximum polygon pair intersection: 9.99762592269735e-07; maximum containment excess: 4.818367926873179e-13.\nRead the public compusophy optimizer for annealing/archive ideas and a participant write-up for ring-start families; no published packing coordinates were copied. Third place's public submission page explicitly hides its coordinates. The top-eight score cluster alone cannot establish that their arrangements are identical. No submission, signing, credential lookup, or seed fitting was performed. Leading topology remains unfound in this scout; no result was fabricated. Sources and exact quotations are in sources.json.",
  "starter_score": 3.5,
  "best_score": 2.9632137903187097,
  "third_place": 2.948526966725367,
  "gap": "0.014686823593342613 radius units above third place (positive is worse; lower radius wins). This scout did not reach a top-three score.",
  "entry": "[{\"x\":-1.092403,\"y\":-1.631216,\"theta\":3.327617},{\"x\":-0.012439,\"y\":-1.963175,\"theta\":3.828314},{\"x\":-1.81223,\"y\":-0.755006,\"theta\":2.749659},{\"x\":1.037503,\"y\":-1.666672,\"theta\":4.35216},{\"x\":-1.315457,\"y\":-0.446002,\"theta\":0.186017},{\"x\":-1.939091,\"y\":0.306815,\"theta\":2.052057},{\"x\":0.537609,\"y\":-1.19821,\"theta\":1.832973},{\"x\":1.759807,\"y\":-0.870222,\"theta\":4.974575},{\"x\":-0.730972,\"y\":0.415884,\"theta\":0.691819},{\"x\":1.951242,\"y\":0.216468,\"theta\":5.080374},{\"x\":-1.417883,\"y\":1.357871,\"theta\":1.660832},{\"x\":0.318648,\"y\":0.789685,\"theta\":6.16847},{\"x\":1.591524,\"y\":1.149459,\"theta\":5.844962},{\"x\":-0.562159,\"y\":1.881006,\"theta\":0.626433},{\"x\":0.790667,\"y\":1.796956,\"theta\":0.679056}]",
  "entry_sha256": "5c6eb7e32f753cd36e0bc1ef118c2085e4b747e65eaffbf4f96b33dbb0711ec2",
  "tried": [
    "Shipped starter, original scorer VALID radius 3.5.",
    "Threefold/fivefold rotational random starts, reduced-space penalty minimization, then unrestricted separating-line SLSQP: original scorer VALID radius 2.972197304446773.",
    "Reflection random starts with 1, 3 or 5 axis pieces, then unrestricted polish: original scorer VALID radius 3.009795443239462.",
    "Reflection preserved through a separating-line polish before release: original scorer VALID radius 2.9889454684281827.",
    "Fixed-radius overlap minimization and compression/expansion cycles: original scorer VALID radius 2.9721973495156306.",
    "Seven/eight paired-circle constructions with randomized cuts, removing/adding a half-circle, then relaxation: original scorer VALID radius 3.0172329318053706 after multiplying positions by 1.0000003 to survive input rounding.",
    "Analytic intersection-area penalty instead of penetration-depth penalty: original scorer VALID radius 2.972197381674963.",
    "Valid single-piece simulated annealing with adaptive moves and cooling, followed by local polish: original scorer VALID radius 2.9821200957475953.",
    "Joint neighboring-piece rotations/translations during annealing, followed by local polish: original scorer VALID radius 2.963499022119323.",
    "Unrestricted inner/outer ring counts, mixed radial/tangential orientations and soft-to-hard penalties; produced the improved ring basin: original scorer VALID radius 2.9634993046431743.",
    "Mixed left/right portions of two archive packings and relaxed the seam; crossover produced the next improved basin: original scorer VALID radius 2.963499201484037.",
    "Forced outer pieces into a central group of five/six through early optimization, then released all positions: original scorer VALID radius 2.963499136703503.",
    "Permuted inner-piece orientations while holding the outer ring fixed through early optimization, then released the cage: original scorer VALID radius 2.963499265040703.",
    "Shared-layout continuation, random starts, basin hopping, single flat-pair rotations, swaps and inner-piece mutations: original scorer VALID radius 2.9634992497219774.",
    "Tolerance-aware area polish and rigid-transform rounding search on the first strong basin: original scorer VALID radius 2.9719183751803646.",
    "The same tolerance/rounding approach on the improved ring basin: original scorer VALID radius 2.9676861154785494.",
    "Full polygon-overlap tolerance correction and mixed-integer microunit-grid polish on that ring basin: original scorer VALID radius 2.9676830041548317.",
    "BEST: full 4096-point polygon tolerance correction, continuous local polish, and integer six-decimal-grid search on the crossover basin; original scorer VALID radius 2.9632137903187097. No claim of global optimality or recovery of the leaderboard arrangement."
  ],
  "width": "Many seats would help mainly by discovering different contact arrangements. More polishing of this incumbent cannot plausibly close the observed radius gap: it needs another structural improvement. This seat improved the starter substantially but has not demonstrated a top-three route. Successful improvements arrived from ring/basin exploration and archive crossover, while repeated local polish often returned to the same minima.\nFor 100 seats, use 50 independent arrangement explorers split across ring counts, reflected/asymmetric starts and cut changes; 25 crossover/basin-hopping workers with separate diverse archives; 15 annealers with different collective moves and cooling schedules; 5 full-tolerance/grid polishers; and 5 independent original-scorer validators. Exchange complete coordinates and contact-graph fingerprints, not just scores, and preserve distinct basins instead of having every worker clone one incumbent. The leaders' hidden coordinates prevent confirming their topology; the tight score cluster is suggestive, not proof. There is no measured success probability for reaching third place, and allocating 100 identical runs is not justified by this scout.",
  "next": "1. Search for a new contact topology using independent archives and left/right crossover; explicitly vary which pieces occupy the center and preserve diverse higher-radius basins. Require an original-scorer result below 2.949 as a concrete discovery milestone before claiming a podium path.\n2. Once that topology is found, solve its active contacts in double precision, optimize against the actual 4096-point polygon area limit of 1e-6, then optimize rounded x/y/theta on the six-decimal grid. Rotation/translation and integer-grid search matter more than adding ignored decimal digits.\n3. Reload the exact final JSON with the unmodified run.py loader, validate every pair and containment, record the full-precision score and SHA-256, refresh public third place, and hand the entry to the operator for manual submission. The leading arrangement is still missing from this scout; nothing was fabricated or submitted."
}