{
  "note": "任务书 12 第 5.1 节的关键想法清单和死路清单，出处照抄。英文说明给 Jev 看。",
  "key": [
    {
      "id": "K1",
      "name": "联合优化",
      "description": "Optimize the centers and radii of all 26 circles together (78 numbers) with a constrained continuous optimizer such as scipy SLSQP, with constraints that every circle stays inside the square and no two circles overlap.",
      "source": "最大的一跳：OpenEvolve 2.377→2.634；AdaEvolve 2.541→2.610；参考项目 12-real-1、12-real-2 第 1 轮采纳；16-real-1 关掉它少 0.132"
    },
    {
      "id": "K2",
      "name": "扰动重优化",
      "description": "Starting from the current best solution, perturb the circle centers by a moderate amount (about 0.01 to 0.06), run the joint optimization again, and keep the result only if it is better; this includes annealing-style acceptance and larger perturbations after the search stagnates.",
      "source": "AlphaEvolve、ShinkaEvolve、Discovery Loop；参考项目 12-real-2 第 2 轮靠它从 2.6155 到 2.635983，15-tight-2 也到了 2.635983"
    },
    {
      "id": "K3",
      "name": "结构化起点与多起点",
      "description": "Start from structured layouts such as hexagonal or staggered rows, or from many random starting layouts, run the optimization from each start, and keep the best result.",
      "source": "ThetaEvolve、TTT-Discover 只靠\"错排起点 + 一次 SLSQP\"就到 2.635983；CodeEvolve 10 次重启"
    },
    {
      "id": "K4",
      "name": "固定圆心求最优半径",
      "description": "Keep the circle centers fixed and solve a linear program for the radii that maximizes their sum.",
      "source": "ShinkaEvolve 容差 0 那次的第一步、Discovery Loop 的种子；16-real-1 消融撑 28%"
    },
    {
      "id": "K5",
      "name": "严格合法收尾",
      "description": "As a final step, shrink all radii by a tiny amount or refine the solution so that it is strictly valid under zero tolerance.",
      "source": "ShinkaEvolve、ThetaEvolve 严格版；本任务容差为 0（TASK.md）"
    }
  ],
  "deadEnds": [
    {
      "id": "D1",
      "name": "只做几何构造",
      "description": "Place the circle centers by a hand-designed rule (hexagonal grid, square grid, concentric rings) and only tune the arrangement and its parameters, without using continuous optimization to move the centers.",
      "source": "各家卡在 2.2–2.54；等半径六角的上限是 2.438966；OpenEvolve 第一阶段提示词要求只写构造，卡在 2.377；参考项目 9a、9b-real-2 卡在 2.517、2.541"
    },
    {
      "id": "D2",
      "name": "只优化半径",
      "description": "Keep the circle centers fixed and only change how the radii are allocated, as the whole route rather than as a helper step.",
      "source": "上限受布局限制，2.5414 是反复出现的平台"
    }
  ]
}