{
  "boundary": "selectors expose immutable posterior-only selected-equilibrium outputs; signal-ownership-aware equilibria and centralized role allocation are separate",
  "claim_ids": [
    "DD-C-0104",
    "DD-C-0105",
    "DD-C-0106",
    "DD-C-0107",
    "DD-C-0108",
    "DD-C-0109",
    "DD-C-0110"
  ],
  "rows": [
    {
      "accuracy": "1/2",
      "checks": {
        "centralized_bound": true,
        "metric_bounds": true,
        "payoff_budget_private": true,
        "payoff_budget_shared": true,
        "private_metric_agreement": true,
        "private_selection_agreement": true,
        "shared_metric_agreement": true
      },
      "dependence": "0",
      "dependence_index": "0",
      "direct_private_metrics": {
        "average_action_quality": "1/2",
        "centralized_top_two": "1",
        "collision": "1/2",
        "discovery": "3/4",
        "diversity": "1/2",
        "expected_distinct_actions": "3/2",
        "implementation_gap": "1/4",
        "payoff_per_agent": "3/8"
      },
      "gain_class": "neutral",
      "private_correspondence": {
        "best_pure_discovery": "1",
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          {
            "average_action_quality": "1/2",
            "collision": "0",
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            "diversity": "1",
            "payoff_first": "1/2",
            "payoff_second": "1/2",
            "strategies": [
              "constant-0",
              "constant-1"
            ]
          },
          {
            "average_action_quality": "1/2",
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            "payoff_first": "3/8",
            "payoff_second": "3/8",
            "strategies": [
              "oppose",
              "oppose"
            ]
          },
          {
            "average_action_quality": "1/2",
            "collision": "1/2",
            "discovery": "3/4",
            "diversity": "1/2",
            "payoff_first": "3/8",
            "payoff_second": "3/8",
            "strategies": [
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              "follow"
            ]
          },
          {
            "average_action_quality": "1/2",
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            "diversity": "1/2",
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            "payoff_second": "3/8",
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              "follow",
              "oppose"
            ]
          },
          {
            "average_action_quality": "1/2",
            "collision": "1/2",
            "discovery": "3/4",
            "diversity": "1/2",
            "payoff_first": "3/8",
            "payoff_second": "3/8",
            "strategies": [
              "follow",
              "follow"
            ]
          },
          {
            "average_action_quality": "1/2",
            "collision": "0",
            "discovery": "1",
            "diversity": "1",
            "payoff_first": "1/2",
            "payoff_second": "1/2",
            "strategies": [
              "constant-1",
              "constant-0"
            ]
          }
        ],
        "equilibrium_count": 6,
        "worst_pure_discovery": "3/4"
      },
      "private_metrics": {
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        "discovery": "3/4",
        "diversity": "1/2",
        "expected_distinct_actions": "3/2",
        "implementation_gap": "1/4",
        "payoff_per_agent": "3/8"
      },
      "private_selection": {
        "follow_probability": "1/2",
        "regime": "degenerate-continuum-selected-half",
        "unique_in_symmetric_class": false
      },
      "selected_sharing_gain": "0",
      "shared_metrics": {
        "average_action_quality": "1/2",
        "centralized_top_two": "1",
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        "discovery": "3/4",
        "diversity": "1/2",
        "expected_distinct_actions": "3/2",
        "implementation_gap": "1/4",
        "payoff_per_agent": "3/8"
      },
      "shared_pure_correspondence": {
        "best_pure_discovery": "1",
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        "states": [
          {
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            ],
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              [
                0,
                1
              ],
              [
                1,
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              ]
            ],
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              "1/2",
              "1/2"
            ],
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              0,
              0
            ]
          },
          {
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              "1",
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            ],
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              [
                0,
                1
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                1,
                0
              ]
            ],
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              "1/2",
              "1/2"
            ],
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              0,
              1
            ]
          },
          {
            "discoveries": [
              "1",
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            ],
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              [
                0,
                1
              ],
              [
                1,
                0
              ]
            ],
            "on_path": true,
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              "1/2",
              "1/2"
            ],
            "probability": "1/4",
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              1,
              0
            ]
          },
          {
            "discoveries": [
              "1",
              "1"
            ],
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              [
                0,
                1
              ],
              [
                1,
                0
              ]
            ],
            "on_path": true,
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              "1/2",
              "1/2"
            ],
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            "signals": [
              1,
              1
            ]
          }
        ],
        "worst_pure_discovery": "1"
      },
      "shared_selection": {
        "agreement_action_probability": "1/2",
        "agreement_posterior": "1/2",
        "agreement_regime": "interior-anti-crowding",
        "disagreement_action_probability": "1/2",
        "disagreement_posterior": "1/2"
      }
    },
    {
      "accuracy": "1/2",
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        "payoff_budget_private": true,
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        "private_selection_agreement": true,
        "shared_metric_agreement": true
      },
      "dependence": "1/6",
      "dependence_index": "1/6",
      "direct_private_metrics": {
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        "centralized_top_two": "1",
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        "discovery": "17/24",
        "diversity": "5/12",
        "expected_distinct_actions": "17/12",
        "implementation_gap": "7/24",
        "payoff_per_agent": "17/48"
      },
      "gain_class": "neutral",
      "private_correspondence": {
        "best_pure_discovery": "1",
        "equilibria": [
          {
            "average_action_quality": "1/2",
            "collision": "0",
            "discovery": "1",
            "diversity": "1",
            "payoff_first": "1/2",
            "payoff_second": "1/2",
            "strategies": [
              "constant-0",
              "constant-1"
            ]
          },
          {
            "average_action_quality": "1/2",
            "collision": "5/12",
            "discovery": "19/24",
            "diversity": "7/12",
            "payoff_first": "19/48",
            "payoff_second": "19/48",
            "strategies": [
              "oppose",
              "follow"
            ]
          },
          {
            "average_action_quality": "1/2",
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            "discovery": "19/24",
            "diversity": "7/12",
            "payoff_first": "19/48",
            "payoff_second": "19/48",
            "strategies": [
              "follow",
              "oppose"
            ]
          },
          {
            "average_action_quality": "1/2",
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            "diversity": "1",
            "payoff_first": "1/2",
            "payoff_second": "1/2",
            "strategies": [
              "constant-1",
              "constant-0"
            ]
          }
        ],
        "equilibrium_count": 4,
        "worst_pure_discovery": "19/24"
      },
      "private_metrics": {
        "average_action_quality": "1/2",
        "centralized_top_two": "1",
        "collision": "1/2",
        "discovery": "3/4",
        "diversity": "1/2",
        "expected_distinct_actions": "3/2",
        "implementation_gap": "1/4",
        "payoff_per_agent": "3/8"
      },
      "private_selection": {
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        "regime": "interior-anti-crowding",
        "unique_in_symmetric_class": true
      },
      "selected_sharing_gain": "0",
      "shared_metrics": {
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        "expected_distinct_actions": "3/2",
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        "payoff_per_agent": "3/8"
      },
      "shared_pure_correspondence": {
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          {
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            ],
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              [
                0,
                1
              ],
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                1,
                0
              ]
            ],
            "on_path": true,
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              "1/2",
              "1/2"
            ],
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              0,
              0
            ]
          },
          {
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                0,
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              ],
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                1,
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              ]
            ],
            "on_path": true,
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              "1/2",
              "1/2"
            ],
            "probability": "5/24",
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              0,
              1
            ]
          },
          {
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            ],
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            ],
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              "1/2"
            ],
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              1,
              0
            ]
          },
          {
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            ],
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                0,
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                1,
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            ],
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              "1/2"
            ],
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              1,
              1
            ]
          }
        ],
        "worst_pure_discovery": "1"
      },
      "shared_selection": {
        "agreement_action_probability": "1/2",
        "agreement_posterior": "1/2",
        "agreement_regime": "interior-anti-crowding",
        "disagreement_action_probability": "1/2",
        "disagreement_posterior": "1/2"
      }
    },
    {
      "accuracy": "1/2",
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        "metric_bounds": true,
        "payoff_budget_private": true,
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        "private_metric_agreement": true,
        "private_selection_agreement": true,
        "shared_metric_agreement": true
      },
      "dependence": "1/4",
      "dependence_index": "1/4",
      "direct_private_metrics": {
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        "centralized_top_two": "1",
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        "discovery": "11/16",
        "diversity": "3/8",
        "expected_distinct_actions": "11/8",
        "implementation_gap": "5/16",
        "payoff_per_agent": "11/32"
      },
      "gain_class": "neutral",
      "private_correspondence": {
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        "equilibria": [
          {
            "average_action_quality": "1/2",
            "collision": "0",
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            "payoff_first": "1/2",
            "payoff_second": "1/2",
            "strategies": [
              "constant-0",
              "constant-1"
            ]
          },
          {
            "average_action_quality": "1/2",
            "collision": "3/8",
            "discovery": "13/16",
            "diversity": "5/8",
            "payoff_first": "13/32",
            "payoff_second": "13/32",
            "strategies": [
              "oppose",
              "follow"
            ]
          },
          {
            "average_action_quality": "1/2",
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            "payoff_first": "13/32",
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            "strategies": [
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            ]
          },
          {
            "average_action_quality": "1/2",
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          }
        ],
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      },
      "private_metrics": {
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      },
      "private_selection": {
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      },
      "selected_sharing_gain": "0",
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      },
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          {
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                0,
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              ],
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                1,
                0
              ]
            ],
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              "1/2"
            ],
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              0,
              0
            ]
          },
          {
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            ],
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                0,
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                1,
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              ]
            ],
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              "1/2"
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          },
          {
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            ],
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              "1/2"
            ],
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          },
          {
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                0,
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            ],
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              "1/2"
            ],
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              1,
              1
            ]
          }
        ],
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      },
      "shared_selection": {
        "agreement_action_probability": "1/2",
        "agreement_posterior": "1/2",
        "agreement_regime": "interior-anti-crowding",
        "disagreement_action_probability": "1/2",
        "disagreement_posterior": "1/2"
      }
    },
    {
      "accuracy": "1/2",
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        "shared_metric_agreement": true
      },
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        "expected_distinct_actions": "5/4",
        "implementation_gap": "3/8",
        "payoff_per_agent": "5/16"
      },
      "gain_class": "neutral",
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          {
            "average_action_quality": "1/2",
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            "payoff_first": "1/2",
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            "strategies": [
              "constant-0",
              "constant-1"
            ]
          },
          {
            "average_action_quality": "1/2",
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            ]
          },
          {
            "average_action_quality": "1/2",
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          },
          {
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            ]
          }
        ],
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      },
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        "payoff_per_agent": "3/8"
      },
      "private_selection": {
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        "regime": "interior-anti-crowding",
        "unique_in_symmetric_class": true
      },
      "selected_sharing_gain": "0",
      "shared_metrics": {
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        "payoff_per_agent": "3/8"
      },
      "shared_pure_correspondence": {
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            ],
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              "1/2"
            ],
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            ]
          },
          {
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            ],
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              "1/2"
            ],
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          },
          {
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            ],
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              "1/2"
            ],
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              1,
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            ]
          },
          {
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              ]
            ],
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              "1/2"
            ],
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              1,
              1
            ]
          }
        ],
        "worst_pure_discovery": "1"
      },
      "shared_selection": {
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        "agreement_posterior": "1/2",
        "agreement_regime": "interior-anti-crowding",
        "disagreement_action_probability": "1/2",
        "disagreement_posterior": "1/2"
      }
    },
    {
      "accuracy": "1/2",
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        "payoff_budget_shared": true,
        "private_metric_agreement": true,
        "private_selection_agreement": true,
        "shared_metric_agreement": true
      },
      "dependence": "7/12",
      "dependence_index": "7/12",
      "direct_private_metrics": {
        "average_action_quality": "1/2",
        "centralized_top_two": "1",
        "collision": "19/24",
        "discovery": "29/48",
        "diversity": "5/24",
        "expected_distinct_actions": "29/24",
        "implementation_gap": "19/48",
        "payoff_per_agent": "29/96"
      },
      "gain_class": "neutral",
      "private_correspondence": {
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        "equilibria": [
          {
            "average_action_quality": "1/2",
            "collision": "0",
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