{
  "scope": "T129 fixed-graph accumulation, local-scale controls and response comparisons.\n\nScalar graph potential differences; original graph-model cost Q=||P w||\u00b2.\nNot a direct finite-deformation central-force material or a phase diagram.\n",
  "scaling": [
    {
      "n": 4,
      "nodes": 16,
      "edges": 24,
      "faces": 9,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 0.7905694150420949,
      "coherent_Q": 7.374999999999999,
      "coherent_equal_edge_rms_Q": 11.799999999999997,
      "coherent_equal_edge_rms_face_circulation": 1.2649110640673518,
      "edge_random_Q_mean": 8.984196428571428,
      "edge_random_Q_std": 3.290870541329494,
      "edge_random_expected_Q": 9,
      "face_random_Q_mean": 2.9711607142857144,
      "face_random_Q_std": 0.9383760862253309,
      "face_random_expected_Q": 2.8928571428571423,
      "samples": 200,
      "max_node_imbalance": 9.992007221626409e-16
    },
    {
      "n": 6,
      "nodes": 36,
      "edges": 60,
      "faces": 25,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 1.20761472884912,
      "coherent_Q": 41.67307692307692,
      "coherent_equal_edge_rms_Q": 28.57582417582417,
      "coherent_equal_edge_rms_face_circulation": 0.828078671210825,
      "edge_random_Q_mean": 24.613293512043516,
      "edge_random_Q_std": 4.56047866718059,
      "edge_random_expected_Q": 25,
      "face_random_Q_mean": 9.018114996114996,
      "face_random_Q_std": 2.36910987352179,
      "face_random_expected_Q": 9.123193473193476,
      "samples": 200,
      "max_node_imbalance": 3.9968028886505635e-15
    },
    {
      "n": 8,
      "nodes": 64,
      "edges": 112,
      "faces": 49,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 1.620185174601965,
      "coherent_Q": 136.90073529411765,
      "coherent_equal_edge_rms_Q": 52.15266106442577,
      "coherent_equal_edge_rms_face_circulation": 0.6172133998483676,
      "edge_random_Q_mean": 49.18428990258972,
      "edge_random_Q_std": 7.195308365018387,
      "edge_random_expected_Q": 49,
      "face_random_Q_mean": 19.646059459396998,
      "face_random_Q_std": 4.440437326503153,
      "face_random_expected_Q": 19.472204091778842,
      "samples": 200,
      "max_node_imbalance": 1.3322676295501878e-14
    },
    {
      "n": 12,
      "nodes": 144,
      "edges": 264,
      "faces": 121,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 2.4409697526461347,
      "coherent_Q": 712.5921395110672,
      "coherent_equal_edge_rms_Q": 119.595883554305,
      "coherent_equal_edge_rms_face_circulation": 0.4096732451993514,
      "edge_random_Q_mean": 120.53253790866806,
      "edge_random_Q_std": 10.944651459346005,
      "edge_random_expected_Q": 121,
      "face_random_Q_mean": 54.48858557358104,
      "face_random_Q_std": 11.70760640126115,
      "face_random_expected_Q": 53.927218809687595,
      "samples": 200,
      "max_node_imbalance": 5.706546346573305e-14
    },
    {
      "n": 16,
      "nodes": 256,
      "edges": 480,
      "faces": 225,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 3.2596012026013246,
      "coherent_Q": 2274.279575643469,
      "coherent_equal_edge_rms_Q": 214.04984241350292,
      "coherent_equal_edge_rms_face_circulation": 0.30678599553894814,
      "edge_random_Q_mean": 224.59511786919887,
      "edge_random_Q_std": 15.098905932422142,
      "edge_random_expected_Q": 225,
      "face_random_Q_mean": 108.8013191581229,
      "face_random_Q_std": 23.272740143105977,
      "face_random_expected_Q": 108.38632845706412,
      "samples": 200,
      "max_node_imbalance": 4.845013279464183e-13
    },
    {
      "n": 24,
      "nodes": 576,
      "edges": 1104,
      "faces": 529,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 4.894725051862804,
      "coherent_Q": 11594.551973254871,
      "coherent_equal_edge_rms_Q": 483.94651714455125,
      "coherent_equal_edge_rms_face_circulation": 0.20430156738209967,
      "edge_random_Q_mean": 531.05492849961,
      "edge_random_Q_std": 22.29102150093846,
      "edge_random_expected_Q": 529,
      "face_random_Q_mean": 275.5234602418102,
      "face_random_Q_std": 46.52363221102808,
      "face_random_expected_Q": 282.92255086154665,
      "samples": 200,
      "max_node_imbalance": 2.1467272404152027e-12
    },
    {
      "n": 32,
      "nodes": 1024,
      "edges": 1984,
      "faces": 961,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 6.528782428600298,
      "coherent_Q": 36734.783499454745,
      "coherent_equal_edge_rms_Q": 861.8131026265041,
      "coherent_equal_edge_rms_face_circulation": 0.1531679162134967,
      "edge_random_Q_mean": 967.0181372164175,
      "edge_random_Q_std": 31.200737816359933,
      "edge_random_expected_Q": 961,
      "face_random_Q_mean": 553.064928199852,
      "face_random_Q_std": 97.54822224261761,
      "face_random_expected_Q": 551.5956648822944,
      "samples": 200,
      "max_node_imbalance": 1.2222223233493423e-11
    },
    {
      "n": 48,
      "nodes": 2304,
      "edges": 4512,
      "faces": 2209,
      "coherent_face_circulation_rms": 1.0,
      "coherent_preference_edge_rms": 9.795832447185555,
      "coherent_Q": 186297.44942874063,
      "coherent_equal_edge_rms_Q": 1941.441070903072,
      "coherent_equal_edge_rms_face_circulation": 0.1020842287157852,
      "edge_random_Q_mean": 2207.876610150765,
      "edge_random_Q_std": 47.67245490989001,
      "edge_random_expected_Q": 2209,
      "face_random_Q_mean": 1373.361985917057,
      "face_random_Q_std": 181.31498667021222,
      "face_random_expected_Q": 1393.7758277376743,
      "samples": 200,
      "max_node_imbalance": 4.836664402319002e-11
    }
  ],
  "finite_range_slopes": {
    "coherent_Q": 4.014695705529559,
    "coherent_equal_edge_rms_Q": 2.0101285683021355,
    "edge_random_expected_Q": 2.0944777758466553,
    "face_random_expected_Q": 2.3454459364933222
  },
  "slope_fit_n_min": 12,
  "slope_fit_n_max": 48,
  "disorder_fixed_graph": [
    {
      "gamma": 0.0,
      "samples": 2000,
      "Q_mean": 2274.2795756434684,
      "Q_std": 4.548610803745213e-13,
      "expected_Q": 2274.279575643469,
      "fraction_Q_below_coherent": 0.0,
      "minimum_Q": 2274.279575643469
    },
    {
      "gamma": 0.5,
      "samples": 2000,
      "Q_mean": 2331.6718761544003,
      "Q_std": 48.11795853194155,
      "expected_Q": 2330.529575643469,
      "fraction_Q_below_coherent": 0.112,
      "minimum_Q": 2174.071011601757
    },
    {
      "gamma": 1.0,
      "samples": 2000,
      "Q_mean": 2501.746522788897,
      "Q_std": 97.2604883397691,
      "expected_Q": 2499.279575643469,
      "fraction_Q_below_coherent": 0.0085,
      "minimum_Q": 2177.7604900785655
    },
    {
      "gamma": 2.0,
      "samples": 2000,
      "Q_mean": 3179.9428544285893,
      "Q_std": 202.15871540967083,
      "expected_Q": 3174.279575643469,
      "fraction_Q_below_coherent": 0.0,
      "minimum_Q": 2477.398145743234
    },
    {
      "gamma": 4.0,
      "samples": 2000,
      "Q_mean": 5888.523671190763,
      "Q_std": 459.1406486714436,
      "expected_Q": 5874.279575643469,
      "fraction_Q_below_coherent": 0.0,
      "minimum_Q": 4265.143680761288
    },
    {
      "gamma": 8.0,
      "samples": 2000,
      "Q_mean": 16714.437918646272,
      "Q_std": 1261.560764329107,
      "expected_Q": 16674.279575643468,
      "fraction_Q_below_coherent": 0.0,
      "minimum_Q": 12594.515645552267
    }
  ],
  "local_and_cut_response": {
    "cut_edge": 25,
    "removed_edges": 1,
    "remaining_stiffness_each": 1.0,
    "full_conductance": 1.0909090909090908,
    "cut_conductance": 1.0744383750487672,
    "local_change_max_difference": 1.1546319456101628e-14,
    "cut_shape_after_amplitude_normalization_max_difference": 3.5360603334311236e-14,
    "cases": [
      {
        "kind": "coherent",
        "Q_before": 712.5921395110672,
        "removed_edge_current": -1.7522304634821548,
        "local_preference_change_norm": 0.13992021056020484,
        "local_preference_response_radius90": 1.0,
        "Q_after_cut": 706.3190491369776,
        "Q_release": 6.273090374089634,
        "exact_release": 6.2730903740899135,
        "cut_response_norm": 1.7896309052246189,
        "cut_response_radius90": 2.0
      },
      {
        "kind": "random",
        "Q_before": 117.05302688089334,
        "removed_edge_current": -0.059380808407251795,
        "local_preference_change_norm": 0.1399202105602048,
        "local_preference_response_radius90": 1.0,
        "Q_after_cut": 117.04582258896397,
        "Q_release": 0.007204291929369333,
        "exact_release": 0.007204291929371341,
        "cut_response_norm": 0.060648260669807726,
        "cut_response_radius90": 2.0
      }
    ]
  },
  "structure_without_stress_spanning": {
    "nodes": 10,
    "edges": 11,
    "cycle_rank": 2,
    "structure_spans": true,
    "current_spans": false,
    "Q": 8.0,
    "bridge_current": [
      0.0,
      0.0,
      0.0
    ],
    "before_conductance": 0.23076923076923075,
    "cut_Q": 8.0,
    "cut_conductance": 3.697785493223493e-32,
    "cut_structure_spans": false,
    "thresholds": [
      {
        "threshold": 1e-12,
        "current_spans": false
      },
      {
        "threshold": 1e-10,
        "current_spans": false
      },
      {
        "threshold": 1e-08,
        "current_spans": false
      },
      {
        "threshold": 1e-06,
        "current_spans": false
      }
    ]
  },
  "cost_definition": "Q=sum(i_e^2); original model E=alpha Q-mu N; ideal elastic analogue energy has an additional 1/2",
  "matching_note": "fixed edge RMS and fixed elementary-cycle circulation are different controls; face-sign disorder is an own control, not original model A"
}