{
  "protocol": "Assignments permute real frozen text states; hidden pairs are used only to place the true assignment in the ranking. The energy terms are the cross-modal relation MSE and conditional KL; the language-only terms of the falsified free-particle energy are permutation-invariant on this space.",
  "meta": {
    "dataset": "visual_genome_5k",
    "tier": "region_closed",
    "samples": 512,
    "subset_seed": 1,
    "bundle_channels": false
  },
  "args": {
    "dataset": "vg",
    "text_orbits": "artifacts/text_orbits_qwen0p5b.pt",
    "text_mode": "orbit_mean",
    "vg_vision": "artifacts/vg_5k/vision_features.pt",
    "vg_text": "artifacts/vg_5k/text_features.pt",
    "vg_ground_truth": "artifacts/vg_5k/ground_truth.private.jsonl",
    "vg_bundle_channels": false,
    "split": "test",
    "samples": 512,
    "subset_seed": 1,
    "random_perms": 1000,
    "derangement_samples": 200,
    "descent_restarts": 2,
    "descent_max_steps": 200000,
    "descent_objective": "m30_total",
    "descent_verify_top": 64,
    "device": "cpu",
    "seed": 20260729,
    "output": "artifacts/manifold_gate/vg512_region_closed_seed1_scalar.json",
    "trajectory_output": null
  },
  "channel_names": [
    "mean"
  ],
  "gate_a_global_ranking": {
    "true": {
      "mse": 1.6515487328675447,
      "mse_channels": [
        1.6515487328675447
      ],
      "mse_channel_mean": 1.6515487328675447,
      "conditional_kl": 5.9846260976727566,
      "m30_total": 4.5000226852696406
    },
    "similarity_shift": {
      "mse": 1.8542038709707924,
      "mse_channels": [
        1.8542038709707924
      ],
      "mse_channel_mean": 1.8542038709707924,
      "conditional_kl": 6.164616929558872,
      "m30_total": 4.94133112785336
    },
    "random": {
      "mse": {
        "mean": 1.9998544454574585,
        "std": 0.05984543636441231,
        "min": 1.8279703855514526,
        "true_z": 5.820087909698486,
        "true_rank_among_random": 0,
        "count": 1000
      },
      "mse_channel_mean": {
        "mean": 1.9998544454574585,
        "std": 0.05984543636441231,
        "min": 1.8279703855514526,
        "true_z": 5.820087909698486,
        "true_rank_among_random": 0,
        "count": 1000
      },
      "conditional_kl": {
        "mean": 6.160747528076172,
        "std": 0.012881768867373466,
        "min": 6.126026153564453,
        "true_z": 13.672131538391113,
        "true_rank_among_random": 0,
        "count": 1000
      },
      "m30_total": {
        "mean": 5.231857776641846,
        "std": 0.12098576128482819,
        "min": 4.88247013092041,
        "true_z": 6.048933982849121,
        "true_rank_among_random": 0,
        "count": 1000
      }
    }
  },
  "gate_b_transpositions": {
    "pairs": 130816,
    "improving_pairs": 28278,
    "improving_fraction": 0.2161662181996086,
    "delta_mean": 0.0019567591873738766,
    "delta_min": -0.06470630204987719,
    "identity_is_local_min_mse": false,
    "worst_improving_swaps": [
      {
        "pair": [
          205,
          379
        ],
        "delta_mse": -0.06470630204987719,
        "text_cosine": 0.9405932934989035,
        "visual_cosine": 0.014687241765777596
      },
      {
        "pair": [
          66,
          205
        ],
        "delta_mse": -0.06380311620035345,
        "text_cosine": 0.9205223555377072,
        "visual_cosine": -0.007733132388556489
      },
      {
        "pair": [
          154,
          379
        ],
        "delta_mse": -0.06182349409992374,
        "text_cosine": 0.9414433619435776,
        "visual_cosine": 0.12552948276053955
      },
      {
        "pair": [
          46,
          379
        ],
        "delta_mse": -0.06177283147805319,
        "text_cosine": 0.9427488462148406,
        "visual_cosine": 0.06489281786813333
      },
      {
        "pair": [
          336,
          379
        ],
        "delta_mse": -0.06167120887413124,
        "text_cosine": 0.943367530156104,
        "visual_cosine": 0.07655640412195952
      },
      {
        "pair": [
          183,
          379
        ],
        "delta_mse": -0.06145587892424647,
        "text_cosine": 0.9566444897871585,
        "visual_cosine": 0.13577289226153977
      },
      {
        "pair": [
          46,
          66
        ],
        "delta_mse": -0.05867227346487836,
        "text_cosine": 0.9239657279178864,
        "visual_cosine": 0.0324886980169832
      },
      {
        "pair": [
          280,
          379
        ],
        "delta_mse": -0.058060181075123354,
        "text_cosine": 0.9505445577071259,
        "visual_cosine": 0.21448360314604037
      },
      {
        "pair": [
          241,
          379
        ],
        "delta_mse": -0.05803008919328146,
        "text_cosine": 0.9452909962180366,
        "visual_cosine": 0.12875603740925373
      },
      {
        "pair": [
          223,
          379
        ],
        "delta_mse": -0.05783303858366183,
        "text_cosine": 0.9389676382085085,
        "visual_cosine": 0.10803450424988954
      },
      {
        "pair": [
          221,
          379
        ],
        "delta_mse": -0.056933224419541933,
        "text_cosine": 0.9488295099546681,
        "visual_cosine": 0.11118152110541739
      },
      {
        "pair": [
          379,
          425
        ],
        "delta_mse": -0.05656871671106512,
        "text_cosine": 0.9554980502110559,
        "visual_cosine": 0.21514276432413382
      },
      {
        "pair": [
          212,
          379
        ],
        "delta_mse": -0.05527689001850749,
        "text_cosine": 0.956155841947316,
        "visual_cosine": 0.21599569958492532
      },
      {
        "pair": [
          115,
          379
        ],
        "delta_mse": -0.05487197342093929,
        "text_cosine": 0.9475599001382317,
        "visual_cosine": 0.15574988298308967
      },
      {
        "pair": [
          28,
          379
        ],
        "delta_mse": -0.05465015440522952,
        "text_cosine": 0.9413998408735998,
        "visual_cosine": 0.10501731344941531
      },
      {
        "pair": [
          66,
          154
        ],
        "delta_mse": -0.054176873190848136,
        "text_cosine": 0.9321338695145743,
        "visual_cosine": 0.022143230671108707
      },
      {
        "pair": [
          66,
          223
        ],
        "delta_mse": -0.05380270281669261,
        "text_cosine": 0.9240761281581971,
        "visual_cosine": 0.05586222586326198
      },
      {
        "pair": [
          66,
          241
        ],
        "delta_mse": -0.05350183739580523,
        "text_cosine": 0.920607925704046,
        "visual_cosine": 0.03703040569739222
      },
      {
        "pair": [
          153,
          379
        ],
        "delta_mse": -0.05252812104716774,
        "text_cosine": 0.9470905062686079,
        "visual_cosine": 0.21381881477198808
      },
      {
        "pair": [
          162,
          379
        ],
        "delta_mse": -0.05188687825680716,
        "text_cosine": 0.9454407512436758,
        "visual_cosine": 0.09433780902667131
      }
    ]
  },
  "derangement_curve": [
    {
      "k": 2,
      "delta_mean": 0.0019321494037285447,
      "delta_std": 0.004689590539783239,
      "improving_fraction": 0.195
    },
    {
      "k": 4,
      "delta_mean": 0.004396525677293539,
      "delta_std": 0.008218545466661453,
      "improving_fraction": 0.18
    },
    {
      "k": 8,
      "delta_mean": 0.007437502034008503,
      "delta_std": 0.010923884809017181,
      "improving_fraction": 0.16
    },
    {
      "k": 16,
      "delta_mean": 0.015836434438824654,
      "delta_std": 0.01538482028990984,
      "improving_fraction": 0.125
    },
    {
      "k": 32,
      "delta_mean": 0.03078111633658409,
      "delta_std": 0.023188168182969093,
      "improving_fraction": 0.045
    },
    {
      "k": 64,
      "delta_mean": 0.061035942286252975,
      "delta_std": 0.03195176273584366,
      "improving_fraction": 0.01
    },
    {
      "k": 128,
      "delta_mean": 0.1171056255698204,
      "delta_std": 0.04438166692852974,
      "improving_fraction": 0.0
    },
    {
      "k": 256,
      "delta_mean": 0.2154708355665207,
      "delta_std": 0.05587908998131752,
      "improving_fraction": 0.0
    },
    {
      "k": 512,
      "delta_mean": 0.34968018531799316,
      "delta_std": 0.05444056913256645,
      "improving_fraction": 0.0
    }
  ],
  "gate_c_descent_from_true": {
    "start_accuracy": 1.0,
    "final_accuracy": 0.033203125,
    "final_objective": 2.44409510285621,
    "final_energy": {
      "mse": 0.6381732719644498,
      "mse_channels": [
        0.6381732719644498
      ],
      "mse_channel_mean": 0.6381732719644498,
      "conditional_kl": 5.838742794636552,
      "m30_total": 2.44409510285621
    },
    "accepted_moves": 748,
    "moved_fraction": 0.966796875,
    "mse_local_min_certificate": false,
    "trajectory": [
      {
        "step": 0,
        "objective": 4.369927945846397,
        "accuracy": 0.99609375
      },
      {
        "step": 50,
        "objective": 3.1699645346871628,
        "accuracy": 0.802734375
      },
      {
        "step": 100,
        "objective": 2.8872163145203498,
        "accuracy": 0.611328125
      },
      {
        "step": 150,
        "objective": 2.762076906976623,
        "accuracy": 0.4609375
      },
      {
        "step": 200,
        "objective": 2.6859562633549854,
        "accuracy": 0.376953125
      },
      {
        "step": 250,
        "objective": 2.6236145622459714,
        "accuracy": 0.294921875
      },
      {
        "step": 300,
        "objective": 2.57972754515737,
        "accuracy": 0.236328125
      },
      {
        "step": 350,
        "objective": 2.5434692994152774,
        "accuracy": 0.166015625
      },
      {
        "step": 400,
        "objective": 2.515499834659864,
        "accuracy": 0.119140625
      },
      {
        "step": 450,
        "objective": 2.495801289346254,
        "accuracy": 0.09375
      },
      {
        "step": 500,
        "objective": 2.4814460738576205,
        "accuracy": 0.064453125
      },
      {
        "step": 550,
        "objective": 2.4718114748304165,
        "accuracy": 0.0546875
      },
      {
        "step": 600,
        "objective": 2.462072377322613,
        "accuracy": 0.048828125
      },
      {
        "step": 650,
        "objective": 2.4532856167585813,
        "accuracy": 0.04296875
      },
      {
        "step": 700,
        "objective": 2.4473830738839606,
        "accuracy": 0.029296875
      }
    ],
    "final_permutation": [
      249,
      46,
      233,
      209,
      300,
      424,
      313,
      429,
      111,
      318,
      22,
      282,
      55,
      42,
      14,
      27,
      207,
      17,
      422,
      202,
      262,
      303,
      304,
      23,
      29,
      231,
      169,
      306,
      288,
      478,
      71,
      32,
      480,
      52,
      39,
      443,
      228,
      454,
      263,
      31,
      333,
      321,
      150,
      40,
      36,
      16,
      66,
      128,
      200,
      219,
      492,
      240,
      102,
      247,
      138,
      235,
      432,
      351,
      368,
      287,
      175,
      159,
      434,
      179,
      385,
      412,
      314,
      309,
      450,
      310,
      355,
      156,
      185,
      163,
      440,
      264,
      485,
      272,
      302,
      193,
      80,
      506,
      442,
      142,
      469,
      245,
      56,
      199,
      45,
      124,
      204,
      292,
      261,
      494,
      381,
      76,
      96,
      181,
      389,
      250,
      462,
      226,
      97,
      477,
      356,
      151,
      137,
      107,
      448,
      153,
      374,
      186,
      253,
      7,
      365,
      15,
      339,
      132,
      161,
      57,
      289,
      87,
      122,
      444,
      234,
      414,
      446,
      182,
      218,
      93,
      455,
      417,
      420,
      296,
      315,
      347,
      180,
      394,
      140,
      12,
      205,
      468,
      305,
      246,
      223,
      255,
      244,
      489,
      1,
      453,
      217,
      401,
      211,
      327,
      379,
      409,
      491,
      129,
      106,
      268,
      61,
      256,
      236,
      362,
      345,
      403,
      358,
      461,
      90,
      501,
      364,
      68,
      298,
      439,
      173,
      479,
      416,
      308,
      411,
      241,
      118,
      484,
      230,
      297,
      280,
      431,
      94,
      72,
      387,
      239,
      312,
      481,
      131,
      43,
      285,
      380,
      286,
      162,
      294,
      112,
      201,
      421,
      172,
      123,
      210,
      507,
      177,
      99,
      117,
      357,
      397,
      38,
      319,
      109,
      147,
      101,
      238,
      447,
      213,
      405,
      437,
      360,
      376,
      342,
      63,
      470,
      145,
      467,
      74,
      168,
      3,
      203,
      65,
      125,
      354,
      49,
      126,
      348,
      438,
      279,
      410,
      330,
      277,
      299,
      81,
      324,
      48,
      373,
      445,
      472,
      75,
      499,
      252,
      197,
      340,
      451,
      383,
      113,
      260,
      58,
      41,
      413,
      307,
      10,
      464,
      503,
      473,
      334,
      367,
      143,
      407,
      353,
      212,
      498,
      167,
      149,
      488,
      301,
      82,
      316,
      457,
      281,
      344,
      248,
      121,
      115,
      196,
      133,
      190,
      270,
      343,
      8,
      13,
      157,
      105,
      336,
      98,
      426,
      393,
      9,
      4,
      291,
      456,
      490,
      259,
      108,
      26,
      258,
      496,
      283,
      390,
      482,
      332,
      400,
      44,
      341,
      363,
      37,
      338,
      399,
      487,
      146,
      328,
      350,
      227,
      370,
      67,
      320,
      329,
      85,
      396,
      378,
      293,
      418,
      214,
      419,
      152,
      459,
      222,
      78,
      408,
      195,
      136,
      91,
      120,
      266,
      295,
      119,
      510,
      290,
      187,
      369,
      349,
      30,
      194,
      51,
      35,
      184,
      104,
      77,
      441,
      322,
      386,
      34,
      504,
      164,
      254,
      189,
      242,
      19,
      158,
      251,
      372,
      183,
      69,
      28,
      359,
      377,
      174,
      460,
      155,
      430,
      493,
      188,
      323,
      271,
      18,
      335,
      388,
      404,
      366,
      391,
      103,
      130,
      84,
      395,
      371,
      415,
      92,
      11,
      83,
      317,
      47,
      269,
      220,
      392,
      33,
      208,
      62,
      0,
      425,
      509,
      154,
      406,
      433,
      178,
      73,
      192,
      232,
      139,
      224,
      284,
      216,
      474,
      398,
      170,
      311,
      5,
      428,
      267,
      89,
      6,
      352,
      86,
      276,
      325,
      100,
      225,
      511,
      449,
      54,
      141,
      274,
      427,
      166,
      257,
      176,
      135,
      435,
      497,
      375,
      24,
      331,
      114,
      95,
      361,
      64,
      50,
      458,
      278,
      229,
      79,
      215,
      2,
      237,
      144,
      382,
      466,
      486,
      110,
      206,
      116,
      505,
      53,
      337,
      70,
      127,
      384,
      21,
      465,
      452,
      59,
      160,
      60,
      423,
      273,
      148,
      20,
      475,
      346,
      198,
      165,
      402,
      326,
      243,
      191,
      476,
      221,
      436,
      171,
      265,
      502,
      134,
      500,
      483,
      463,
      25,
      495,
      508,
      88,
      471,
      275
    ]
  },
  "gate_c_descent_from_random": [
    {
      "start_accuracy": 0.001953125,
      "final_accuracy": 0.001953125,
      "final_objective": 2.3479748516707404,
      "final_energy": {
        "mse": 0.5904302149564162,
        "mse_channels": [
          0.5904302149564162
        ],
        "mse_channel_mean": 0.5904302149564162,
        "conditional_kl": 5.835572108789539,
        "m30_total": 2.3479748516707404
      },
      "accepted_moves": 810,
      "moved_fraction": 0.9921875,
      "mse_local_min_certificate": false,
      "trajectory": [
        {
          "step": 0,
          "objective": 5.14488708567028,
          "accuracy": 0.001953125
        },
        {
          "step": 50,
          "objective": 3.553393027797632,
          "accuracy": 0.001953125
        },
        {
          "step": 100,
          "objective": 3.116621588543678,
          "accuracy": 0.001953125
        },
        {
          "step": 150,
          "objective": 2.880577415129924,
          "accuracy": 0.001953125
        },
        {
          "step": 200,
          "objective": 2.7160473643810423,
          "accuracy": 0.001953125
        },
        {
          "step": 250,
          "objective": 2.60750162297464,
          "accuracy": 0.001953125
        },
        {
          "step": 300,
          "objective": 2.53645562583565,
          "accuracy": 0.001953125
        },
        {
          "step": 350,
          "objective": 2.486366099883642,
          "accuracy": 0.001953125
        },
        {
          "step": 400,
          "objective": 2.449537778892605,
          "accuracy": 0.001953125
        },
        {
          "step": 450,
          "objective": 2.4226684250942085,
          "accuracy": 0.0
        },
        {
          "step": 500,
          "objective": 2.401752395801379,
          "accuracy": 0.0
        },
        {
          "step": 550,
          "objective": 2.384395702091102,
          "accuracy": 0.0
        },
        {
          "step": 600,
          "objective": 2.3724916253011115,
          "accuracy": 0.0
        },
        {
          "step": 650,
          "objective": 2.362153197846242,
          "accuracy": 0.001953125
        },
        {
          "step": 700,
          "objective": 2.3554742037721557,
          "accuracy": 0.001953125
        },
        {
          "step": 750,
          "objective": 2.351592774443901,
          "accuracy": 0.001953125
        },
        {
          "step": 800,
          "objective": 2.348086888531469,
          "accuracy": 0.001953125
        }
      ]
    },
    {
      "start_accuracy": 0.0,
      "final_accuracy": 0.005859375,
      "final_objective": 2.3746819125340863,
      "final_energy": {
        "mse": 0.6044047390975571,
        "mse_channels": [
          0.6044047390975571
        ],
        "mse_channel_mean": 0.6044047390975571,
        "conditional_kl": 5.829362171694861,
        "m30_total": 2.3746819125340863
      },
      "accepted_moves": 759,
      "moved_fraction": 0.990234375,
      "mse_local_min_certificate": false,
      "trajectory": [
        {
          "step": 0,
          "objective": 5.051127873390432,
          "accuracy": 0.0
        },
        {
          "step": 50,
          "objective": 3.539315315998911,
          "accuracy": 0.0
        },
        {
          "step": 100,
          "objective": 3.1149268659600717,
          "accuracy": 0.001953125
        },
        {
          "step": 150,
          "objective": 2.8914776731537,
          "accuracy": 0.001953125
        },
        {
          "step": 200,
          "objective": 2.738158488888165,
          "accuracy": 0.001953125
        },
        {
          "step": 250,
          "objective": 2.642374740652749,
          "accuracy": 0.005859375
        },
        {
          "step": 300,
          "objective": 2.5722662348244705,
          "accuracy": 0.005859375
        },
        {
          "step": 350,
          "objective": 2.5139342365666906,
          "accuracy": 0.00390625
        },
        {
          "step": 400,
          "objective": 2.47262065414534,
          "accuracy": 0.00390625
        },
        {
          "step": 450,
          "objective": 2.4430651620532586,
          "accuracy": 0.00390625
        },
        {
          "step": 500,
          "objective": 2.4208576671129585,
          "accuracy": 0.00390625
        },
        {
          "step": 550,
          "objective": 2.4044564189635125,
          "accuracy": 0.00390625
        },
        {
          "step": 600,
          "objective": 2.392696456280015,
          "accuracy": 0.00390625
        },
        {
          "step": 650,
          "objective": 2.3842900798271276,
          "accuracy": 0.005859375
        },
        {
          "step": 700,
          "objective": 2.3790345365721377,
          "accuracy": 0.005859375
        },
        {
          "step": 750,
          "objective": 2.3750385127977625,
          "accuracy": 0.005859375
        }
      ]
    }
  ],
  "verdict": {
    "true_m30_total": 4.5000226852696406,
    "identity_is_local_min_mse": false,
    "descent_from_true_stays": 0.033203125,
    "on_manifold_counterfeit_found": true,
    "best_random_descent_m30_total": 2.3479748516707404
  }
}