World Alignment: unpaired cross-modal correspondence by relational identifiability

Method: scene states are sets of part states; relation fields are built
within each modality and are invariant to how each side labels its own
features; the cross-modal bridge is a coupling searched under an energy
that is a closed-form functional of one matrix; solving is spectral
initialisation followed by exact local refinement.

Evidence: in a procedurally generated closed world, blind recovery of a
hidden image-caption correspondence reaches 95.3% at 256 scenes against
0.39% chance, and the recovered pairs transfer to 200 held-out scenes at
93.0% exact retrieval with random-pair and shuffled-image controls at or
near chance. Cross-modal value correspondence is derived from disjoint
corpora rather than declared. On Visual Genome the field correlation
reaches 0.656 against the 0.9 that polynomial recovery needs, with the
deficit attributed away from segmentation and discretisation.

Protocol: no image-text pair enters any objective, optimiser,
initialisation, or model selection; hidden pairs score orderings only.

Co-Authored-By: Claude <noreply@anthropic.com>

1 files changed, 1145 insertions, 0 deletions

diff --git a/artifacts/manifold_gate/vg512_visible_relations_seed0_scalar.json b/artifacts/manifold_gate/vg512_visible_relations_seed0_scalar.json
new file mode 100644
index 0000000..3b62d37
--- /dev/null
+++ b/artifacts/manifold_gate/vg512_visible_relations_seed0_scalar.json
@@ -0,0 +1,1145 @@
+{
+  "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": "visible_relations",
+    "samples": 512,
+    "subset_seed": 0,
+    "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_tiers/text_features_visible_relations.pt",
+    "vg_ground_truth": "artifacts/vg_5k/ground_truth.private.jsonl",
+    "vg_bundle_channels": false,
+    "split": "test",
+    "samples": 512,
+    "subset_seed": 0,
+    "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_visible_relations_seed0_scalar.json",
+    "trajectory_output": null
+  },
+  "channel_names": [
+    "mean"
+  ],
+  "gate_a_global_ranking": {
+    "true": {
+      "mse": 1.4717835012445672,
+      "mse_channels": [
+        1.4717835012445672
+      ],
+      "mse_channel_mean": 1.4717835012445672,
+      "conditional_kl": 5.968007727757813,
+      "m30_total": 4.137168548040697
+    },
+    "similarity_shift": {
+      "mse": 1.7293597443292565,
+      "mse_channels": [
+        1.7293597443292565
+      ],
+      "mse_channel_mean": 1.7293597443292565,
+      "conditional_kl": 6.148225399493324,
+      "m30_total": 4.688364568557178
+    },
+    "random": {
+      "mse": {
+        "mean": 2.0038411617279053,
+        "std": 0.05808873474597931,
+        "min": 1.7806980609893799,
+        "true_z": 9.159394264221191,
+        "true_rank_among_random": 0,
+        "count": 1000
+      },
+      "mse_channel_mean": {
+        "mean": 2.0038411617279053,
+        "std": 0.05808873474597931,
+        "min": 1.7806980609893799,
+        "true_z": 9.159394264221191,
+        "true_rank_among_random": 0,
+        "count": 1000
+      },
+      "conditional_kl": {
+        "mean": 6.156534194946289,
+        "std": 0.00829392485320568,
+        "min": 6.131365776062012,
+        "true_z": 22.730690002441406,
+        "true_rank_among_random": 0,
+        "count": 1000
+      },
+      "m30_total": {
+        "mean": 5.238989353179932,
+        "std": 0.11693011969327927,
+        "min": 4.790948390960693,
+        "true_z": 9.422901153564453,
+        "true_rank_among_random": 0,
+        "count": 1000
+      }
+    }
+  },
+  "gate_b_transpositions": {
+    "pairs": 130816,
+    "improving_pairs": 23412,
+    "improving_fraction": 0.17896893346379647,
+    "delta_mean": 0.002980705542127867,
+    "delta_min": -0.05056307950251094,
+    "identity_is_local_min_mse": false,
+    "worst_improving_swaps": [
+      {
+        "pair": [
+          150,
+          433
+        ],
+        "delta_mse": -0.05056307950251094,
+        "text_cosine": 0.9454795294170473,
+        "visual_cosine": 0.015450217703071843
+      },
+      {
+        "pair": [
+          119,
+          433
+        ],
+        "delta_mse": -0.05054901771345786,
+        "text_cosine": 0.9528133656622267,
+        "visual_cosine": 0.06594341264786825
+      },
+      {
+        "pair": [
+          102,
+          433
+        ],
+        "delta_mse": -0.05053417681193542,
+        "text_cosine": 0.9642451117370466,
+        "visual_cosine": 0.06057722018289307
+      },
+      {
+        "pair": [
+          332,
+          433
+        ],
+        "delta_mse": -0.04561659689666343,
+        "text_cosine": 0.9704587447488836,
+        "visual_cosine": 0.254645657215378
+      },
+      {
+        "pair": [
+          163,
+          433
+        ],
+        "delta_mse": -0.04471826068142126,
+        "text_cosine": 0.9661196382265661,
+        "visual_cosine": 0.08575847621183837
+      },
+      {
+        "pair": [
+          245,
+          433
+        ],
+        "delta_mse": -0.04402158801547627,
+        "text_cosine": 0.963429125301189,
+        "visual_cosine": 0.32392893843045517
+      },
+      {
+        "pair": [
+          50,
+          433
+        ],
+        "delta_mse": -0.043589376231549244,
+        "text_cosine": 0.9688035100438744,
+        "visual_cosine": 0.21323794017292516
+      },
+      {
+        "pair": [
+          392,
+          433
+        ],
+        "delta_mse": -0.04191438919387446,
+        "text_cosine": 0.9603847980862464,
+        "visual_cosine": 0.18498394025619516
+      },
+      {
+        "pair": [
+          225,
+          433
+        ],
+        "delta_mse": -0.040448057381542744,
+        "text_cosine": 0.9603364203411391,
+        "visual_cosine": 0.14080634948066656
+      },
+      {
+        "pair": [
+          187,
+          433
+        ],
+        "delta_mse": -0.04036040340949781,
+        "text_cosine": 0.9565432095417611,
+        "visual_cosine": 0.16897480318538813
+      },
+      {
+        "pair": [
+          412,
+          433
+        ],
+        "delta_mse": -0.03945616752740333,
+        "text_cosine": 0.9533033730298265,
+        "visual_cosine": 0.3143936606273374
+      },
+      {
+        "pair": [
+          212,
+          433
+        ],
+        "delta_mse": -0.039123560794400596,
+        "text_cosine": 0.9608494764367717,
+        "visual_cosine": 0.2842317288233234
+      },
+      {
+        "pair": [
+          433,
+          498
+        ],
+        "delta_mse": -0.0378671378247089,
+        "text_cosine": 0.9687232009357419,
+        "visual_cosine": 0.13798397785505803
+      },
+      {
+        "pair": [
+          433,
+          470
+        ],
+        "delta_mse": -0.03750848088934985,
+        "text_cosine": 0.9597514644692255,
+        "visual_cosine": 0.3018466738128574
+      },
+      {
+        "pair": [
+          180,
+          433
+        ],
+        "delta_mse": -0.03716789084723679,
+        "text_cosine": 0.9476805683213432,
+        "visual_cosine": 0.16397094048305214
+      },
+      {
+        "pair": [
+          31,
+          433
+        ],
+        "delta_mse": -0.036332523870666836,
+        "text_cosine": 0.957539011939088,
+        "visual_cosine": 0.1068629875582747
+      },
+      {
+        "pair": [
+          140,
+          433
+        ],
+        "delta_mse": -0.035355310900221947,
+        "text_cosine": 0.9596050421692573,
+        "visual_cosine": 0.2023845699084794
+      },
+      {
+        "pair": [
+          8,
+          433
+        ],
+        "delta_mse": -0.0351586264958246,
+        "text_cosine": 0.9654667157558119,
+        "visual_cosine": 0.38412422696105014
+      },
+      {
+        "pair": [
+          410,
+          433
+        ],
+        "delta_mse": -0.034387601126457445,
+        "text_cosine": 0.9612785394198398,
+        "visual_cosine": 0.09670278236856066
+      },
+      {
+        "pair": [
+          376,
+          433
+        ],
+        "delta_mse": -0.03414024524304242,
+        "text_cosine": 0.9688445602822803,
+        "visual_cosine": 0.2420523404604336
+      }
+    ]
+  },
+  "derangement_curve": [
+    {
+      "k": 2,
+      "delta_mean": 0.0025993201415985823,
+      "delta_std": 0.0046549285762012005,
+      "improving_fraction": 0.145
+    },
+    {
+      "k": 4,
+      "delta_mean": 0.00649539427831769,
+      "delta_std": 0.008177580311894417,
+      "improving_fraction": 0.16
+    },
+    {
+      "k": 8,
+      "delta_mean": 0.011319151148200035,
+      "delta_std": 0.011565388180315495,
+      "improving_fraction": 0.11
+    },
+    {
+      "k": 16,
+      "delta_mean": 0.02397003583610058,
+      "delta_std": 0.015329316258430481,
+      "improving_fraction": 0.02
+    },
+    {
+      "k": 32,
+      "delta_mean": 0.045578815042972565,
+      "delta_std": 0.02171756885945797,
+      "improving_fraction": 0.0
+    },
+    {
+      "k": 64,
+      "delta_mean": 0.0897127240896225,
+      "delta_std": 0.028539210557937622,
+      "improving_fraction": 0.0
+    },
+    {
+      "k": 128,
+      "delta_mean": 0.1738407015800476,
+      "delta_std": 0.03862808644771576,
+      "improving_fraction": 0.0
+    },
+    {
+      "k": 256,
+      "delta_mean": 0.32519611716270447,
+      "delta_std": 0.05331876128911972,
+      "improving_fraction": 0.0
+    },
+    {
+      "k": 512,
+      "delta_mean": 0.5326806902885437,
+      "delta_std": 0.05615127086639404,
+      "improving_fraction": 0.0
+    }
+  ],
+  "gate_c_descent_from_true": {
+    "start_accuracy": 1.0,
+    "final_accuracy": 0.037109375,
+    "final_objective": 2.2841391441805214,
+    "final_energy": {
+      "mse": 0.5519732376658675,
+      "mse_channels": [
+        0.5519732376658675
+      ],
+      "mse_channel_mean": 0.5519732376658675,
+      "conditional_kl": 5.900963344243933,
+      "m30_total": 2.2841391441805214
+    },
+    "accepted_moves": 673,
+    "moved_fraction": 0.962890625,
+    "mse_local_min_certificate": false,
+    "trajectory": [
+      {
+        "step": 0,
+        "objective": 4.036089902485733,
+        "accuracy": 0.99609375
+      },
+      {
+        "step": 50,
+        "objective": 3.0040949706432825,
+        "accuracy": 0.80078125
+      },
+      {
+        "step": 100,
+        "objective": 2.7449894619442476,
+        "accuracy": 0.611328125
+      },
+      {
+        "step": 150,
+        "objective": 2.5969882990102438,
+        "accuracy": 0.45703125
+      },
+      {
+        "step": 200,
+        "objective": 2.5035933177908194,
+        "accuracy": 0.341796875
+      },
+      {
+        "step": 250,
+        "objective": 2.4428887614170582,
+        "accuracy": 0.27734375
+      },
+      {
+        "step": 300,
+        "objective": 2.4021188415619057,
+        "accuracy": 0.21875
+      },
+      {
+        "step": 350,
+        "objective": 2.3705488268511172,
+        "accuracy": 0.169921875
+      },
+      {
+        "step": 400,
+        "objective": 2.345823514121186,
+        "accuracy": 0.138671875
+      },
+      {
+        "step": 450,
+        "objective": 2.326289215336553,
+        "accuracy": 0.11328125
+      },
+      {
+        "step": 500,
+        "objective": 2.3111323904000294,
+        "accuracy": 0.08203125
+      },
+      {
+        "step": 550,
+        "objective": 2.2993051420283113,
+        "accuracy": 0.064453125
+      },
+      {
+        "step": 600,
+        "objective": 2.291767646258156,
+        "accuracy": 0.046875
+      },
+      {
+        "step": 650,
+        "objective": 2.2867593184699704,
+        "accuracy": 0.041015625
+      }
+    ],
+    "final_permutation": [
+      37,
+      387,
+      278,
+      200,
+      232,
+      179,
+      425,
+      7,
+      157,
+      274,
+      83,
+      209,
+      447,
+      362,
+      18,
+      128,
+      418,
+      131,
+      415,
+      156,
+      52,
+      80,
+      71,
+      509,
+      11,
+      63,
+      350,
+      420,
+      323,
+      451,
+      30,
+      433,
+      269,
+      346,
+      188,
+      267,
+      494,
+      444,
+      134,
+      108,
+      40,
+      508,
+      193,
+      390,
+      44,
+      320,
+      271,
+      176,
+      328,
+      58,
+      480,
+      221,
+      207,
+      261,
+      474,
+      332,
+      5,
+      330,
+      219,
+      338,
+      138,
+      284,
+      381,
+      498,
+      382,
+      427,
+      307,
+      231,
+      23,
+      137,
+      234,
+      8,
+      456,
+      265,
+      436,
+      500,
+      310,
+      303,
+      315,
+      298,
+      345,
+      393,
+      492,
+      15,
+      70,
+      252,
+      172,
+      247,
+      254,
+      289,
+      211,
+      260,
+      123,
+      184,
+      46,
+      402,
+      119,
+      168,
+      454,
+      225,
+      410,
+      503,
+      53,
+      292,
+      49,
+      348,
+      48,
+      107,
+      178,
+      14,
+      136,
+      275,
+      302,
+      371,
+      92,
+      380,
+      311,
+      117,
+      112,
+      133,
+      1,
+      372,
+      60,
+      146,
+      431,
+      141,
+      326,
+      462,
+      214,
+      76,
+      78,
+      227,
+      162,
+      201,
+      411,
+      159,
+      455,
+      174,
+      266,
+      339,
+      139,
+      313,
+      383,
+      115,
+      55,
+      417,
+      322,
+      461,
+      32,
+      259,
+      121,
+      334,
+      106,
+      212,
+      99,
+      103,
+      438,
+      489,
+      0,
+      327,
+      458,
+      161,
+      349,
+      67,
+      319,
+      111,
+      177,
+      440,
+      171,
+      33,
+      77,
+      182,
+      360,
+      386,
+      392,
+      142,
+      19,
+      169,
+      329,
+      90,
+      460,
+      89,
+      305,
+      38,
+      93,
+      452,
+      122,
+      373,
+      394,
+      88,
+      487,
+      25,
+      308,
+      268,
+      194,
+      129,
+      132,
+      406,
+      510,
+      86,
+      95,
+      358,
+      486,
+      28,
+      496,
+      65,
+      409,
+      446,
+      218,
+      283,
+      469,
+      180,
+      75,
+      466,
+      51,
+      317,
+      321,
+      287,
+      256,
+      12,
+      370,
+      43,
+      257,
+      239,
+      314,
+      238,
+      281,
+      437,
+      164,
+      388,
+      365,
+      471,
+      423,
+      477,
+      270,
+      3,
+      312,
+      105,
+      378,
+      243,
+      355,
+      158,
+      96,
+      192,
+      143,
+      223,
+      235,
+      73,
+      430,
+      288,
+      342,
+      419,
+      41,
+      22,
+      343,
+      155,
+      499,
+      220,
+      187,
+      258,
+      363,
+      69,
+      185,
+      130,
+      244,
+      216,
+      391,
+      102,
+      203,
+      150,
+      21,
+      264,
+      470,
+      2,
+      351,
+      464,
+      376,
+      429,
+      435,
+      175,
+      17,
+      357,
+      50,
+      421,
+      97,
+      408,
+      35,
+      9,
+      341,
+      10,
+      389,
+      291,
+      56,
+      479,
+      309,
+      295,
+      81,
+      505,
+      79,
+      208,
+      304,
+      98,
+      400,
+      293,
+      273,
+      213,
+      91,
+      276,
+      186,
+      467,
+      463,
+      149,
+      445,
+      154,
+      369,
+      6,
+      422,
+      395,
+      318,
+      403,
+      506,
+      279,
+      377,
+      127,
+      296,
+      290,
+      147,
+      181,
+      251,
+      413,
+      228,
+      148,
+      24,
+      253,
+      374,
+      263,
+      453,
+      385,
+      493,
+      233,
+      473,
+      4,
+      240,
+      344,
+      475,
+      84,
+      352,
+      347,
+      237,
+      224,
+      331,
+      476,
+      439,
+      222,
+      204,
+      282,
+      490,
+      324,
+      94,
+      66,
+      414,
+      280,
+      379,
+      262,
+      459,
+      356,
+      62,
+      250,
+      173,
+      47,
+      191,
+      118,
+      249,
+      135,
+      457,
+      424,
+      285,
+      366,
+      472,
+      325,
+      337,
+      54,
+      299,
+      167,
+      384,
+      104,
+      368,
+      300,
+      202,
+      34,
+      36,
+      246,
+      511,
+      294,
+      197,
+      16,
+      397,
+      333,
+      478,
+      116,
+      286,
+      126,
+      189,
+      501,
+      85,
+      248,
+      375,
+      407,
+      483,
+      206,
+      57,
+      405,
+      100,
+      64,
+      45,
+      151,
+      359,
+      145,
+      109,
+      255,
+      404,
+      242,
+      399,
+      491,
+      74,
+      432,
+      495,
+      163,
+      82,
+      449,
+      217,
+      210,
+      443,
+      412,
+      434,
+      468,
+      497,
+      401,
+      198,
+      215,
+      297,
+      364,
+      125,
+      68,
+      124,
+      488,
+      354,
+      13,
+      448,
+      229,
+      426,
+      465,
+      31,
+      335,
+      190,
+      416,
+      507,
+      442,
+      26,
+      502,
+      428,
+      152,
+      441,
+      241,
+      316,
+      29,
+      114,
+      101,
+      195,
+      87,
+      361,
+      120,
+      166,
+      165,
+      336,
+      450,
+      110,
+      140,
+      59,
+      272,
+      113,
+      481,
+      306,
+      199,
+      484,
+      61,
+      72,
+      153,
+      170,
+      277,
+      230,
+      398,
+      482,
+      27,
+      205,
+      485,
+      196,
+      340,
+      353,
+      367,
+      226,
+      20,
+      301,
+      42,
+      504,
+      39,
+      396,
+      183,
+      236,
+      144,
+      160,
+      245
+    ]
+  },
+  "gate_c_descent_from_random": [
+    {
+      "start_accuracy": 0.001953125,
+      "final_accuracy": 0.001953125,
+      "final_objective": 2.2986974676937493,
+      "final_energy": {
+        "mse": 0.5572359088601652,
+        "mse_channels": [
+          0.5572359088601652
+        ],
+        "mse_channel_mean": 0.5572359088601652,
+        "conditional_kl": 5.921128249867095,
+        "m30_total": 2.2986974676937493
+      },
+      "accepted_moves": 786,
+      "moved_fraction": 0.994140625,
+      "mse_local_min_certificate": false,
+      "trajectory": [
+        {
+          "step": 0,
+          "objective": 5.197856043548812,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 50,
+          "objective": 3.6246038212854557,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 100,
+          "objective": 3.164414241397255,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 150,
+          "objective": 2.939607618548007,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 200,
+          "objective": 2.7447945813014134,
+          "accuracy": 0.0
+        },
+        {
+          "step": 250,
+          "objective": 2.628339595128332,
+          "accuracy": 0.0
+        },
+        {
+          "step": 300,
+          "objective": 2.547931396314548,
+          "accuracy": 0.0
+        },
+        {
+          "step": 350,
+          "objective": 2.484709691369049,
+          "accuracy": 0.0
+        },
+        {
+          "step": 400,
+          "objective": 2.433397659353605,
+          "accuracy": 0.0
+        },
+        {
+          "step": 450,
+          "objective": 2.394079749167995,
+          "accuracy": 0.0
+        },
+        {
+          "step": 500,
+          "objective": 2.363902156389477,
+          "accuracy": 0.0
+        },
+        {
+          "step": 550,
+          "objective": 2.3413969947514417,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 600,
+          "objective": 2.3259410995794925,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 650,
+          "objective": 2.3160112487522206,
+          "accuracy": 0.001953125
+        },
+        {
+          "step": 700,
+          "objective": 2.308551453476427,
+          "accuracy": 0.0
+        },
+        {
+          "step": 750,
+          "objective": 2.3029278444732855,
+          "accuracy": 0.001953125
+        }
+      ]
+    },
+    {
+      "start_accuracy": 0.0,
+      "final_accuracy": 0.009765625,
+      "final_objective": 2.265278257348334,
+      "final_energy": {
+        "mse": 0.541804771765918,
+        "mse_channels": [
+          0.541804771765918
+        ],
+        "mse_channel_mean": 0.541804771765918,
+        "conditional_kl": 5.908343569082491,
+        "m30_total": 2.265278257348334
+      },
+      "accepted_moves": 779,
+      "moved_fraction": 0.994140625,
+      "mse_local_min_certificate": false,
+      "trajectory": [
+        {
+          "step": 0,
+          "objective": 4.971222264891033,
+          "accuracy": 0.0
+        },
+        {
+          "step": 50,
+          "objective": 3.5705983585083563,
+          "accuracy": 0.0
+        },
+        {
+          "step": 100,
+          "objective": 3.126768088621347,
+          "accuracy": 0.0
+        },
+        {
+          "step": 150,
+          "objective": 2.8637858869772934,
+          "accuracy": 0.0
+        },
+        {
+          "step": 200,
+          "objective": 2.680101845021605,
+          "accuracy": 0.0
+        },
+        {
+          "step": 250,
+          "objective": 2.564101870929306,
+          "accuracy": 0.0
+        },
+        {
+          "step": 300,
+          "objective": 2.484654824680079,
+          "accuracy": 0.0
+        },
+        {
+          "step": 350,
+          "objective": 2.426162852488167,
+          "accuracy": 0.00390625
+        },
+        {
+          "step": 400,
+          "objective": 2.3796121472377463,
+          "accuracy": 0.00390625
+        },
+        {
+          "step": 450,
+          "objective": 2.3465863436089927,
+          "accuracy": 0.00390625
+        },
+        {
+          "step": 500,
+          "objective": 2.3204555586291113,
+          "accuracy": 0.005859375
+        },
+        {
+          "step": 550,
+          "objective": 2.301818044364172,
+          "accuracy": 0.005859375
+        },
+        {
+          "step": 600,
+          "objective": 2.289287216093343,
+          "accuracy": 0.0078125
+        },
+        {
+          "step": 650,
+          "objective": 2.2794507296197324,
+          "accuracy": 0.0078125
+        },
+        {
+          "step": 700,
+          "objective": 2.2726524575546176,
+          "accuracy": 0.009765625
+        },
+        {
+          "step": 750,
+          "objective": 2.267518096700906,
+          "accuracy": 0.009765625
+        }
+      ]
+    }
+  ],
+  "verdict": {
+    "true_m30_total": 4.137168548040697,
+    "identity_is_local_min_mse": false,
+    "descent_from_true_stays": 0.037109375,
+    "on_manifold_counterfeit_found": true,
+    "best_random_descent_m30_total": 2.265278257348334
+  }
+}
\ No newline at end of file