{
  "E0_exact_SRSD": {
    "failures": 0,
    "interpretation": "Exact encode/decode is lossless; representation alone cannot correct or create drift.",
    "trials": 10000
  },
  "E1_matched_omega_spiral": {
    "checkpoints": [
      {
        "direct_anchor_float32_mean_norm_error": 2.7008580404282168e-08,
        "direct_anchor_float32_mean_state_error": 4.670512532657806e-08,
        "iterative_float32_mean_norm_error": 2.7008580404282168e-08,
        "iterative_float32_mean_state_error": 4.670512532657806e-08,
        "steps": 1
      },
      {
        "direct_anchor_float32_mean_norm_error": 2.2842000312918442e-08,
        "direct_anchor_float32_mean_state_error": 4.064638795096149e-08,
        "iterative_float32_mean_norm_error": 1.5165936961087853e-07,
        "iterative_float32_mean_state_error": 2.641320009012103e-07,
        "steps": 10
      },
      {
        "direct_anchor_float32_mean_norm_error": 3.061086311360352e-08,
        "direct_anchor_float32_mean_state_error": 4.32743583633836e-08,
        "iterative_float32_mean_norm_error": 1.5261761136834903e-06,
        "iterative_float32_mean_state_error": 2.4773438260051245e-06,
        "steps": 100
      },
      {
        "direct_anchor_float32_mean_norm_error": 2.8610490077985232e-08,
        "direct_anchor_float32_mean_state_error": 4.345837094513818e-08,
        "iterative_float32_mean_norm_error": 1.51849973660384e-05,
        "iterative_float32_mean_state_error": 2.4475959819884656e-05,
        "steps": 1000
      },
      {
        "direct_anchor_float32_mean_norm_error": 3.137558883363478e-08,
        "direct_anchor_float32_mean_state_error": 4.406939214551433e-08,
        "iterative_float32_mean_norm_error": 0.000152530950329236,
        "iterative_float32_mean_state_error": 0.00024528154882307257,
        "steps": 10000
      },
      {
        "direct_anchor_float32_mean_norm_error": 2.2983118052807838e-08,
        "direct_anchor_float32_mean_state_error": 3.797501573613895e-08,
        "iterative_float32_mean_norm_error": 0.0015233372006562703,
        "iterative_float32_mean_state_error": 0.0024513936625792402,
        "steps": 100000
      }
    ],
    "interpretation": "Direct procedural reconstruction prevents cumulative roundoff when the dynamics are known exactly. A generic direct renderer with the same true dynamics gives the same advantage.",
    "operator": "R(2*pi*lambda) direct-sum R(2*pi*mu)"
  },
  "E2_adversarial_mismatch": {
    "checkpoints": [
      {
        "generic_true_model_anchor_mean_state_error": 5.063848515711516e-08,
        "iterative_float32_mean_state_error": 5.063848515711516e-08,
        "omega_anchor_wrong_model_mean_state_error": 1.3762525814949393e-05,
        "steps": 1
      },
      {
        "generic_true_model_anchor_mean_state_error": 4.974656708111715e-08,
        "iterative_float32_mean_state_error": 3.5233200977679154e-07,
        "omega_anchor_wrong_model_mean_state_error": 0.00013781469129874014,
        "steps": 10
      },
      {
        "generic_true_model_anchor_mean_state_error": 4.225505509465035e-08,
        "iterative_float32_mean_state_error": 3.374912191766849e-06,
        "omega_anchor_wrong_model_mean_state_error": 0.0013780858227469936,
        "steps": 100
      },
      {
        "generic_true_model_anchor_mean_state_error": 3.925888436414186e-08,
        "iterative_float32_mean_state_error": 3.357802341978846e-05,
        "omega_anchor_wrong_model_mean_state_error": 0.01378073275815529,
        "steps": 1000
      },
      {
        "generic_true_model_anchor_mean_state_error": 4.260353022344707e-08,
        "iterative_float32_mean_state_error": 0.00033561418815651373,
        "omega_anchor_wrong_model_mean_state_error": 0.13767470564389384,
        "steps": 10000
      },
      {
        "generic_true_model_anchor_mean_state_error": 4.245650887610816e-08,
        "iterative_float32_mean_state_error": 0.003362465223402241,
        "omega_anchor_wrong_model_mean_state_error": 1.2490808891976917,
        "steps": 100000
      }
    ],
    "delta_alpha": 1e-05,
    "delta_beta": -1.7e-05,
    "interpretation": "A fixed OMEGA anchor becomes wrong if the actual dynamics are not OMEGA-aligned. The correct generic model remains stable."
  },
  "E3_synthetic_embedding_proxy": {
    "D": 64,
    "N": 800,
    "clusters": 20,
    "interpretation": "Relational geometry (kNN) can remain nearly intact even while absolute state is wrong under a common wrong rotation. Absolute fidelity and relational fidelity must be scored separately.",
    "matched_omega_dynamics": {
      "direct_omega_anchor_float16": {
        "knn10_retention": 0.9996250000000001,
        "mean_cosine_to_true": 0.9999999593317983,
        "mean_norm_error": 5.269838952923572e-05,
        "mean_state_error": 0.0002897516408615663
      },
      "iterative_float16": {
        "knn10_retention": 0.9788750000000002,
        "mean_cosine_to_true": 0.9664732735436181,
        "mean_norm_error": 2.3531944629843458,
        "mean_state_error": 2.400493307093935
      }
    },
    "mismatched_dynamics": {
      "generic_true_model_anchor": {
        "knn10_retention": 0.9992500000000001,
        "mean_cosine_to_true": 0.9999999215762898,
        "mean_norm_error": 7.63619086616868e-05,
        "mean_state_error": 0.0004043373728864426
      },
      "iterative_float16": {
        "knn10_retention": 0.9776250000000001,
        "mean_cosine_to_true": 0.8796500505210123,
        "mean_norm_error": 0.5824826240892169,
        "mean_state_error": 0.6631514018378712
      },
      "omega_anchor_wrong_model": {
        "knn10_retention": 0.9996250000000001,
        "mean_cosine_to_true": 0.8367363719453803,
        "mean_norm_error": 5.269838952923572e-05,
        "mean_state_error": 0.5713154323821569
      }
    },
    "steps": 5000
  },
  "E4_uniform_random_dynamics_control": {
    "best_random_anchor_mean_state_error": 1.3205833891650154,
    "fraction_random_anchors_better_than_omega": 0.56,
    "interpretation": "Across uniformly random dynamics, OMEGA performs like an ordinary fixed anchor; no universal privilege is detected.",
    "omega_anchor_mean_state_error": 1.333999099759267,
    "random_anchor_mean_of_means": 1.331827580157937,
    "random_anchor_std_of_means": 0.005436836085627981,
    "random_fixed_anchor_controls": 200,
    "tasks": 2000,
    "worst_random_anchor_mean_state_error": 1.3409388135205922
  },
  "constants_approx_noncanonical": {
    "alpha": 2.135967408492575,
    "alpha_plus_beta_over_2pi": 0.9999999999999999,
    "beta": 4.1472178986870105,
    "lambda": 0.33994977134477894,
    "mu": 0.660050228655221,
    "omega0": 4.759626642339688,
    "phi": 1.618033988749895
  },
  "experiment": "OMEGA_DRIFT_EXPERIMENT_v0_1",
  "scope": {
    "embedding_test_is_synthetic_proxy": true,
    "omega_spiral_operator_is_new_experimental_operator": true,
    "real_ai_embedding_model_used": false,
    "srsd_is_frozen_external": true,
    "v0_2_reference_geometry_is_not_modified": true
  },
  "seed": 20260831
}