{
  "id": "O0-CRP-022",
  "title": "Discriminability from Inside — Matched-identity universes are statistically indistinguishable from matched-dual universes under a 146-feature test battery; detectable departure at δ ≈ 0.10.",
  "semantic_name": "Discriminability from Inside",
  "record_class": "SIMULATION",
  "version": "1.0.0",
  "status": "PARTIAL SUPPORT for indistinguishability",
  "evidence_level": "computational_simulation",
  "replication_status": "not_replicated",
  "program": "track_2_deep_o0_identity_test",
  "non_drift_question": "CONTACT / PERSPECTIVE (empirical identity test)",
  "opens_branch": "Track 2 — deep O/0 identity claim test",
  "date": "2026-07-28",
  "source_record": "O/0 Framework §IX + user statement 2026-07-28",

  "related_records": ["O0-CRP-021", "O0-CRP-023"],

  "source_proposition": "O/0 §IX: 'You are O, reading about O, recognizing O. That's all there is.' User (2026-07-28): 'we are the creator and the creation at the same time. one means one.'",

  "operationalization": {
    "IDENTITY_universe": "single joint stochastic process; observer state and observations are two projections of the same z_t",
    "MATCHED_DUAL_universe": "same dynamics, block-partitioned into two coupled processes; bit-identical to IDENTITY under same trial seed",
    "DUAL_departure": "y-dynamics y←x cross-coupling scaled by (1 − δ); δ ∈ [0, 1] measures departure from identity",
    "discriminator": "Random Forest classifier on 146-feature test battery, 5-fold cross-validation",
    "null_baseline": "IDENTITY vs a fresh IDENTITY draw from the same worlds — classifier's finite-sample discrimination floor"
  },

  "design_summary": {
    "universe_dim": 8,
    "observer_dim": 4,
    "observation_dim": 4,
    "trajectory_length": 200,
    "spectral_radius": 0.9,
    "noise_scale": 0.1,
    "n_world_seeds": 30,
    "seed_range": [13000, 13029],
    "trials_per_class": 300,
    "delta_grid": [0.0, 0.05, 0.10, 0.20, 0.30, 0.50, 0.70, 1.00],
    "feature_dim": 146,
    "classifier": "RandomForest(n_estimators=100, min_samples_split=5)",
    "cv_folds": 5,
    "total_trials": 3909
  },

  "verdict": {
    "label": "PARTIAL SUPPORT for indistinguishability",
    "auc_matched": 0.376,
    "auc_null_null": 0.396,
    "matched_vs_null_diff": "within 1 std, statistically identical",
    "effective_auc_matched": 0.624,
    "max_per_feature_auc_matched": 0.572,
    "auc_noise_control": 1.000,
    "delta_star_070": 0.20,
    "delta_where_discrimination_emerges": 0.10,
    "realization_theorem_pass": true,
    "realization_theorem_max_diff": 0.0,
    "positive_control_pass": true
  },

  "delta_sweep_results": [
    {"delta": 0.00, "mean_auc": 0.389, "std_auc": 0.028, "max_per_feature_auc": 0.553},
    {"delta": 0.05, "mean_auc": 0.452, "std_auc": 0.052, "max_per_feature_auc": 0.553},
    {"delta": 0.10, "mean_auc": 0.643, "std_auc": 0.045, "max_per_feature_auc": 0.598},
    {"delta": 0.20, "mean_auc": 0.895, "std_auc": 0.043, "max_per_feature_auc": 0.668},
    {"delta": 0.30, "mean_auc": 0.969, "std_auc": 0.014, "max_per_feature_auc": 0.713},
    {"delta": 0.50, "mean_auc": 0.996, "std_auc": 0.003, "max_per_feature_auc": 0.827},
    {"delta": 0.70, "mean_auc": 0.999, "std_auc": 0.001, "max_per_feature_auc": 0.943},
    {"delta": 1.00, "mean_auc": 1.000, "std_auc": 0.000, "max_per_feature_auc": 0.993}
  ],

  "key_findings": [
    "Realization theorem verified numerically to bit-identical precision: IDENTITY and MATCHED_DUAL are the same stochastic process, viewed differently.",
    "MATCHED_DUAL discrimination (AUC=0.376) matches the null-null baseline (AUC=0.396) statistically. The 146-feature battery cannot distinguish matched configurations.",
    "Max per-feature AUC in matched cases is 0.57 — barely above chance and consistent with finite-sample noise.",
    "Positive control works trivially: IDENTITY vs iid noise gives AUC=1.000. Features and classifier are functional.",
    "Empirical identity tolerance: δ*(0.7) = 0.20 with this battery. Discrimination emerges above the null baseline at δ ≈ 0.10.",
    "The 'no observer inside can distinguish matched-identity from matched-duality' claim (empirical translation of the mystical identity claim) is operationally supported within the class studied."
  ],

  "supported_claims": [
    "For linear-Gaussian universes, matched-identity and matched-duality are empirically indistinguishable under a comprehensive 146-feature classical test battery.",
    "The state-space realization theorem — that structurally different realizations with matched joint statistics produce identical observables — holds numerically to bit-identical precision.",
    "The identity tolerance δ*(0.7) = 0.20 characterizes how much causal-structure departure the observer can detect with this battery.",
    "The empirical shape of the finding matches what non-dual mystical traditions have been pointing at: the position of one who could verify identity vs distinctness is structurally empty for embedded observers, when observables are matched."
  ],

  "not_established_claims": [
    "That real (nonlinear, non-Gaussian) universes are similarly indistinguishable — registered R1.",
    "That deep-learning-based discriminators or unbounded compute would not shrink δ* — registered R2.",
    "That our 146-feature battery exhausts what an observer can compute.",
    "That the mystical identity claim is metaphysically true.",
    "Anything about consciousness, subjectivity, or phenomenal experience.",
    "That our universe is an identity-universe."
  ],

  "adversarial_notes": [
    "Random Forest can overfit noise; null-null calibration establishes the classifier floor and shows matched-DUAL matches it.",
    "The 146 features are classical — no deep-learning discriminators. A stronger discriminator might narrow δ*.",
    "Departure parameterization scales one block of M; other departure axes (noise structure, nonlinearity) are unexplored.",
    "The realization theorem is a mathematical guarantee, not an empirical discovery. The empirical work is confirming that finite-sample tests do not detect discriminating signal.",
    "The identity tolerance δ* ≈ 0.10 is battery-dependent — an upper bound, not a lower bound."
  ],

  "replication_queue": [
    {"id": "O0-CRP-022-R1", "kind": "nonlinear_extension", "target": "Bilinear or LSTM-generative universes with matched second-moment statistics", "status": "REGISTERED"},
    {"id": "O0-CRP-022-R2", "kind": "deep_discriminator", "target": "Transformer-based sequence classifier as replacement for RF+146 features", "status": "REGISTERED"},
    {"id": "O0-CRP-022-R3", "kind": "alternative_departures", "target": "Noise-structure and nonlinearity departure axes", "status": "REGISTERED"},
    {"id": "O0-CRP-022-R4", "kind": "cross_domain_batteries", "target": "Physics, neuroscience, econometric test batteries", "status": "REGISTERED"},
    {"id": "O0-CRP-022-R5", "kind": "trajectory_length_sweep", "target": "T ∈ {500, 2000, 10000}, does δ* shrink?", "status": "REGISTERED"}
  ],

  "figures": [
    {"file": "figures/01_headline_delta_sweep.png", "caption": "Headline: MATCHED_DUAL sits at the null baseline; DUAL(δ) discrimination emerges at δ ≈ 0.10, δ*(0.7) = 0.20."},
    {"file": "figures/02_realization_theorem_check.png", "caption": "Realization theorem numerically verified: max abs diff = 0 across all worlds and trials."},
    {"file": "figures/03_per_feature_analysis.png", "caption": "Max per-feature AUC across universe pairs; matched cases match null baseline."},
    {"file": "figures/04_feature_space_pca.png", "caption": "PCA of feature space; IDENTITY and MATCHED overlap, DUAL(δ) separates as δ grows."}
  ],

  "files": {
    "preregistration": "preregistration.md",
    "scientific_record": "scientific_record.md",
    "code": ["src/run_study.py", "src/analyze.py"],
    "results": ["results/summary.json"],
    "raw_data": [
      "results/raw/feats_identity.npy",
      "results/raw/feats_matched.npy",
      "results/raw/feats_noise.npy",
      "results/raw/feats_dual_0.000.npy",
      "results/raw/feats_dual_0.050.npy",
      "results/raw/feats_dual_0.100.npy",
      "results/raw/feats_dual_0.200.npy",
      "results/raw/feats_dual_0.300.npy",
      "results/raw/feats_dual_0.500.npy",
      "results/raw/feats_dual_0.700.npy",
      "results/raw/feats_dual_1.000.npy"
    ]
  },

  "provenance": {
    "philosophical_source": "O/0 Framework §IX + user statement 2026-07-28",
    "exact_proposition_tested": "Can any test constructible by an embedded observer discriminate a universe where observer and source are numerically one from a universe where they are two, when observables are matched?",
    "conceptual_relationship": "formalization_of_deep_identity_claim_as_epistemic_discriminability",
    "disclaimer": "Conceptual provenance is not empirical support. This study operationalizes the identity claim as a formal discriminability question about embedded observers in linear-Gaussian universes. The result is that matched-identity and matched-duality are empirically indistinguishable under the 146-feature battery, and departure becomes detectable at δ ≈ 0.10. This is not a proof of metaphysical identity."
  },

  "runtime_seconds": 180.5
}