{
  "id": "O0-CRP-020",
  "title": "Study S3 · Parameter-Space Critical-Point Cartography — GAMMA_H and GAMMA_U Analytical Sweeps",
  "semantic_name": "Study S3",
  "record_class": "SIMULATION",
  "version": "1.0.0",
  "status": "STRONG PREDICTION SUPPORT",
  "evidence_level": "computational_simulation",
  "replication_status": "not_replicated",
  "program": "contact_and_revelation",
  "non_drift_question": "methodological",
  "opens_branch": "NONE (parameter-sensitivity followup, extends O0-CRP-019)",
  "date": "2026-07-27",
  "source_record": "O0-CRP-011",

  "related_records": ["O0-CRP-011", "O0-CRP-012", "O0-CRP-018", "O0-CRP-019"],

  "design_summary": {
    "n_sweeps": 2,
    "sweep_A": {"parameter": "GAMMA_H", "n_values": 41, "range": [0.001, 5.0]},
    "sweep_B": {"parameter": "GAMMA_U", "n_values": 41, "range": [0.0001, 1.0]},
    "n_conditions": 2,
    "conditions": ["R (opaque)", "D (visible)"],
    "n_seeds": 30,
    "seed_range": [11000, 11029],
    "n_messages_per_trial": 200,
    "alpha": 0.9,
    "regime": "ANCHOR",
    "held_constants": {"GAMMA_K": 0.10, "VISIBLE_HIDDEN_SKEPTIC": 0.2, "ETA_KNOWLEDGE": 0.1},
    "total_trials": 4920
  },

  "locked_analytical_models": {
    "h_R_of_GAMMA_H": "h(R, gamma_H) = (1 + 180*gamma_H) / (2 + 200*gamma_H)  [alpha=0.9, T=200]",
    "h_D": "h(D) = 1 / (2 + T * VISIBLE_HIDDEN_SKEPTIC) = 1/42 = 0.02381 (invariant to gamma_H)",
    "u_R_of_GAMMA_U_at_ANCHOR": "u(R, gamma_U) = (0.1 + 180*gamma_U) / (10.1 + 180*gamma_U)",
    "u_D_at_ANCHOR": "u(D) = 0.1/10.1 = 0.00990 (invariant to gamma_U; no D-side update at all)",
    "GAMMA_H_crossover_prediction": "-0.00543 (unphysical, no positive crossover)",
    "GAMMA_U_crossover_prediction": "~5.6e-8 (essentially zero, no positive crossover)",
    "saturation_limits": {"h_R_saturates_at": 0.9, "u_R_saturates_at": 1.0}
  },

  "null_gates": {
    "determinism": {"passed": true},
    "consistency_with_O0_CRP_019": {"passed": true,
      "note": "Endpoints at Study B defaults reproduce O0-CRP-019 within seed-level variance"}
  },

  "verdict": {
    "label": "STRONG PREDICTION SUPPORT",
    "rmse_delta_h": 0.007559,
    "rmse_delta_u": 0.008303,
    "sign_match_h": "10/10",
    "sign_match_u": "10/10",
    "positive_crossover_h": false,
    "positive_crossover_u": false,
    "monotone_h": true,
    "monotone_u": true,
    "structural_asymmetry_confirmed": "Among GAMMA_K, GAMMA_H, GAMMA_U, only GAMMA_K produces a positive-value crossover"
  },

  "gamma_h_prediction_vs_observation": [
    {"gamma_h": 0.001, "pred_delta": 0.51256, "obs_delta": 0.51316, "err": 0.00060},
    {"gamma_h": 0.003, "pred_delta": 0.56850, "obs_delta": 0.56956, "err": 0.00106},
    {"gamma_h": 0.010, "pred_delta": 0.67619, "obs_delta": 0.68965, "err": 0.01346},
    {"gamma_h": 0.030, "pred_delta": 0.77619, "obs_delta": 0.78812, "err": 0.01193},
    {"gamma_h": 0.100, "pred_delta": 0.83983, "obs_delta": 0.84524, "err": 0.00541},
    {"gamma_h": 0.300, "pred_delta": 0.86329, "obs_delta": 0.86941, "err": 0.00612},
    {"gamma_h": 0.500, "pred_delta": 0.86835, "obs_delta": 0.87488, "err": 0.00653},
    {"gamma_h": 1.000, "pred_delta": 0.87223, "obs_delta": 0.87914, "err": 0.00691},
    {"gamma_h": 2.000, "pred_delta": 0.87420, "obs_delta": 0.88092, "err": 0.00672},
    {"gamma_h": 5.000, "pred_delta": 0.87540, "obs_delta": 0.88205, "err": 0.00665}
  ],

  "gamma_u_prediction_vs_observation": [
    {"gamma_u": 0.0001, "pred_delta": 0.00176, "obs_delta": 0.00177, "err": 0.00001},
    {"gamma_u": 0.001,  "pred_delta": 0.01734, "obs_delta": 0.01850, "err": 0.00116},
    {"gamma_u": 0.003,  "pred_delta": 0.05025, "obs_delta": 0.04623, "err": -0.00402},
    {"gamma_u": 0.010,  "pred_delta": 0.14976, "obs_delta": 0.13621, "err": -0.01355},
    {"gamma_u": 0.020,  "pred_delta": 0.26017, "obs_delta": 0.26155, "err": 0.00138},
    {"gamma_u": 0.050,  "pred_delta": 0.46654, "obs_delta": 0.44995, "err": -0.01659},
    {"gamma_u": 0.100,  "pred_delta": 0.63423, "obs_delta": 0.62224, "err": -0.01199},
    {"gamma_u": 0.300,  "pred_delta": 0.83410, "obs_delta": 0.83797, "err": 0.00387},
    {"gamma_u": 0.500,  "pred_delta": 0.88221, "obs_delta": 0.88941, "err": 0.00720},
    {"gamma_u": 1.000,  "pred_delta": 0.93697, "obs_delta": 0.93782, "err": 0.00085}
  ],

  "three_parameter_cartography": [
    {"parameter": "GAMMA_K", "register": "k_hat", "update_type": "EMA on signal",
     "D_baseline": "large positive (approximately 3.0)",
     "positive_crossover": true, "crossover_value": 0.0641,
     "source_study": "O0-CRP-019"},
    {"parameter": "GAMMA_H", "register": "h_hat", "update_type": "Beta posterior",
     "D_baseline": "near zero (approximately 0.024)",
     "positive_crossover": false, "analytical_crossover": -0.00543,
     "source_study": "O0-CRP-020"},
    {"parameter": "GAMMA_U", "register": "u_hat", "update_type": "Beta posterior",
     "D_baseline": "near zero (approximately 0.010, prior-only)",
     "positive_crossover": false, "analytical_crossover": 5.6e-8,
     "source_study": "O0-CRP-020"}
  ],

  "key_findings": [
    "Analytical models predict h_hat and u_hat endpoint means to RMSE 0.008 across 41-point log sweeps",
    "Sign matches at 10 of 10 preregistered points in both sweeps",
    "No positive-value crossover in either GAMMA_H or GAMMA_U",
    "h_hat(R) saturates at 0.9 (source's accuracy) as GAMMA_H grows",
    "u_hat(R) saturates at 1.0 as GAMMA_U grows",
    "Structural asymmetry: only GAMMA_K produces a positive-value crossover among the three REVELATION-hedging parameters",
    "Mechanistic reason established: k_hat has large positive D-baseline; h_hat and u_hat have near-zero D-baseline"
  ],

  "supported_claims": [
    "Beta-posterior analytical models for h_hat(R, GAMMA_H) and u_hat(R, GAMMA_U) work to RMSE 0.008",
    "The REVELATION effect on h_hat and u_hat is monotone-positive across the entire tested parameter range",
    "The REVELATION effect on k_hat is fragile (has crossover); on h_hat and u_hat it is robust",
    "Prediction-vs-observation methodology from O0-CRP-019 replicates with no framework adjustment"
  ],

  "not_established_claims": [
    "Robustness at other prior regimes (registered R2)",
    "Cross-parameter interactions (registered R1)",
    "PP-observer analogs (registered R3)",
    "Any claim about real observers"
  ],

  "adversarial_notes": [
    "Prediction success is not trivial: at higher seed variance or shorter T, the analytical models could fail. That they didn't is scientifically informative.",
    "GAMMA_H residuals show small systematic positive bias (all positive errors); GAMMA_U residuals are unbiased in sign but slightly larger magnitude. Both within tolerance.",
    "The no-crossover finding is a consequence of Study B's specific D-side update design. Under different D-side rules, the crossovers could shift."
  ],

  "replication_queue": [
    {"id": "O0-CRP-020-R1", "kind": "2D_sweep", "target": "alpha x GAMMA_H", "status": "REGISTERED"},
    {"id": "O0-CRP-020-R2", "kind": "regime_sweep", "target": "GAMMA_U at FLAT and SKEPTICAL", "status": "REGISTERED"},
    {"id": "O0-CRP-020-R3", "kind": "cross_architecture", "target": "PP observer analog parameters", "status": "REGISTERED"}
  ],

  "figures": [
    {"file": "figures/01_gamma_h_curve.png", "caption": "Δĥ vs GAMMA_H — analytical vs observed"},
    {"file": "figures/02_gamma_u_curve.png", "caption": "Δû vs GAMMA_U — analytical vs observed"},
    {"file": "figures/03_three_parameter_asymmetry.png", "caption": "The headline result: k̂ has crossover, ĥ and û don't"},
    {"file": "figures/04_prediction_scatter.png", "caption": "10-point scatter y=x diagonals for both sweeps"},
    {"file": "figures/05_saturation_curves.png", "caption": "ĥ(R) → 0.9 and û(R) → 1.0 saturation limits"}
  ],

  "files": {
    "preregistration": "preregistration.md",
    "scientific_record": "scientific_record.md",
    "code": ["src/run_sweep.py", "src/analyze.py"],
    "results": ["results/summary.json", "results/run_log.txt"],
    "raw_data": ["data/raw/sweeps.jsonl"]
  },

  "provenance": {
    "philosophical_source": "None (metascientific study)",
    "conceptual_relationship": "parameter_sensitivity_analysis, extends O0-CRP-019 methodology",
    "disclaimer": "Metascientific. Documents parameter-space structure of Study B's observer. No ontological claims."
  },

  "runtime_seconds": 42.2
}