{
  "id": "O0-CRP-033",
  "title": "Capacity Ceiling · Dimensionality Scaling of the Track 2 Discriminability Finding",
  "program": "CONTACT_AND_REVELATION",
  "track": "Track 2 followup — capacity-ceiling test",
  "status": "complete",
  "record_class": "REPLICATION",
  "version": "1.0.0",
  "date_completed": "2026-07-29",
  "preregistration_frozen_before_execution": true,
  "verdict": {
    "preregistered": "SCALE_INVARIANT",
    "for_claim": "does the CRP-022 discriminability pattern hold at n_total = 16 and 32?"
  },
  "key_findings": [
    {
      "n_total": 8,
      "feature_count": 143,
      "delta_star_070": 0.20,
      "matched_dual_auc": 0.347,
      "positive_control_auc": 1.0,
      "matched_in_chance_band": true,
      "realization_bit_identical": true,
      "in_class": true
    },
    {
      "n_total": 16,
      "feature_count": 399,
      "delta_star_070": 0.20,
      "matched_dual_auc": 0.307,
      "positive_control_auc": 1.0,
      "matched_in_chance_band": true,
      "realization_bit_identical": true,
      "in_class": true
    },
    {
      "n_total": 32,
      "feature_count": 1295,
      "delta_star_070": 0.10,
      "matched_dual_auc": 0.306,
      "positive_control_auc": 1.0,
      "matched_in_chance_band": true,
      "realization_bit_identical": true,
      "in_class": true,
      "note": "delta*(0.7) sharpens at higher dimensions — coupling detection becomes MORE sensitive with more channels, not less"
    }
  ],
  "response_to_toy_model_critique": {
    "critique": "n=8 is a toy dimension; the finding may not survive scaling",
    "response": "Finding survives 4x dimensionality scaling (n=8→32) and 9x feature-count scaling (143→1295). Matched-source indistinguishability holds at every n; realization theorem holds bit-identically at every n; DUAL discriminability actually STRENGTHENS at higher n (delta*(0.7) goes from 0.20 at n=8 to 0.10 at n=32)."
  },
  "delta_star_scaling": {
    "n_8": 0.20,
    "n_16": 0.20,
    "n_32": 0.10,
    "interpretation": "Higher dimensionality gives the classifier more channels of coupling signal to integrate over. DUAL universes become distinguishable at smaller delta. This is favorable scaling — the archive's operational claim about detecting coupling becomes tighter, not looser, at scale."
  },
  "sample": {
    "world_seeds": "22000-22029",
    "trials_per_class": 200,
    "trial_offset": 600000,
    "trajectory_length_T": 200,
    "total_trajectories": 6600,
    "runtime_seconds": 70.1,
    "note": "runtime after resumable feature caching; full first-pass compute was ~30 minutes"
  },
  "related": ["O0-CRP-022", "O0-CRP-024", "O0-CRP-025", "O0-CRP-026", "O0-CRP-027", "O0-CRP-030", "O0-CRP-031", "O0-CRP-032", "O0-SCOPE-001"],
  "followups_registered": [
    { "id": "CRP-033b", "topic": "Heavy-tailed noise scaling (Student-t, Cauchy)" },
    { "id": "CRP-033c", "topic": "Dimensionality scaling of chaotic systems (Lorenz at n_nodes ∈ {8, 16, 32})" },
    { "id": "CRP-033d", "topic": "n > 32 with linear-kernel SVM (RandomForest saturates)" }
  ],
  "core_claims_preserved_across_scaling": [
    "Matched-source indistinguishability at n=8, 16, 32 (matched-dual AUC 0.347, 0.307, 0.306)",
    "Realization theorem bit-identical at every n",
    "Positive control AUC = 1.0 at every n"
  ]
}