{
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 "createdUtc": "2026-10-30T23:05:05Z",
 "observationalData": "none",
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 "note": "This study uses no observational, survey, experimental or simulated data set. Every graph P(n,5) is generated deterministically from Definition 3.1 of the manuscript by code/graph_constructor.py (two independent constructors; canonical edge lists with SHA-256 digests recorded in results/t1_graph_invariants.json and in every result record). Random seeds used as inputs to deterministic checks (order-independence test, lemma checks, simulated-annealing attacks) are recorded in results/metrics.json. The inputs listed below are the downloaded literature full texts and the archived software dependencies; they are the only external files the run consumed.",
 "graphGeneration": {
  "generator": "code/graph_constructor.py",
  "definition": "P(n,k): vertices u_i, v_i (i in Z_n); edges u_i u_{i+1}, u_i v_i, v_i v_{i+k}",
  "range": "11 <= n <= 48 tabulated; 26 <= n <= 154 for boundary certificates; n <= 300 for construction replays",
  "invariantRecord": "results/t1_graph_invariants.json"
 },
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 ],
 "largeArtifactsNotShipped": {
  "description": "DRAT proofs of the boundary window (39.0 GB) are not shipped; SHA-256 digests of every CNF and proof are in results/boundary_certificates.jsonl and results/tables/boundary_window_p18.csv; regenerate with: PYTHONPATH=.pydeps:code python3 code/run_boundary_window.py 18 26 154 12"
 }
}