{
  "name": "MathConstraint-Easy",
  "version": "1.0",
  "description": "MathConstraint-Easy: a 266-instance subset of MathConstraint with a lighter solver-time distribution and hinted SAT variants. Spans 25 NP-hard problem types from constraint programming (pycsp3) and SAT-modulo-symmetries on graphs (pysms). One instance per unique problem; SAT instances split 50/50 into hinted/unhinted by deterministic seed.",
  "license": "CC-BY-4.0",
  "total_instances": 266,
  "satisfiable_instances": 206,
  "unsatisfiable_instances": 60,
  "hint_distribution": {
    "hinted_sat": 103,
    "unhinted_sat": 103,
    "unsat": 60
  },
  "sat_unsat_split": {
    "sat_pct": 77.44
  },
  "total_problem_types": 25,
  "problem_types": [
    "all_interval",
    "costas_array",
    "golomb",
    "graceful_graph",
    "knight_tour",
    "langford",
    "low_autocorrelation",
    "magic_sequence",
    "pigeons",
    "pysms_chromatic_girth",
    "pysms_clique_coloring",
    "pysms_combined_graph",
    "pysms_contains_cliques",
    "pysms_degree_bounds",
    "pysms_girth_degree",
    "pysms_graph_builder",
    "pysms_independent_connectivity",
    "pysms_min_connectivity",
    "pysms_min_degree",
    "pysms_min_girth",
    "pysms_mtf",
    "pysms_num_edges_bounds",
    "queens",
    "ramsey",
    "sudoku"
  ],
  "instances_per_type": {
    "all_interval": 12,
    "costas_array": 9,
    "golomb": 6,
    "graceful_graph": 8,
    "knight_tour": 4,
    "langford": 8,
    "low_autocorrelation": 12,
    "magic_sequence": 12,
    "pigeons": 12,
    "pysms_chromatic_girth": 12,
    "pysms_clique_coloring": 12,
    "pysms_combined_graph": 12,
    "pysms_contains_cliques": 12,
    "pysms_degree_bounds": 12,
    "pysms_girth_degree": 12,
    "pysms_graph_builder": 12,
    "pysms_independent_connectivity": 12,
    "pysms_min_connectivity": 12,
    "pysms_min_degree": 12,
    "pysms_min_girth": 12,
    "pysms_mtf": 12,
    "pysms_num_edges_bounds": 12,
    "queens": 12,
    "ramsey": 12,
    "sudoku": 3
  },
  "solver_wall_time_ms": {
    "p25": 79.42,
    "p50": 201.05,
    "p75": 1045.8,
    "p90": 1791.3,
    "p99": 11848.33,
    "max": 56542.2
  },
  "generator": {
    "profile": "easy",
    "seed": 20260423,
    "samples_per_type": 12,
    "sat_hint_fraction": 0.5,
    "partial_assignment_fraction": 0.2
  },
  "schema": {
    "name": "instance identifier",
    "problem_type": "problem family",
    "params": "parameters that define the instance",
    "prompt": "natural-language problem statement",
    "satisfiable": "ground-truth verdict (bool)",
    "solution": "reference solution if SAT (else null)",
    "difficulty": "solver wall-time and difficulty metadata",
    "partial_assignment": "optional revealed positions for hinted SAT instances"
  },
  "known_issues": [
    "Two low_autocorrelation instances (n=10, n=17) are labelled satisfiable but the current solver believes them unsatisfiable due to a bound-formula tightening post-generation. Under current code, both are uniformly graded as failures by all models. Reported headline accuracies are biased ~0.75pp uniformly downward."
  ]
}