{
  "name": "low_autocorrelation_n11__v3_h",
  "problem_type": "low_autocorrelation",
  "params": {
    "n": 11
  },
  "prompt": "Find a binary sequence of length 11 over the alphabet {-1, +1} with low aperiodic autocorrelation: specifically, the sum over k=1..10 of C_k^2, where C_k = sum_{i=0}^{n-k-1} seq[i]*seq[i+k], must be at most 23.\n\nReturn seq as a list of 11 integers, each -1 or +1, or state \"UNSATISFIABLE\" if no such sequence exists.\n\nPartial assignment (fixed values that must be respected):\n- seq[1]=1, seq[8]=1\n- c[6]=0, c[9]=1\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "seq": [
      -1,
      1,
      -1,
      1,
      1,
      -1,
      1,
      1,
      1,
      -1,
      -1
    ],
    "c": [
      -2,
      -1,
      0,
      -1,
      2,
      -3,
      0,
      -1,
      0,
      1
    ]
  },
  "difficulty": {
    "solve_time_ms": 974.3,
    "search_space": 2048,
    "num_variables": 21,
    "num_constraints": 17,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 66.73,
    "solve_pct_type": 4.17
  },
  "partial_assignment": {
    "seq": {
      "1": 1,
      "8": 1
    },
    "c": {
      "6": 0,
      "9": 1
    }
  }
}