{
  "schema": "crs/counting-wall/v1",
  "what_this_is": "The measured frontier of exact model counting in the linear-integer fragment on one machine. The cap applies to the ENUMERATED PRODUCT (all variables but the widest, which is closed-formed), not to the box volume.",
  "exact_cap": 2097152,
  "largest_exact_enumerated_product": 2097152,
  "all_exact_counts_agree_with_volume": true,
  "all_bounded_intervals_bracket_truth": true,
  "honest_scope": "Timings are from one machine. The wall is EXPONENTIAL in variable count, which is inherent to enumeration rather than an implementation defect: at k variables of width w the enumerated product is w**(k-1). Beyond the cap the service returns BOUNDED with a stated confidence, or REFUSED when the caller forbids a bounded answer. It never returns a point estimate.",
  "rows": [
    {
      "n_variables": 1,
      "width": 4,
      "box_volume": 4,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.03,
      "count": 4,
      "agrees_with_volume": true
    },
    {
      "n_variables": 1,
      "width": 8,
      "box_volume": 8,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.01,
      "count": 8,
      "agrees_with_volume": true
    },
    {
      "n_variables": 1,
      "width": 16,
      "box_volume": 16,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.01,
      "count": 16,
      "agrees_with_volume": true
    },
    {
      "n_variables": 1,
      "width": 32,
      "box_volume": 32,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.01,
      "count": 32,
      "agrees_with_volume": true
    },
    {
      "n_variables": 1,
      "width": 64,
      "box_volume": 64,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.01,
      "count": 64,
      "agrees_with_volume": true
    },
    {
      "n_variables": 1,
      "width": 128,
      "box_volume": 128,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.01,
      "count": 128,
      "agrees_with_volume": true
    },
    {
      "n_variables": 1,
      "width": 256,
      "box_volume": 256,
      "enumerated_product": 1,
      "verdict": "EXACT",
      "ms": 0.01,
      "count": 256,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 4,
      "box_volume": 16,
      "enumerated_product": 4,
      "verdict": "EXACT",
      "ms": 0.02,
      "count": 16,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 8,
      "box_volume": 64,
      "enumerated_product": 8,
      "verdict": "EXACT",
      "ms": 0.02,
      "count": 64,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 16,
      "box_volume": 256,
      "enumerated_product": 16,
      "verdict": "EXACT",
      "ms": 0.02,
      "count": 256,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 32,
      "box_volume": 1024,
      "enumerated_product": 32,
      "verdict": "EXACT",
      "ms": 0.02,
      "count": 1024,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 64,
      "box_volume": 4096,
      "enumerated_product": 64,
      "verdict": "EXACT",
      "ms": 0.04,
      "count": 4096,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 128,
      "box_volume": 16384,
      "enumerated_product": 128,
      "verdict": "EXACT",
      "ms": 0.07,
      "count": 16384,
      "agrees_with_volume": true
    },
    {
      "n_variables": 2,
      "width": 256,
      "box_volume": 65536,
      "enumerated_product": 256,
      "verdict": "EXACT",
      "ms": 0.13,
      "count": 65536,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 4,
      "box_volume": 64,
      "enumerated_product": 16,
      "verdict": "EXACT",
      "ms": 0.02,
      "count": 64,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 8,
      "box_volume": 512,
      "enumerated_product": 64,
      "verdict": "EXACT",
      "ms": 0.05,
      "count": 512,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 16,
      "box_volume": 4096,
      "enumerated_product": 256,
      "verdict": "EXACT",
      "ms": 0.21,
      "count": 4096,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 32,
      "box_volume": 32768,
      "enumerated_product": 1024,
      "verdict": "EXACT",
      "ms": 0.64,
      "count": 32768,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 64,
      "box_volume": 262144,
      "enumerated_product": 4096,
      "verdict": "EXACT",
      "ms": 2.51,
      "count": 262144,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 128,
      "box_volume": 2097152,
      "enumerated_product": 16384,
      "verdict": "EXACT",
      "ms": 10.36,
      "count": 2097152,
      "agrees_with_volume": true
    },
    {
      "n_variables": 3,
      "width": 256,
      "box_volume": 16777216,
      "enumerated_product": 65536,
      "verdict": "EXACT",
      "ms": 40.66,
      "count": 16777216,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 4,
      "box_volume": 256,
      "enumerated_product": 64,
      "verdict": "EXACT",
      "ms": 0.08,
      "count": 256,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 8,
      "box_volume": 4096,
      "enumerated_product": 512,
      "verdict": "EXACT",
      "ms": 0.46,
      "count": 4096,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 16,
      "box_volume": 65536,
      "enumerated_product": 4096,
      "verdict": "EXACT",
      "ms": 3.33,
      "count": 65536,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 32,
      "box_volume": 1048576,
      "enumerated_product": 32768,
      "verdict": "EXACT",
      "ms": 25.3,
      "count": 1048576,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 64,
      "box_volume": 16777216,
      "enumerated_product": 262144,
      "verdict": "EXACT",
      "ms": 205.17,
      "count": 16777216,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 128,
      "box_volume": 268435456,
      "enumerated_product": 2097152,
      "verdict": "EXACT",
      "ms": 1614.84,
      "count": 268435456,
      "agrees_with_volume": true
    },
    {
      "n_variables": 4,
      "width": 256,
      "box_volume": 4294967296,
      "enumerated_product": 16777216,
      "verdict": "BOUNDED",
      "ms": 36.06,
      "ci_low": 4294175188,
      "ci_high": 4294967296,
      "brackets_truth": true
    },
    {
      "n_variables": 5,
      "width": 4,
      "box_volume": 1024,
      "enumerated_product": 256,
      "verdict": "EXACT",
      "ms": 0.27,
      "count": 1024,
      "agrees_with_volume": true
    },
    {
      "n_variables": 5,
      "width": 8,
      "box_volume": 32768,
      "enumerated_product": 4096,
      "verdict": "EXACT",
      "ms": 3.73,
      "count": 32768,
      "agrees_with_volume": true
    },
    {
      "n_variables": 5,
      "width": 16,
      "box_volume": 1048576,
      "enumerated_product": 65536,
      "verdict": "EXACT",
      "ms": 59.49,
      "count": 1048576,
      "agrees_with_volume": true
    },
    {
      "n_variables": 5,
      "width": 32,
      "box_volume": 33554432,
      "enumerated_product": 1048576,
      "verdict": "EXACT",
      "ms": 1000.2,
      "count": 33554432,
      "agrees_with_volume": true
    },
    {
      "n_variables": 5,
      "width": 64,
      "box_volume": 1073741824,
      "enumerated_product": 16777216,
      "verdict": "BOUNDED",
      "ms": 47.89,
      "ci_low": 1073543797,
      "ci_high": 1073741824,
      "brackets_truth": true
    }
  ]
}