{
  "what": "Certified bilinear algorithms for polynomial multiplication over F2, found by the generation front and decided by instruments/bilinear. Every entry is a witness: the scheme is stored in full, so any reader can re-decide it. Published bounds it is measured against live in corpus/bilinear-bounds.json and are not results of this repository.",
  "instrument": "instruments/bilinear/tensor.js",
  "ring": "F2",
  "schemeFormat": "each term is [u, v, w], three bitmasks over the a-, b- and c-coordinates; bit i of u is the coefficient of input a_i, and so on. rank is the number of terms.",
  "entries": [
    {
      "target": "C7",
      "statement": "a rank-r bilinear algorithm for the cyclic product of two degree-6 polynomials over F2, modulo X^7 - 1",
      "rank": 13,
      "naive": 49,
      "equations": 343,
      "standing": "MATCH",
      "publishedUpper": 13,
      "publishedLower": 13,
      "search": {
        "proposer": "flip@v1",
        "seeds": 8,
        "steps": 300000,
        "slack": 2,
        "pluses": 703,
        "seconds": 19.9,
        "costUsd": 0
      },
      "scheme": [
        [
          83,
          39,
          46
        ],
        [
          101,
          101,
          83
        ],
        [
          75,
          57,
          78
        ],
        [
          57,
          114,
          39
        ],
        [
          23,
          23,
          116
        ],
        [
          105,
          105,
          57
        ],
        [
          114,
          75,
          105
        ],
        [
          116,
          83,
          92
        ],
        [
          127,
          127,
          127
        ],
        [
          46,
          46,
          58
        ],
        [
          58,
          78,
          23
        ],
        [
          78,
          58,
          101
        ],
        [
          29,
          116,
          114
        ]
      ]
    },
    {
      "target": "C8",
      "statement": "a rank-r bilinear algorithm for the cyclic product of two degree-7 polynomials over F2, modulo X^8 - 1",
      "rank": 25,
      "naive": 64,
      "equations": 512,
      "standing": "above",
      "publishedUpper": 22,
      "publishedLower": 19,
      "search": {
        "proposer": "flip@v1",
        "seeds": 12,
        "steps": 800000,
        "slack": 3,
        "pluses": 7881,
        "seconds": 667.4,
        "costUsd": 0
      },
      "scheme": [
        [
          180,
          225,
          37
        ],
        [
          170,
          170,
          183
        ],
        [
          65,
          102,
          204
        ],
        [
          160,
          153,
          34
        ],
        [
          218,
          255,
          255
        ],
        [
          240,
          30,
          67
        ],
        [
          102,
          92,
          85
        ],
        [
          153,
          192,
          170
        ],
        [
          150,
          45,
          97
        ],
        [
          153,
          102,
          40
        ],
        [
          30,
          105,
          7
        ],
        [
          102,
          153,
          185
        ],
        [
          18,
          85,
          35
        ],
        [
          108,
          153,
          17
        ],
        [
          119,
          60,
          165
        ],
        [
          255,
          39,
          247
        ],
        [
          51,
          54,
          59
        ],
        [
          195,
          187,
          248
        ],
        [
          129,
          170,
          170
        ],
        [
          51,
          44,
          255
        ],
        [
          238,
          136,
          112
        ],
        [
          71,
          85,
          118
        ],
        [
          187,
          195,
          120
        ],
        [
          204,
          57,
          145
        ],
        [
          204,
          155,
          255
        ]
      ]
    },
    {
      "target": "P2",
      "statement": "a rank-r bilinear algorithm for the full product of two degree-1 polynomials over F2",
      "rank": 3,
      "naive": 4,
      "equations": 12,
      "standing": "unpublished",
      "publishedUpper": null,
      "publishedLower": null,
      "search": {
        "proposer": "flip@v1",
        "seeds": 8,
        "steps": 300000,
        "slack": 2,
        "pluses": 0,
        "seconds": 0,
        "costUsd": 0
      },
      "scheme": [
        [
          2,
          2,
          6
        ],
        [
          3,
          3,
          2
        ],
        [
          1,
          1,
          3
        ]
      ]
    },
    {
      "target": "P3",
      "statement": "a rank-r bilinear algorithm for the full product of two degree-2 polynomials over F2",
      "rank": 6,
      "naive": 9,
      "equations": 45,
      "standing": "unpublished",
      "publishedUpper": null,
      "publishedLower": null,
      "search": {
        "proposer": "flip@v1",
        "seeds": 8,
        "steps": 300000,
        "slack": 2,
        "pluses": 0,
        "seconds": 0,
        "costUsd": 0
      },
      "scheme": [
        [
          7,
          7,
          8
        ],
        [
          2,
          2,
          6
        ],
        [
          3,
          3,
          10
        ],
        [
          4,
          4,
          20
        ],
        [
          5,
          5,
          12
        ],
        [
          1,
          1,
          15
        ]
      ]
    },
    {
      "target": "P4",
      "statement": "a rank-r bilinear algorithm for the full product of two degree-3 polynomials over F2",
      "rank": 9,
      "naive": 16,
      "equations": 112,
      "standing": "unpublished",
      "publishedUpper": null,
      "publishedLower": null,
      "search": {
        "proposer": "flip@v1",
        "seeds": 8,
        "steps": 300000,
        "slack": 2,
        "pluses": 427,
        "seconds": 3.1,
        "costUsd": 0
      },
      "scheme": [
        [
          12,
          12,
          54
        ],
        [
          11,
          11,
          12
        ],
        [
          13,
          13,
          10
        ],
        [
          4,
          4,
          36
        ],
        [
          1,
          1,
          9
        ],
        [
          6,
          6,
          20
        ],
        [
          14,
          14,
          18
        ],
        [
          15,
          15,
          14
        ],
        [
          8,
          8,
          108
        ]
      ]
    },
    {
      "target": "T6",
      "statement": "a rank-r bilinear algorithm for the truncated product of two degree-5 polynomials over F2 (the low 6 coefficients)",
      "rank": 14,
      "naive": 21,
      "equations": 216,
      "standing": "MATCH",
      "publishedUpper": 14,
      "publishedLower": 13,
      "search": {
        "proposer": "flip@v1",
        "seeds": 8,
        "steps": 300000,
        "slack": 2,
        "pluses": 1915,
        "seconds": 24.8,
        "costUsd": 0
      },
      "scheme": [
        [
          60,
          1,
          11
        ],
        [
          1,
          38,
          32
        ],
        [
          5,
          14,
          60
        ],
        [
          4,
          13,
          12
        ],
        [
          17,
          3,
          48
        ],
        [
          61,
          1,
          43
        ],
        [
          7,
          10,
          52
        ],
        [
          2,
          23,
          42
        ],
        [
          14,
          5,
          40
        ],
        [
          1,
          21,
          26
        ],
        [
          27,
          2,
          16
        ],
        [
          13,
          4,
          8
        ],
        [
          6,
          8,
          36
        ],
        [
          3,
          22,
          10
        ]
      ]
    },
    {
      "target": "T7",
      "statement": "a rank-r bilinear algorithm for the truncated product of two degree-6 polynomials over F2 (the low 7 coefficients)",
      "rank": 18,
      "naive": 28,
      "equations": 343,
      "standing": "MATCH",
      "publishedUpper": 18,
      "publishedLower": 16,
      "search": {
        "proposer": "flip@v1",
        "seeds": 8,
        "steps": 300000,
        "slack": 2,
        "pluses": 1946,
        "seconds": 40.1,
        "costUsd": 0
      },
      "scheme": [
        [
          31,
          4,
          28
        ],
        [
          30,
          5,
          92
        ],
        [
          12,
          13,
          88
        ],
        [
          58,
          3,
          62
        ],
        [
          11,
          8,
          40
        ],
        [
          15,
          14,
          56
        ],
        [
          6,
          30,
          48
        ],
        [
          3,
          63,
          96
        ],
        [
          2,
          44,
          32
        ],
        [
          81,
          1,
          64
        ],
        [
          32,
          3,
          44
        ],
        [
          57,
          1,
          50
        ],
        [
          1,
          1,
          19
        ],
        [
          24,
          2,
          76
        ],
        [
          1,
          100,
          64
        ],
        [
          7,
          24,
          112
        ],
        [
          59,
          2,
          82
        ],
        [
          9,
          10,
          8
        ]
      ]
    },
    {
      "target": "T8",
      "statement": "a rank-r bilinear algorithm for the truncated product of two degree-7 polynomials over F2 (the low 8 coefficients)",
      "rank": 23,
      "naive": 36,
      "equations": 512,
      "standing": "above",
      "publishedUpper": 22,
      "publishedLower": 19,
      "search": {
        "proposer": "flip@v1",
        "seeds": 12,
        "steps": 800000,
        "slack": 3,
        "pluses": 7889,
        "seconds": 220.6,
        "costUsd": 0
      },
      "scheme": [
        [
          15,
          31,
          176
        ],
        [
          6,
          61,
          252
        ],
        [
          48,
          7,
          32
        ],
        [
          14,
          22,
          8
        ],
        [
          121,
          2,
          192
        ],
        [
          4,
          18,
          152
        ],
        [
          7,
          60,
          164
        ],
        [
          2,
          115,
          18
        ],
        [
          11,
          10,
          200
        ],
        [
          3,
          78,
          206
        ],
        [
          157,
          1,
          128
        ],
        [
          3,
          77,
          142
        ],
        [
          12,
          29,
          56
        ],
        [
          81,
          3,
          64
        ],
        [
          1,
          59,
          4
        ],
        [
          1,
          165,
          128
        ],
        [
          19,
          14,
          112
        ],
        [
          21,
          11,
          224
        ],
        [
          41,
          6,
          160
        ],
        [
          20,
          15,
          16
        ],
        [
          1,
          1,
          155
        ],
        [
          2,
          113,
          210
        ],
        [
          6,
          38,
          216
        ]
      ]
    },
    {
      "target": "T9",
      "statement": "a rank-r bilinear algorithm for the truncated product of two degree-8 polynomials over F2 (the low 9 coefficients)",
      "rank": 27,
      "naive": 45,
      "equations": 729,
      "standing": "above",
      "publishedUpper": 26,
      "publishedLower": 21,
      "search": {
        "proposer": "flip@v1",
        "seeds": 12,
        "steps": 800000,
        "slack": 3,
        "pluses": 7907,
        "seconds": 355.4,
        "costUsd": 0
      },
      "scheme": [
        [
          78,
          75,
          448
        ],
        [
          26,
          30,
          496
        ],
        [
          7,
          5,
          460
        ],
        [
          413,
          1,
          256
        ],
        [
          39,
          8,
          288
        ],
        [
          32,
          61,
          64
        ],
        [
          1,
          1,
          29
        ],
        [
          24,
          28,
          368
        ],
        [
          11,
          33,
          40
        ],
        [
          6,
          4,
          340
        ],
        [
          3,
          2,
          274
        ],
        [
          4,
          64,
          192
        ],
        [
          33,
          9,
          96
        ],
        [
          75,
          76,
          448
        ],
        [
          38,
          48,
          64
        ],
        [
          223,
          166,
          384
        ],
        [
          161,
          2,
          128
        ],
        [
          17,
          19,
          144
        ],
        [
          1,
          321,
          256
        ],
        [
          14,
          42,
          72
        ],
        [
          221,
          165,
          384
        ],
        [
          3,
          246,
          128
        ],
        [
          10,
          39,
          488
        ],
        [
          15,
          45,
          136
        ],
        [
          18,
          16,
          272
        ],
        [
          114,
          6,
          192
        ],
        [
          2,
          3,
          326
        ]
      ]
    }
  ],
  "generated": "2026-08-31"
}