{"family": "golomb", "model": "baseline", "tag": "v0", "target": "(6, 17)", "proposal_raw": "(the family's baseline() construction)", "obj": "(0, 1, 3, 7, 12, 20)", "outcome": "refuted", "statement": "[0, 1, 3, 7, 12, 20] is a Golomb ruler with 6 marks and length <= 17", "witness": "length 20, 15 differences, bounds violated", "certificate": {"marks": [0, 1, 3, 7, 12, 20], "length": 20, "repeatedDifferences": []}, "key": "64acab25edcf8684", "latency_s": 0.0, "usage": null}
{"family": "golomb", "model": "baseline", "tag": "v0", "target": "(8, 34)", "proposal_raw": "(the family's baseline() construction)", "obj": "(0, 1, 3, 7, 12, 20, 30, 44)", "outcome": "refuted", "statement": "[0, 1, 3, 7, 12, 20, 30, 44] is a Golomb ruler with 8 marks and length <= 34", "witness": "length 44, 28 differences, bounds violated", "certificate": {"marks": [0, 1, 3, 7, 12, 20, 30, 44], "length": 44, "repeatedDifferences": []}, "key": "82f103345b568304", "latency_s": 0.0, "usage": null}
{"family": "golomb", "model": "baseline", "tag": "v0", "target": "(10, 55)", "proposal_raw": "(the family's baseline() construction)", "obj": "(0, 1, 3, 7, 12, 20, 30, 44, 65, 80)", "outcome": "refuted", "statement": "[0, 1, 3, 7, 12, 20, 30, 44, 65, 80] is a Golomb ruler with 10 marks and length <= 55", "witness": "length 80, 45 differences, bounds violated", "certificate": {"marks": [0, 1, 3, 7, 12, 20, 30, 44, 65, 80], "length": 80, "repeatedDifferences": []}, "key": "cb1dbc4d96173390", "latency_s": 0.0, "usage": null}
{"family": "golomb", "model": "baseline", "tag": "v0", "target": "(11, 72)", "proposal_raw": "(the family's baseline() construction)", "obj": "(0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96)", "outcome": "refuted", "statement": "[0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96] is a Golomb ruler with 11 marks and length <= 72", "witness": "length 96, 55 differences, bounds violated", "certificate": {"marks": [0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96], "length": 96, "repeatedDifferences": []}, "key": "850a36f1779cf8af", "latency_s": 0.0, "usage": null}
{"family": "golomb", "model": "baseline", "tag": "v0", "target": "(12, 85)", "proposal_raw": "(the family's baseline() construction)", "obj": "(0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122)", "outcome": "refuted", "statement": "[0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122] is a Golomb ruler with 12 marks and length <= 85", "witness": "length 122, 66 differences, bounds violated", "certificate": {"marks": [0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122], "length": 122, "repeatedDifferences": []}, "key": "4a7432bc675e4fd1", "latency_s": 0.0, "usage": null}
{"family": "golomb", "model": "baseline", "tag": "v0", "target": "(13, 106)", "proposal_raw": "(the family's baseline() construction)", "obj": "(0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122, 147)", "outcome": "refuted", "statement": "[0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122, 147] is a Golomb ruler with 13 marks and length <= 106", "witness": "length 147, 78 differences, bounds violated", "certificate": {"marks": [0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, 122, 147], "length": 147, "repeatedDifferences": []}, "key": "5f43a95d9569b3ac", "latency_s": 0.0, "usage": null}
{"family": "capset", "model": "baseline", "tag": "v0", "target": "(3, 9)", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1))", "outcome": "rejected", "statement": "a cap of size 8 in F_3^3", "witness": null, "certificate": null, "key": "0cbda4520fa19e54", "latency_s": 0.0, "usage": null}
{"family": "capset", "model": "baseline", "tag": "v0", "target": "(4, 20)", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (0, 0, 1, 1), (0, 1, 0, 0), (0, 1, 0, 1), (0, 1, 1, 0), (0, 1, 1, 1), (1, 0, 0, 0), (1, 0, 0, 1), (1, 0, 1, 0), (1, 0, 1, 1), (1, 1, 0, 0), (1, 1, 0, 1), (1, 1, 1, 0), (1, 1, 1, 1))", "outcome": "rejected", "statement": "a cap of size 16 in F_3^4", "witness": null, "certificate": null, "key": "6a53884a80b559bd", "latency_s": 0.0, "usage": null}
{"family": "capset", "model": "baseline", "tag": "v0", "target": "(5, 45)", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 0, 0, 0), (0, 0, 0, 0, 1), (0, 0, 0, 1, 0), (0, 0, 0, 1, 1), (0, 0, 1, 0, 0), (0, 0, 1, 0, 1), (0, 0, 1, 1, 0), (0, 0, 1, 1, 1), (0, 1, 0, 0, 0), (0, 1, 0, 0, 1), (0, 1, 0, 1, 0), (0, 1, 0, 1, 1), (0, 1, 1, 0, 0), (0, 1, 1, 0, 1), (0, 1, 1, 1, 0), (0, 1, 1, 1, 1), (1, 0, 0, 0, 0), (1, 0, 0, 0, 1), (1, 0, 0, 1, 0), (1, 0, 0, 1, 1), (1, 0, 1, 0, 0), (1, 0, 1, 0, 1), (1, 0, 1, 1, 0), (1, 0, 1, 1, 1), (1, 1, 0, 0, 0), (1, 1, 0, 0, 1), (1, 1, 0, 1, 0), (1, 1, 0, 1, 1), (1, 1, 1, 0, 0), (1, 1, 1, 0, 1), (1, 1, 1, 1, 0), (1, 1, 1, 1, 1))", "outcome": "rejected", "statement": "a cap of size 32 in F_3^5", "witness": null, "certificate": null, "key": "6a6f7f7efcbf6449", "latency_s": 0.0, "usage": null}
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{"family": "code", "model": "baseline", "tag": "v0", "target": "(7, 3, 16)", "proposal_raw": "(the family's baseline() construction)", "obj": "('0000000', '0000111', '0011001', '0011110', '0101010', '0101101', '0110011', '0110100', '1001011', '1001100', '1010010', '1010101', '1100001', '1100110', '1111000', '1111111')", "outcome": "certified", "statement": "a binary (7, 16, 3) code", "witness": "16 words, minimum distance 3", "certificate": {"words": ["0000000", "0000111", "0011001", "0011110", "0101010", "0101101", "0110011", "0110100", "1001011", "1001100", "1010010", "1010101", "1100001", "1100110", "1111000", "1111111"], "minDistance": 3, "closestPair": ["0000000", "0000111"]}, "key": "6bdb13b52f7299b4", "latency_s": 0.0, "usage": null}
{"family": "code", "model": "baseline", "tag": "v0", "target": "(8, 3, 20)", "proposal_raw": "(the family's baseline() construction)", "obj": "('00000000', '00000111', '00011001', '00011110', '00101010', '00101101', '00110011', '00110100', '01001011', '01001100', '01010010', '01010101', '01100001', '01100110', '01111000', '01111111')", "outcome": "rejected", "statement": "a binary (8, 16, 3) code", "witness": null, "certificate": null, "key": "0a337768f90c6ce4", "latency_s": 0.0, "usage": null}
{"family": "code", "model": "baseline", "tag": "v0", "target": "(10, 3, 72)", "proposal_raw": "(the family's baseline() construction)", "obj": "('0000000000', '0000000111', '0000011001', '0000011110', '0000101010', '0000101101', '0000110011', '0000110100', '0001001011', '0001001100', '0001010010', '0001010101', '0001100001', '0001100110', '0001111000', '0001111111', '0110000001', '0110000110', '0110011000', '0110011111', '0110101011', '0110101100', '0110110010', '0110110101', '0111001010', '0111001101', '0111010011', '0111010100', '0111100000', '0111100111', '0111111001', '0111111110', '1010000010', '1010000101', '1010011011', '1010011100', '1010101000', '1010101111', '1010110001', '1010110110', '1011001001', '1011001110', '1011010000', '1011010111', '1011100011', '1011100100', '1011111010', '1011111101', '1100000011', '1100000100', '1100011010', '1100011101', '1100101001', '1100101110', '1100110000', '1100110111', '1101001000', '1101001111', '1101010001', '1101010110', '1101100010', '1101100101', '1101111011', '1101111100')", "outcome": "rejected", "statement": "a binary (10, 64, 3) code", "witness": null, "certificate": null, "key": "33aba75c6ad27f9f", "latency_s": 0.0, "usage": null}
{"family": "code", "model": "baseline", "tag": "v0", "target": "(12, 4, 144)", "proposal_raw": "(the family's baseline() construction)", "obj": "('000000000000', '000000001111', '000000110011', '000000111100', '000001010101', '000001011010', '000001100110', '000001101001', '000010010110', '000010011001', '000010100101', '000010101010', '000011000011', '000011001100', '000011110000', '000011111111', '001100000011', '001100001100', '001100110000', '001100111111', '001101010110', '001101011001', '001101100101', '001101101010', '001110010101', '001110011010', '001110100110', '001110101001', '001111000000', '001111001111', '001111110011', '001111111100', '010100000101', '010100001010', '010100110110', '010100111001', '010101010000', '010101011111', '010101100011', '010101101100', '010110010011', '010110011100', '010110100000', '010110101111', '010111000110', '010111001001', '010111110101', '010111111010', '011000000110', '011000001001', '011000110101', '011000111010', '011001010011', '011001011100', '011001100000', '011001101111', '011010010000', '011010011111', '011010100011', '011010101100', '011011000101', '011011001010', '011011110110', '011011111001', '100100000110', '100100001001', '100100110101', '100100111010', '100101010011', '100101011100', '100101100000', '100101101111', '100110010000', '100110011111', '100110100011', '100110101100', '100111000101', '100111001010', '100111110110', '100111111001', '101000000101', '101000001010', '101000110110', '101000111001', '101001010000', '101001011111', '101001100011', '101001101100', '101010010011', '101010011100', '101010100000', '101010101111', '101011000110', '101011001001', '101011110101', '101011111010', '110000000011', '110000001100', '110000110000', '110000111111', '110001010110', '110001011001', '110001100101', '110001101010', '110010010101', '110010011010', '110010100110', '110010101001', '110011000000', '110011001111', '110011110011', '110011111100', '111100000000', '111100001111', '111100110011', '111100111100', '111101010101', '111101011010', '111101100110', '111101101001', '111110010110', '111110011001', '111110100101', '111110101010', '111111000011', '111111001100', '111111110000', '111111111111')", "outcome": "rejected", "statement": "a binary (12, 128, 4) code", "witness": null, "certificate": null, "key": "881b8bbaefb6e533", "latency_s": 0.0, "usage": null}
{"family": "code", "model": "baseline", "tag": "v0", "target": "(16, 6, 256)", "proposal_raw": "(the family's baseline() construction)", "obj": "('0000000000000000', '0000000000111111', '0000000111000111', '0000000111111000', '0000011001001011', '0000011001110100', '0000011110001100', '0000011110110011', '0000101010010101', '0000101010101010', '0000101101010010', '0000101101101101', '0000110011011110', '0000110011100001', '0000110100011001', '0000110100100110', '0011000001001101', '0011000001110010', '0011000110001010', '0011000110110101', '0011011000000110', '0011011000111001', '0011011111000001', '0011011111111110', '0011101011011000', '0011101011100111', '0011101100011111', '0011101100100000', '0011110010010011', '0011110010101100', '0011110101010100', '0011110101101011', '0101000010010110', '0101000010101001', '0101000101010001', '0101000101101110', '0101011011011101', '0101011011100010', '0101011100011010', '0101011100100101', '0101101000000011', '0101101000111100', '0101101111000100', '0101101111111011', '0101110001001000', '0101110001110111', '0101110110001111', '0101110110110000', '0110000011011011', '0110000011100100', '0110000100011100', '0110000100100011', '0110011010010000', '0110011010101111', '0110011101010111', '0110011101101000', '0110101001001110', '0110101001110001', '0110101110001001', '0110101110110110', '0110110000000101', '0110110000111010', '0110110111000010', '0110110111111101', '1001001001010111', '1001001001101000', '1001001110010000', '1001001110101111', '1001010000011100', '1001010000100011', '1001010111011011', '1001010111100100', '1001100011000010', '1001100011111101', '1001100100000101', '1001100100111010', '1001111010001001', '1001111010110110', '1001111101001110', '1001111101110001', '1010001000011010', '1010001000100101', '1010001111011101', '1010001111100010', '1010010001010001', '1010010001101110', '1010010110010110', '1010010110101001', '1010100010001111', '1010100010110000', '1010100101001000', '1010100101110111', '1010111011000100', '1010111011111011', '1010111100000011', '1010111100111100', '1100001011000001', '1100001011111110', '1100001100000110', '1100001100111001', '1100010010001010', '1100010010110101', '1100010101001101', '1100010101110010', '1100100001010100', '1100100001101011', '1100100110010011', '1100100110101100', '1100111000011111', '1100111000100000', '1100111111011000', '1100111111100111', '1111001010001100', '1111001010110011', '1111001101001011', '1111001101110100', '1111010011000111', '1111010011111000', '1111010100000000', '1111010100111111', '1111100000011001', '1111100000100110', '1111100111011110', '1111100111100001', '1111111001010010', '1111111001101101', '1111111110010101', '1111111110101010')", "outcome": "rejected", "statement": "a binary (16, 128, 6) code", "witness": null, "certificate": null, "key": "5950f1c3f3ad206d", "latency_s": 0.0, "usage": null}
{"family": "code", "model": "baseline", "tag": "v0", "target": "(10, 3, 73)", "proposal_raw": "(the family's baseline() construction)", "obj": "('0000000000', '0000000111', '0000011001', '0000011110', '0000101010', '0000101101', '0000110011', '0000110100', '0001001011', '0001001100', '0001010010', '0001010101', '0001100001', '0001100110', '0001111000', '0001111111', '0110000001', '0110000110', '0110011000', '0110011111', '0110101011', '0110101100', '0110110010', '0110110101', '0111001010', '0111001101', '0111010011', '0111010100', '0111100000', '0111100111', '0111111001', '0111111110', '1010000010', '1010000101', '1010011011', '1010011100', '1010101000', '1010101111', '1010110001', '1010110110', '1011001001', '1011001110', '1011010000', '1011010111', '1011100011', '1011100100', '1011111010', '1011111101', '1100000011', '1100000100', '1100011010', '1100011101', '1100101001', '1100101110', '1100110000', '1100110111', '1101001000', '1101001111', '1101010001', '1101010110', '1101100010', '1101100101', '1101111011', '1101111100')", "outcome": "rejected", "statement": "a binary (10, 64, 3) code", "witness": null, "certificate": null, "key": "33aba75c6ad27f9f", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(3, 4, 8)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 8, (1, 4))", "outcome": "certified", "statement": "R(3,4) > 8", "witness": "8 vertices; clique of size 3: no; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 8, "data": [1, 4]}, "cliqueFound": false, "independentFound": false}, "key": "903552cff478b32a", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(3, 5, 13)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 13, (1, 3, 4, 9, 10, 12))", "outcome": "refuted", "statement": "R(3,5) > 13", "witness": "13 vertices; clique of size 3: yes; independent set of size 5: no", "certificate": {"graph": {"kind": "circulant", "n": 13, "data": [1, 3, 4, 9, 10, 12]}, "cliqueFound": true, "independentFound": false}, "key": "cf7ac50a0e04e819", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(4, 4, 17)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 17, (1, 2, 4, 8, 9, 13, 15, 16))", "outcome": "certified", "statement": "R(4,4) > 17", "witness": "17 vertices; clique of size 4: no; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8, 9, 13, 15, 16]}, "cliqueFound": false, "independentFound": false}, "key": "918c4890faf99cb1", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(3, 6, 17)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 17, (1, 2, 4, 8, 9, 13, 15, 16))", "outcome": "refuted", "statement": "R(3,6) > 17", "witness": "17 vertices; clique of size 3: yes; independent set of size 6: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8, 9, 13, 15, 16]}, "cliqueFound": true, "independentFound": false}, "key": "918c4890faf99cb1", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(4, 5, 24)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 24, (1, 4, 9, 12, 16))", "outcome": "refuted", "statement": "R(4,5) > 24", "witness": "24 vertices; clique of size 4: yes; independent set of size 5: no", "certificate": {"graph": {"kind": "circulant", "n": 24, "data": [1, 4, 9, 12, 16]}, "cliqueFound": true, "independentFound": false}, "key": "fcb8341b5a190d0b", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(3, 9, 35)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 35, (1, 4, 9, 11, 14, 15, 16, 21, 25, 29, 30))", "outcome": "refuted", "statement": "R(3,9) > 35", "witness": "35 vertices; clique of size 3: yes; independent set of size 9: no", "certificate": {"graph": {"kind": "circulant", "n": 35, "data": [1, 4, 9, 11, 14, 15, 16, 21, 25, 29, 30]}, "cliqueFound": true, "independentFound": false}, "key": "806bdbfce9beb6a2", "latency_s": 0.0, "usage": null}
{"family": "ramsey", "model": "baseline", "tag": "v0", "target": "(4, 6, 36)", "proposal_raw": "(the family's baseline() construction)", "obj": "('circulant', 36, (1, 4, 9, 13, 16, 25, 28))", "outcome": "refuted", "statement": "R(4,6) > 36", "witness": "36 vertices; clique of size 4: no; independent set of size 6: yes", "certificate": {"graph": {"kind": "circulant", "n": 36, "data": [1, 4, 9, 13, 16, 25, 28]}, "cliqueFound": false, "independentFound": true}, "key": "b588502ecc194e30", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.6", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.6 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.7", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.7 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.725", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.725 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.77", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.77 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.778", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.778 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.77898", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.77898 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.77898884", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.77898884 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
{"family": "sumdiff3b", "model": "baseline", "tag": "v0", "target": "1.7789889", "proposal_raw": "(the family's baseline() construction)", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.7789889 from a 9-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "bb1fa6c196d04fe7", "latency_s": 0.0, "usage": null}
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{"family": "golomb", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(8, 34)", "proposal_raw": "[0,1,4,9,15,22,32,34]", "obj": "(0, 1, 4, 9, 15, 22, 32, 34)", "outcome": "certified", "statement": "[0, 1, 4, 9, 15, 22, 32, 34] is a Golomb ruler with 8 marks and length <= 34", "witness": "length 34, 28 differences", "certificate": {"marks": [0, 1, 4, 9, 15, 22, 32, 34], "length": 34, "repeatedDifferences": []}, "key": "aea4f96e817e9201", "latency_s": 0.837, "usage": {"in": 90, "out": 20, "usd": 0.00019}}
{"family": "golomb", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(10, 55)", "proposal_raw": "[0,1,6,10,23,26,34,41,53,55]", "obj": "(0, 1, 6, 10, 23, 26, 34, 41, 53, 55)", "outcome": "certified", "statement": "[0, 1, 6, 10, 23, 26, 34, 41, 53, 55] is a Golomb ruler with 10 marks and length <= 55", "witness": "length 55, 45 differences", "certificate": {"marks": [0, 1, 6, 10, 23, 26, 34, 41, 53, 55], "length": 55, "repeatedDifferences": []}, "key": "f6cbb15c637c5874", "latency_s": 0.902, "usage": {"in": 90, "out": 24, "usd": 0.00021}}
{"family": "golomb", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(11, 72)", "proposal_raw": "[0,1,6,10,23,26,34,41,53,55,72]", "obj": "(0, 1, 6, 10, 23, 26, 34, 41, 53, 55, 72)", "outcome": "refuted", "statement": "[0, 1, 6, 10, 23, 26, 34, 41, 53, 55, 72] is a Golomb ruler with 11 marks and length <= 72", "witness": "length 72, 55 differences, repeated [17, 19, 31]", "certificate": {"marks": [0, 1, 6, 10, 23, 26, 34, 41, 53, 55, 72], "length": 72, "repeatedDifferences": [17, 19, 31]}, "key": "6f4bed726ec29ced", "latency_s": 0.859, "usage": {"in": 90, "out": 26, "usd": 0.00022}}
{"family": "golomb", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(12, 85)", "proposal_raw": "[0,1,4,9,15,22,32,34,41,60,61,77]", "obj": "(0, 1, 4, 9, 15, 22, 32, 34, 41, 60, 61, 77)", "outcome": "refuted", "statement": "[0, 1, 4, 9, 15, 22, 32, 34, 41, 60, 61, 77] is a Golomb ruler with 12 marks and length <= 85", "witness": "length 77, 66 differences, repeated [1, 7, 9]", "certificate": {"marks": [0, 1, 4, 9, 15, 22, 32, 34, 41, 60, 61, 77], "length": 77, "repeatedDifferences": [1, 7, 9]}, "key": "8996e195618db419", "latency_s": 0.924, "usage": {"in": 90, "out": 28, "usd": 0.00023}}
{"family": "golomb", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(13, 106)", "proposal_raw": "[0, 1, 3, 6, 13, 20, 31, 35, 72, 78, 81, 85, 106]", "obj": "(0, 1, 3, 6, 13, 20, 31, 35, 72, 78, 81, 85, 106)", "outcome": "refuted", "statement": "[0, 1, 3, 6, 13, 20, 31, 35, 72, 78, 81, 85, 106] is a Golomb ruler with 13 marks and length <= 106", "witness": "length 106, 78 differences, repeated [3, 4, 6]", "certificate": {"marks": [0, 1, 3, 6, 13, 20, 31, 35, 72, 78, 81, 85, 106], "length": 106, "repeatedDifferences": [3, 4, 6]}, "key": "f6e6a4d40a7eac62", "latency_s": 0.905, "usage": {"in": 90, "out": 42, "usd": 0.0003}}
{"family": "capset", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 9)", "proposal_raw": "```json\n[\n  [0, 0, 0],\n  [1, 0, 1],\n  [2, 0, 2],\n  [0, 1, 2],\n  [1, 1, 0],\n  [2, 1, 1],\n  [0, 2, 1],\n  [1, 2, 2],\n  [2, 2, 0]\n]\n```", "obj": "((0, 0, 0), (0, 1, 2), (0, 2, 1), (1, 0, 1), (1, 1, 0), (1, 2, 2), (2, 0, 2), (2, 1, 1), (2, 2, 0))", "outcome": "refuted", "statement": "a cap of size 9 in F_3^3", "witness": "9 distinct points, a line [[0, 0, 0], [0, 1, 2], [0, 2, 1]]", "certificate": {"points": [[0, 0, 0], [0, 1, 2], [0, 2, 1], [1, 0, 1], [1, 1, 0], [1, 2, 2], [2, 0, 2], [2, 1, 1], [2, 2, 0]], "line": [[0, 0, 0], [0, 1, 2], [0, 2, 1]]}, "key": "6d77697e81e7776b", "latency_s": 1.099, "usage": {"in": 105, "out": 110, "usd": 0.000655}}
{"family": "capset", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(4, 20)", "proposal_raw": "```json\n[\n  [0, 0, 0, 0],\n  [1, 0, 0, 1],\n  [2, 0, 0, 2],\n  [0, 1, 1, 1],\n  [0, 2, 2, 2],\n  [1, 1, 0, 2],\n  [1, 2, 0, 1],\n  [2, 1, 0, 0],\n  [2, 2, 0, 0],\n  [0, 1, 2, 0],\n  [0, 2, 1, 0],\n  [1, 1, 1, 0],\n  [1, 2, 2, 0],\n  [2, 1, 2, 0],\n  [2, 2, 1, 0],\n  [1, 0, 1, 2],\n  [1, 0, 2, 1],\n  [2, 0, 1, 1],\n  [2, 0, 2, 2],\n  [0, 0, 1, 2]\n]\n```", "obj": "((0, 0, 0, 0), (0, 0, 1, 2), (0, 1, 1, 1), (0, 1, 2, 0), (0, 2, 1, 0), (0, 2, 2, 2), (1, 0, 0, 1), (1, 0, 1, 2), (1, 0, 2, 1), (1, 1, 0, 2), (1, 1, 1, 0), (1, 2, 0, 1), (1, 2, 2, 0), (2, 0, 0, 2), (2, 0, 1, 1), (2, 0, 2, 2), (2, 1, 0, 0), (2, 1, 2, 0), (2, 2, 0, 0), (2, 2, 1, 0))", "outcome": "refuted", "statement": "a cap of size 20 in F_3^4", "witness": "20 distinct points, a line [[0, 0, 0, 0], [0, 1, 1, 1], [0, 2, 2, 2]]", "certificate": {"points": [[0, 0, 0, 0], [0, 0, 1, 2], [0, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 0], [0, 2, 2, 2], [1, 0, 0, 1], [1, 0, 1, 2], [1, 0, 2, 1], [1, 1, 0, 2], [1, 1, 1, 0], [1, 2, 0, 1], [1, 2, 2, 0], [2, 0, 0, 2], [2, 0, 1, 1], [2, 0, 2, 2], [2, 1, 0, 0], [2, 1, 2, 0], [2, 2, 0, 0], [2, 2, 1, 0]], "line": [[0, 0, 0, 0], [0, 1, 1, 1], [0, 2, 2, 2]]}, "key": "5a85b7dec6121abf", "latency_s": 2.925, "usage": {"in": 105, "out": 291, "usd": 0.00156}}
{"family": "capset", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(5, 45)", "proposal_raw": "```json\n[[0,0,0,0,0],[0,0,0,1,1],[0,0,0,2,2],[0,1,1,0,0],[0,1,1,1,1],[0,1,1,2,2],[0,2,2,0,0],[0,2,2,1,1],[0,2,2,2,2],[1,0,1,0,1],[1,0,1,1,2],[1,0,1,2,0],[1,1,2,0,1],[1,1,2,1,2],[1,1,2,2,0],[1,2,0,0,1],[1,2,0,1,2],[1,2,0,2,0],[2,0,2,0,2],[2,0,2,1,0],[2,0,2,2,1],[2,1,0,0,2],[2,1,0,1,0],[2,1,0,2,1],[2,2,1,0,2],[2,2,1,1,0],[2,2,1,2,1],[0,0,1,1,2],[0,0,2,2,1],[0,1,0,2,1],[0,1,2,1,0],[0,2,1,1,0],[0,2,0,2,1],[1,0,0,1,0],[1,0,2,2,0],[1,1,0,2,2],[1,1,1,1,1],[1,2,1,0,2],[1,2,2,2,1],[2,0,0,0,1],[2,0,1,1,1],[2,1,1,0,0],[2,1,2,0,2],[2,2,0,1,2],[2,2,2,0,0]]\n```", "obj": "((0, 0, 0, 0, 0), (0, 0, 0, 1, 1), (0, 0, 0, 2, 2), (0, 0, 1, 1, 2), (0, 0, 2, 2, 1), (0, 1, 0, 2, 1), (0, 1, 1, 0, 0), (0, 1, 1, 1, 1), (0, 1, 1, 2, 2), (0, 1, 2, 1, 0), (0, 2, 0, 2, 1), (0, 2, 1, 1, 0), (0, 2, 2, 0, 0), (0, 2, 2, 1, 1), (0, 2, 2, 2, 2), (1, 0, 0, 1, 0), (1, 0, 1, 0, 1), (1, 0, 1, 1, 2), (1, 0, 1, 2, 0), (1, 0, 2, 2, 0), (1, 1, 0, 2, 2), (1, 1, 1, 1, 1), (1, 1, 2, 0, 1), (1, 1, 2, 1, 2), (1, 1, 2, 2, 0), (1, 2, 0, 0, 1), (1, 2, 0, 1, 2), (1, 2, 0, 2, 0), (1, 2, 1, 0, 2), (1, 2, 2, 2, 1), (2, 0, 0, 0, 1), (2, 0, 1, 1, 1), (2, 0, 2, 0, 2), (2, 0, 2, 1, 0), (2, 0, 2, 2, 1), (2, 1, 0, 0, 2), (2, 1, 0, 1, 0), (2, 1, 0, 2, 1), (2, 1, 1, 0, 0), (2, 1, 2, 0, 2), (2, 2, 0, 1, 2), (2, 2, 1, 0, 2), (2, 2, 1, 1, 0), (2, 2, 1, 2, 1), (2, 2, 2, 0, 0))", "outcome": "refuted", "statement": "a cap of size 45 in F_3^5", "witness": "45 distinct points, a line [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 2, 2]]", "certificate": {"points": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 2, 2], [0, 0, 1, 1, 2], [0, 0, 2, 2, 1], [0, 1, 0, 2, 1], [0, 1, 1, 0, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 2], [0, 1, 2, 1, 0], [0, 2, 0, 2, 1], [0, 2, 1, 1, 0], [0, 2, 2, 0, 0], [0, 2, 2, 1, 1], [0, 2, 2, 2, 2], [1, 0, 0, 1, 0], [1, 0, 1, 0, 1], [1, 0, 1, 1, 2], [1, 0, 1, 2, 0], [1, 0, 2, 2, 0], [1, 1, 0, 2, 2], [1, 1, 1, 1, 1], [1, 1, 2, 0, 1], [1, 1, 2, 1, 2], [1, 1, 2, 2, 0], [1, 2, 0, 0, 1], [1, 2, 0, 1, 2], [1, 2, 0, 2, 0], [1, 2, 1, 0, 2], [1, 2, 2, 2, 1], [2, 0, 0, 0, 1], [2, 0, 1, 1, 1], [2, 0, 2, 0, 2], [2, 0, 2, 1, 0], [2, 0, 2, 2, 1], [2, 1, 0, 0, 2], [2, 1, 0, 1, 0], [2, 1, 0, 2, 1], [2, 1, 1, 0, 0], [2, 1, 2, 0, 2], [2, 2, 0, 1, 2], [2, 2, 1, 0, 2], [2, 2, 1, 1, 0], [2, 2, 1, 2, 1], [2, 2, 2, 0, 0]], "line": [[0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 2, 2]]}, "key": "588d57d369f5f612", "latency_s": 4.115, "usage": {"in": 105, "out": 459, "usd": 0.0024}}
{"family": "capset", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(6, 112)", "proposal_raw": "```json\n[[0,0,0,0,0,0], [0,0,0,0,1,1], [0,0,0,0,2,2], [0,0,1,1,0,1], [0,0,1,1,1,2], [0,0,1,1,2,0], [0,0,2,2,0,2], [0,0,2,2,1,0], [0,0,2,2,2,1], [0,1,0,1,0,2], [0,1,0,1,1,0], [0,1,0,1,2,1], [0,1,1,2,0,0], [0,1,1,2,1,1], [0,1,1,2,2,2], [0,1,2,0,0,1], [0,1,2,0,1,2], [0,1,2,0,2,0], [0,2,0,2,0,1], [0,2,0,2,1,2], [0,2,0,2,2,0], [0,2,1,0,0,2], [0,2,1,0,1,0], [0,2,1,0,2,1], [0,2,2,1,0,0], [0,2,2,1,1,1], [0,2,2,1,2,2], [1,0,0,1,1,2], [1,0,0,1,2,0], [1,0,1,2,0,2], [1,0,1,2,1,0], [1,0,1,2,2,1], [1,0,2,0,0,0], [1,0,2,0,1,1], [1,0,2,0,2,2], [1,1,0,2,0,0], [1,1,0,2,1,1], [1,1,0,2,2,2], [1,1,1,0,0,1], [1,1,1,0,1,2], [1,1,1,0,2,0], [1,1,2,1,0,2], [1,1,2,1,1,0], [1,1,2,1,2,1], [1,2,0,0,0,2], [1,2,0,0,1,0], [1,2,0,0,2,1], [1,2,1,1,0,0], [1,2,1,1,1,1], [1,2,1,1,2,2], [1,2,2,2,0,1], [1,2,2,2,1,2], [1,2,2,2,2,0], [2,0,0,2,1,0], [2,0,0,2,2,1], [2,0,1,0,1,1], [2,0,1,0,2,2], [2,0,2,1,0,0], [2,0,2,1,1,1], [2,0,2,1,2,2], [2,1,0,0,0,1], [2,1,0,0,1,2], [2,1,0,0,2,0], [2,1,1,1,0,2], [2,1,1,1,1,0], [2,1,1,1,2,1], [2,1,2,2,0,0], [2,1,2,2,1,1], [2,1,2,2,2,2], [2,2,0,1,0,2], [2,2,0,1,1,0], [2,2,0,1,2,1], [2,2,1,2,0,1], [2,2,1,2,1,2], [2,2,1,2,2,0], [2,2,2,0,0,2], [2,2,2,0,1,0], [2,2,2,0,2,1], [0,0,0,1,2,1], [0,0,0,2,1,2], [0,0,1,0,2,0], [0,0,2,2,1,1], [0,1,0,2,2,2], [0,1,1,1,0,2], [0,1,2,1,1,0], [0,2,0,1,1,0], [0,2,1,2,2,1], [0,2,2,0,1,2], [1,0,0,0,1,1], [1,0,1,1,2,2], [1,0,2,2,0,1], [1,1,0,0,2,1], [1,1,1,2,1,0], [1,1,2,0,0,2], [1,2,0,1,1,1], [1,2,1,0,0,1], [1,2,2,1,2,0], [2,0,0,0,2,2], [2,0,1,2,0,0], [2,0,2,0,1,2], [2,1,0,2,0,2], [2,1,1,0,2,0], [2,1,2,1,0,1], [2,2,0,0,0,1], [2,2,1,1,1,2], [2,2,2,2,2,0]]\n```", "obj": "((0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1), (0, 0, 0, 0, 2, 2), (0, 0, 0, 1, 2, 1), (0, 0, 0, 2, 1, 2), (0, 0, 1, 0, 2, 0), (0, 0, 1, 1, 0, 1), (0, 0, 1, 1, 1, 2), (0, 0, 1, 1, 2, 0), (0, 0, 2, 2, 0, 2), (0, 0, 2, 2, 1, 0), (0, 0, 2, 2, 1, 1), (0, 0, 2, 2, 2, 1), (0, 1, 0, 1, 0, 2), (0, 1, 0, 1, 1, 0), (0, 1, 0, 1, 2, 1), (0, 1, 0, 2, 2, 2), (0, 1, 1, 1, 0, 2), (0, 1, 1, 2, 0, 0), (0, 1, 1, 2, 1, 1), (0, 1, 1, 2, 2, 2), (0, 1, 2, 0, 0, 1), (0, 1, 2, 0, 1, 2), (0, 1, 2, 0, 2, 0), (0, 1, 2, 1, 1, 0), (0, 2, 0, 1, 1, 0), (0, 2, 0, 2, 0, 1), (0, 2, 0, 2, 1, 2), (0, 2, 0, 2, 2, 0), (0, 2, 1, 0, 0, 2), (0, 2, 1, 0, 1, 0), (0, 2, 1, 0, 2, 1), (0, 2, 1, 2, 2, 1), (0, 2, 2, 0, 1, 2), (0, 2, 2, 1, 0, 0), (0, 2, 2, 1, 1, 1), (0, 2, 2, 1, 2, 2), (1, 0, 0, 0, 1, 1), (1, 0, 0, 1, 1, 2), (1, 0, 0, 1, 2, 0), (1, 0, 1, 1, 2, 2), (1, 0, 1, 2, 0, 2), (1, 0, 1, 2, 1, 0), (1, 0, 1, 2, 2, 1), (1, 0, 2, 0, 0, 0), (1, 0, 2, 0, 1, 1), (1, 0, 2, 0, 2, 2), (1, 0, 2, 2, 0, 1), (1, 1, 0, 0, 2, 1), (1, 1, 0, 2, 0, 0), (1, 1, 0, 2, 1, 1), (1, 1, 0, 2, 2, 2), (1, 1, 1, 0, 0, 1), (1, 1, 1, 0, 1, 2), (1, 1, 1, 0, 2, 0), (1, 1, 1, 2, 1, 0), (1, 1, 2, 0, 0, 2), (1, 1, 2, 1, 0, 2), (1, 1, 2, 1, 1, 0), (1, 1, 2, 1, 2, 1), (1, 2, 0, 0, 0, 2), (1, 2, 0, 0, 1, 0), (1, 2, 0, 0, 2, 1), (1, 2, 0, 1, 1, 1), (1, 2, 1, 0, 0, 1), (1, 2, 1, 1, 0, 0), (1, 2, 1, 1, 1, 1), (1, 2, 1, 1, 2, 2), (1, 2, 2, 1, 2, 0), (1, 2, 2, 2, 0, 1), (1, 2, 2, 2, 1, 2), (1, 2, 2, 2, 2, 0), (2, 0, 0, 0, 2, 2), (2, 0, 0, 2, 1, 0), (2, 0, 0, 2, 2, 1), (2, 0, 1, 0, 1, 1), (2, 0, 1, 0, 2, 2), (2, 0, 1, 2, 0, 0), (2, 0, 2, 0, 1, 2), (2, 0, 2, 1, 0, 0), (2, 0, 2, 1, 1, 1), (2, 0, 2, 1, 2, 2), (2, 1, 0, 0, 0, 1), (2, 1, 0, 0, 1, 2), (2, 1, 0, 0, 2, 0), (2, 1, 0, 2, 0, 2), (2, 1, 1, 0, 2, 0), (2, 1, 1, 1, 0, 2), (2, 1, 1, 1, 1, 0), (2, 1, 1, 1, 2, 1), (2, 1, 2, 1, 0, 1), (2, 1, 2, 2, 0, 0), (2, 1, 2, 2, 1, 1), (2, 1, 2, 2, 2, 2), (2, 2, 0, 0, 0, 1), (2, 2, 0, 1, 0, 2), (2, 2, 0, 1, 1, 0), (2, 2, 0, 1, 2, 1), (2, 2, 1, 1, 1, 2), (2, 2, 1, 2, 0, 1), (2, 2, 1, 2, 1, 2), (2, 2, 1, 2, 2, 0), (2, 2, 2, 0, 0, 2), (2, 2, 2, 0, 1, 0), (2, 2, 2, 0, 2, 1), (2, 2, 2, 2, 2, 0))", "outcome": "rejected", "statement": "a cap of size 106 in F_3^6", "witness": null, "certificate": null, "key": "19c4664d9f63e312", "latency_s": 8.134, "usage": {"in": 105, "out": 1386, "usd": 0.007035}}
{"family": "capset", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(7, 236)", "proposal_raw": "```json\n[[0,0,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,0,2],[0,0,0,0,0,1,0],[0,0,0,0,0,1,1],[0,0,0,0,0,2,0],[0,0,0,0,0,2,2],[0,0,0,0,1,0,0],[0,0,0,0,1,0,1],[0,0,0,0,1,1,0],[0,0,0,0,1,2,0],[0,0,0,0,2,0,0],[0,0,0,0,2,0,2],[0,0,0,0,2,2,0],[0,0,0,1,0,0,0],[0,0,0,1,0,0,1],[0,0,0,1,0,1,0],[0,0,0,1,0,2,0],[0,0,0,1,1,0,0],[0,0,0,1,2,0,0],[0,0,0,2,0,0,0],[0,0,0,2,0,0,2],[0,0,0,2,0,2,0],[0,0,0,2,2,0,0],[0,0,1,0,0,0,0],[0,0,1,0,0,0,1],[0,0,1,0,0,1,0],[0,0,1,0,0,2,0],[0,0,1,0,1,0,0],[0,0,1,0,2,0,0],[0,0,1,1,0,0,0],[0,0,1,2,0,0,0],[0,0,2,0,0,0,0],[0,0,2,0,0,0,2],[0,0,2,0,0,2,0],[0,0,2,0,2,0,0],[0,0,2,2,0,0,0],[0,1,0,0,0,0,0],[0,1,0,0,0,0,1],[0,1,0,0,0,1,0],[0,1,0,0,1,0,0],[0,1,0,1,0,0,0],[0,1,0,2,0,0,0],[0,1,1,0,0,0,0],[0,1,1,0,0,1,1],[0,1,1,1,1,0,0],[0,1,1,2,2,0,0],[0,1,2,0,0,0,0],[0,1,2,0,0,2,2],[0,1,2,1,2,0,0],[0,1,2,2,1,0,0],[0,2,0,0,0,0,0],[0,2,0,0,0,0,2],[0,2,0,0,0,2,0],[0,2,0,0,2,0,0],[0,2,0,2,0,0,0],[0,2,1,0,0,0,0],[0,2,1,0,0,2,2],[0,2,1,1,2,0,0],[0,2,1,2,1,0,0],[0,2,2,0,0,0,0],[0,2,2,0,0,1,1],[0,2,2,1,1,0,0],[0,2,2,2,2,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0,1],[1,0,0,0,0,1,0],[1,0,0,0,1,0,0],[1,0,0,1,0,0,0],[1,0,0,2,0,0,0],[1,0,1,0,0,0,0],[1,0,1,0,0,1,1],[1,0,1,1,1,0,0],[1,0,1,2,2,0,0],[1,0,2,0,0,0,0],[1,0,2,0,0,2,2],[1,0,2,1,2,0,0],[1,0,2,2,1,0,0],[1,1,0,0,0,0,0],[1,1,0,0,0,1,1],[1,1,0,1,1,0,0],[1,1,0,2,2,0,0],[1,1,1,0,0,0,0],[1,1,1,0,0,0,2],[1,1,1,0,1,2,0],[1,1,1,1,0,1,0],[1,1,1,2,0,2,0],[1,1,2,0,0,0,0],[1,1,2,0,1,1,0],[1,1,2,1,0,2,0],[1,1,2,2,0,0,0],[1,2,0,0,0,0,0],[1,2,0,0,0,2,2],[1,2,0,1,2,0,0],[1,2,0,2,1,0,0],[1,2,1,0,0,0,0],[1,2,1,0,0,1,1],[1,2,1,1,2,0,0],[1,2,1,2,1,0,0],[1,2,2,0,0,0,0],[1,2,2,0,2,2,0],[1,2,2,2,0,1,0],[1,2,2,1,0,0,0],[2,0,0,0,0,0,0],[2,0,0,0,0,0,2],[2,0,0,0,0,2,0],[2,0,0,0,2,0,0],[2,0,0,2,0,0,0],[2,0,1,0,0,0,0],[2,0,1,0,0,2,2],[2,0,1,1,2,0,0],[2,0,1,2,1,0,0],[2,0,2,0,0,0,0],[2,0,2,0,0,1,1],[2,0,2,1,1,0,0],[2,0,2,2,2,0,0],[2,1,0,0,0,0,0],[2,1,0,0,0,1,1],[2,1,0,1,1,0,0],[2,1,0,2,2,0,0],[2,1,1,0,0,0,0],[2,1,1,0,2,2,0],[2,1,1,2,0,1,0],[2,1,1,1,0,0,0],[2,1,2,0,0,0,0],[2,1,2,0,0,0,2],[2,1,2,0,1,1,0],[2,1,2,1,0,2,0],[2,2,0,0,0,0,0],[2,2,0,0,0,2,2],[2,2,0,1,2,0,0],[2,2,0,2,1,0,0],[2,2,1,0,0,0,0],[2,2,1,0,0,0,2],[2,2,1,0,2,1,0],[2,2,1,2,0,2,0],[2,2,2,0,0,0,0],[2,2,2,0,0,1,1],[2,2,2,1,1,0,0],[2,2,2,2,2,0,0],[0,1,1,0,0,0,1],[0,1,1,0,0,2,2],[0,1,1,1,2,0,0],[0,1,1,2,1,0,0],[0,2,1,0,0,0,1],[0,2,1,0,0,1,1],[0,2,1,2,1,0,0],[0,2,2,0,0,0,2],[0,2,2,0,0,2,2],[0,2,2,1,2,0,0],[1,0,1,0,0,0,1],[1,0,1,1,2,0,0],[1,0,1,2,1,0,0],[1,0,2,0,0,0,2],[1,0,2,0,0,1,1],[1,0,2,2,1,0,0],[1,1,1,0,0,0,1],[1,1,1,0,0,2,2],[1,1,1,2,0,1,0],[1,1,2,0,0,0,2],[1,1,2,0,1,2,0],[1,1,2,2,0,1,0],[1,2,1,0,0,0,1],[1,2,1,0,0,2,2],[1,2,1,2,1,0,0],[1,2,2,0,0,0,2],[1,2,2,0,2,1,0],[1,2,2,1,0,0,0],[2,0,1,0,0,0,2],[2,0,1,0,0,1,1],[2,0,1,2,1,0,0],[2,0,2,0,0,0,2],[2,0,2,0,0,2,2],[2,0,2,2,1,0,0],[2,1,1,0,0,0,1],[2,1,1,0,0,1,1],[2,1,1,1,0,0,0],[2,1,2,0,0,0,1],[2,1,2,0,0,2,2],[2,1,2,2,0,2,0],[2,2,1,0,0,0,1],[2,2,1,0,0,2,2],[2,2,1,1,2,0,0],[2,2,2,0,0,0,1],[2,2,2,0,0,2,2],[2,2,2,2,1,0,0]]\n```", 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{"family": "capset", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(7, 237)", "proposal_raw": 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1],[2,0,2,0,0,0,0],[2,0,2,0,0,0,1],[2,0,2,0,0,2,2],[2,0,2,0,1,0,2],[2,0,2,0,2,0,1],[2,0,2,0,2,1,0],[2,0,2,1,0,0,2],[2,0,2,1,0,2,1],[2,0,2,1,1,0,0],[2,0,2,1,2,0,2],[2,0,2,2,0,0,1],[2,0,2,2,0,1,0],[2,0,2,2,2,0,0],[2,1,0,0,0,0,0],[2,1,0,0,0,1,2],[2,1,0,0,1,0,1],[2,1,0,0,1,2,2],[2,1,0,0,2,0,2],[2,1,0,1,0,0,2],[2,1,0,1,1,0,1],[2,1,0,1,2,1,0],[2,1,0,2,0,0,1],[2,1,0,2,1,0,0],[2,1,0,2,2,1,1],[2,1,1,0,0,0,1],[2,1,1,0,0,2,0],[2,1,1,0,1,0,2],[2,1,1,0,2,1,1],[2,1,1,1,0,0,0],[2,1,1,1,0,2,1],[2,1,1,1,2,0,2],[2,1,1,2,0,0,1],[2,1,1,2,1,0,0],[2,1,1,2,2,1,2],[2,1,2,0,0,0,0],[2,1,2,0,0,0,2],[2,1,2,0,0,2,1],[2,1,2,0,2,0,2],[2,1,2,0,2,1,0],[2,1,2,1,0,0,1],[2,1,2,1,1,0,0],[2,1,2,1,2,1,1],[2,1,2,2,0,0,2],[2,1,2,2,0,2,0],[2,1,2,2,1,0,2],[2,1,2,2,2,2,0],[2,2,0,0,0,0,1],[2,2,0,0,0,2,2],[2,2,0,0,1,0,2],[2,2,0,0,2,0,0],[2,2,0,0,2,1,1],[2,2,0,1,0,0,0],[2,2,0,1,0,2,1],[2,2,0,1,1,0,2],[2,2,0,1,2,1,0],[2,2,0,2,0,0,2],[2,2,0,2,0,1,0],[2,2,0,2,1,0,1],[2,2,1,0,0,0,2],[2,2,1,0,0,1,0],[2,2,1,0,1,0,0],[2,2,1,0,2,2,1],[2,2,1,1,0,0,1],[2,2,1,1,1,0,2],[2,2,1,1,2,1,0],[2,2,1,2,0,0,0],[2,2,1,2,0,2,2],[2,2,1,2,2,0,1],[2,2,2,0,0,0,0],[2,2,2,0,0,0,2],[2,2,2,0,0,2,1],[2,2,2,0,2,0,2],[2,2,2,0,2,1,0],[2,2,2,1,0,0,2],[2,2,2,1,0,2,1],[2,2,2,1,1,0,0],[2,2,2,1,2,0,2],[2,2,2,2,0,0,1],[2,2,2,2,0,1,0],[2,2,2,2,2,0,0]]\n```", 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0), (2, 2, 2, 2, 2, 0, 0))", "outcome": "refuted", "statement": "a cap of size 392 in F_3^7", "witness": "392 distinct points, a line [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 2]]", "certificate": {"points": [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 2], [0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 2, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 2, 0, 1], [0, 0, 0, 0, 2, 0, 2], [0, 0, 0, 0, 2, 1, 0], [0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0, 2], [0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 2, 0], [0, 0, 0, 1, 0, 2, 2], [0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0, 2], [0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 1, 2, 0], [0, 0, 0, 1, 2, 0, 0], [0, 0, 0, 1, 2, 0, 1], [0, 0, 0, 1, 2, 1, 2], [0, 0, 0, 1, 2, 2, 1], [0, 0, 0, 2, 0, 0, 1], [0, 0, 0, 2, 0, 0, 2], [0, 0, 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2, 0, 0, 0, 2], [2, 2, 2, 0, 0, 2, 1], [2, 2, 2, 0, 2, 0, 2], [2, 2, 2, 0, 2, 1, 0], [2, 2, 2, 1, 0, 0, 2], [2, 2, 2, 1, 0, 2, 1], [2, 2, 2, 1, 1, 0, 0], [2, 2, 2, 1, 2, 0, 2], [2, 2, 2, 2, 0, 0, 1], [2, 2, 2, 2, 0, 1, 0], [2, 2, 2, 2, 2, 0, 0]], "line": [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 2]]}, "key": "d9904359c20912a9", "latency_s": 27.802, "usage": {"in": 105, "out": 5497, "usd": 0.02759}}
{"family": "code", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(7, 3, 16)", "proposal_raw": "```json\n[\n  \"0000000\",\n  \"0001111\",\n  \"0010110\",\n  \"0011001\",\n  \"0100101\",\n  \"0101010\",\n  \"0110011\",\n  \"0111100\",\n  \"1000011\",\n  \"1001100\",\n  \"1010101\",\n  \"1011010\",\n  \"1100110\",\n  \"1101001\",\n  \"1110000\",\n  \"1111111\"\n]\n```", "obj": "('0000000', '0001111', '0010110', '0011001', '0100101', '0101010', '0110011', '0111100', '1000011', '1001100', '1010101', '1011010', '1100110', '1101001', '1110000', '1111111')", "outcome": "certified", "statement": "a binary (7, 16, 3) code", "witness": "16 words, minimum distance 3", "certificate": {"words": ["0000000", "0001111", "0010110", "0011001", "0100101", "0101010", "0110011", "0111100", "1000011", "1001100", "1010101", "1011010", "1100110", "1101001", "1110000", "1111111"], "minDistance": 3, "closestPair": ["0000000", "0010110"]}, "key": "4e60b304d99c3af4", "latency_s": 1.432, "usage": {"in": 79, "out": 123, "usd": 0.000694}}
{"family": "code", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(8, 3, 20)", "proposal_raw": "```json\n[\n  \"00000000\",\n  \"00011111\",\n  \"00101011\",\n  \"00110100\",\n  \"01001101\",\n  \"01010010\",\n  \"01100110\",\n  \"01111001\",\n  \"10001011\",\n  \"10010100\",\n  \"10100010\",\n  \"10111101\",\n  \"11000101\",\n  \"11011010\",\n  \"11101110\",\n  \"11110001\",\n  \"01001010\",\n  \"10001101\",\n  \"11010011\",\n  \"00101100\"\n]\n```", "obj": "('00000000', '00011111', '00101011', '00101100', '00110100', '01001010', '01001101', '01010010', '01100110', '01111001', '10001011', '10001101', '10010100', '10100010', '10111101', '11000101', '11010011', '11011010', '11101110', '11110001')", "outcome": "refuted", "statement": "a binary (8, 20, 3) code", "witness": "20 words, minimum distance 2", "certificate": {"words": ["00000000", "00011111", "00101011", "00101100", "00110100", "01001010", "01001101", "01010010", "01100110", "01111001", "10001011", "10001101", "10010100", "10100010", "10111101", "11000101", "11010011", "11011010", "11101110", "11110001"], "minDistance": 2, "closestPair": ["00101011", "10001011"]}, "key": "90fbf90b47e22b8b", "latency_s": 1.818, "usage": {"in": 79, "out": 151, "usd": 0.000834}}
{"family": "code", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(10, 3, 72)", "proposal_raw": "```json\n[\n  \"0000000000\",\n  \"0000111111\",\n  \"0011001111\",\n  \"0011110000\",\n  \"0101010011\",\n  \"0101101100\",\n  \"0110100101\",\n  \"0110011010\",\n  \"1000011011\",\n  \"1000100100\",\n  \"1011010010\",\n  \"1011101101\",\n  \"1101000110\",\n  \"1101111001\",\n  \"1110001000\",\n  \"1110110111\",\n  \"0001011101\",\n  \"0001100010\",\n  \"0010010100\",\n  \"0010101011\",\n  \"0100001110\",\n  \"0100110001\",\n  \"0111000011\",\n  \"0111111100\",\n  \"1001001001\",\n  \"1001110110\",\n  \"1010100100\",\n  \"1010011011\",\n  \"1100010111\",\n  \"1100101000\",\n  \"1111011110\",\n  \"1111100001\",\n  \"0010110110\",\n  \"0010001001\",\n  \"0001101100\",\n  \"0001010011\",\n  \"0111101001\",\n  \"0111010110\",\n  \"0100100010\",\n  \"0100011101\",\n  \"1010110001\",\n  \"1010001110\",\n  \"1001011010\",\n  \"1001100101\",\n  \"1111000011\",\n  \"1111111100\",\n  \"1100001000\",\n  \"1100110111\",\n  \"0011010001\",\n  \"0011101110\",\n  \"0000001010\",\n  \"0000110101\",\n  \"0110011100\",\n  \"0110100011\",\n  \"0101110111\",\n  \"0101001000\",\n  \"1101011110\",\n  \"1101100001\",\n  \"1110010011\",\n  \"1110101100\",\n  \"1000110010\",\n  \"1000001101\",\n  \"1011111001\",\n  \"1011000110\",\n  \"0100111000\",\n  \"0100000111\",\n  \"0111001101\",\n  \"0111110010\",\n  \"0001010100\",\n  \"0001101011\",\n  \"0010011111\",\n  \"0010100000\"\n]\n```", "obj": "('0000000000', '0000001010', '0000110101', '0000111111', '0001010011', '0001010100', '0001011101', '0001100010', '0001101011', '0001101100', '0010001001', '0010010100', '0010011111', '0010100000', '0010101011', '0010110110', '0011001111', '0011010001', '0011101110', '0011110000', '0100000111', '0100001110', '0100011101', '0100100010', '0100110001', '0100111000', '0101001000', '0101010011', '0101101100', '0101110111', '0110011010', '0110011100', '0110100011', '0110100101', '0111000011', '0111001101', '0111010110', '0111101001', '0111110010', '0111111100', '1000001101', '1000011011', '1000100100', '1000110010', '1001001001', '1001011010', '1001100101', '1001110110', '1010001110', '1010011011', '1010100100', '1010110001', '1011000110', '1011010010', '1011101101', '1011111001', '1100001000', '1100010111', '1100101000', '1100110111', '1101000110', '1101011110', '1101100001', '1101111001', '1110001000', '1110010011', '1110101100', '1110110111', '1111000011', '1111011110', '1111100001', '1111111100')", "outcome": "refuted", "statement": "a binary (10, 72, 3) code", "witness": "72 words, minimum distance 1", "certificate": {"words": ["0000000000", "0000001010", "0000110101", "0000111111", "0001010011", "0001010100", "0001011101", "0001100010", "0001101011", "0001101100", "0010001001", "0010010100", "0010011111", "0010100000", "0010101011", "0010110110", "0011001111", "0011010001", "0011101110", "0011110000", "0100000111", "0100001110", "0100011101", "0100100010", "0100110001", "0100111000", "0101001000", "0101010011", "0101101100", "0101110111", "0110011010", "0110011100", "0110100011", "0110100101", "0111000011", "0111001101", "0111010110", "0111101001", "0111110010", "0111111100", "1000001101", "1000011011", "1000100100", "1000110010", "1001001001", "1001011010", "1001100101", "1001110110", "1010001110", "1010011011", "1010100100", "1010110001", "1011000110", "1011010010", "1011101101", "1011111001", "1100001000", "1100010111", "1100101000", "1100110111", "1101000110", "1101011110", "1101100001", "1101111001", "1110001000", "1110010011", "1110101100", "1110110111", "1111000011", "1111011110", "1111100001", "1111111100"], "minDistance": 1, "closestPair": ["0001010011", "0101010011"]}, "key": "0572807389d4e8e2", "latency_s": 6.158, "usage": {"in": 79, "out": 587, "usd": 0.003014}}
{"family": "code", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(12, 4, 144)", "proposal_raw": "```json\n[\"000000000000\",\"000000111100\",\"000011001100\",\"000011110000\",\"000101010100\",\"000101101000\",\"000110100100\",\"000110011000\",\"001000110100\",\"001000001000\",\"001011011100\",\"001011100000\",\"001101000100\",\"001101111000\",\"001110110100\",\"001110001000\",\"010000101100\",\"010000010000\",\"010011000100\",\"010011111000\",\"010101111100\",\"010101000000\",\"010110001100\",\"010110110000\",\"011000011100\",\"011000100000\",\"011011010100\",\"011011101000\",\"011101101100\",\"011101010000\",\"011110011100\",\"011110100000\",\"100000011000\",\"100000100100\",\"100011010000\",\"100011101100\",\"100101111000\",\"100101000100\",\"100110001000\",\"100110110100\",\"101000100000\",\"101000011100\",\"101011001000\",\"101011110100\",\"101101110000\",\"101101001100\",\"101110010000\",\"101110101100\",\"110000001100\",\"110000110000\",\"110011100000\",\"110011011100\",\"110101010000\",\"110101101100\",\"110110111000\",\"110110000100\",\"111000010100\",\"111000101000\",\"111011100100\",\"111011011000\",\"111101001100\",\"111101110000\",\"111110000100\",\"111110111000\",\"000000000000\",\"000001110011\",\"000010101011\",\"000011011000\",\"000100100011\",\"000101010000\",\"000110001000\",\"000111111011\",\"001000111011\",\"001001001000\",\"001010010000\",\"001011100011\",\"001100101011\",\"001101011000\",\"001110000000\",\"001111110011\",\"010000101011\",\"010001011000\",\"010010000000\",\"010011110011\",\"010100111011\",\"010101001000\",\"010110010000\",\"010111100011\",\"011000100011\",\"011001010000\",\"011010001000\",\"011011111011\",\"011100110011\",\"011101000000\",\"011110011000\",\"011111101011\",\"100000110000\",\"100001000011\",\"100010011011\",\"100011101000\",\"100100010011\",\"100101100000\",\"100110111000\",\"100111001011\",\"101000001011\",\"101001111000\",\"101010100000\",\"101011010011\",\"101100011011\",\"101101101000\",\"101110110000\",\"101111000011\",\"110000011011\",\"110001101000\",\"110010110000\",\"110011000011\",\"110100001011\",\"110101111000\",\"110110100000\",\"110111010011\",\"111000010011\",\"111001100000\",\"111010111000\",\"111011001011\",\"111100000011\",\"111101110000\",\"111110101011\",\"111111011000\"]\n```", "obj": "('000000000000', '000000000000', '000000111100', '000001110011', '000010101011', '000011001100', '000011011000', '000011110000', '000100100011', '000101010000', '000101010100', '000101101000', '000110001000', '000110011000', '000110100100', '000111111011', '001000001000', '001000110100', '001000111011', '001001001000', '001010010000', '001011011100', '001011100000', '001011100011', '001100101011', '001101000100', '001101011000', '001101111000', '001110000000', '001110001000', '001110110100', '001111110011', '010000010000', '010000101011', '010000101100', '010001011000', '010010000000', '010011000100', '010011110011', '010011111000', '010100111011', '010101000000', '010101001000', '010101111100', '010110001100', '010110010000', '010110110000', '010111100011', '011000011100', '011000100000', '011000100011', '011001010000', '011010001000', '011011010100', '011011101000', '011011111011', '011100110011', '011101000000', '011101010000', '011101101100', '011110011000', '011110011100', '011110100000', '011111101011', '100000011000', '100000100100', '100000110000', '100001000011', '100010011011', '100011010000', '100011101000', '100011101100', '100100010011', '100101000100', '100101100000', '100101111000', '100110001000', '100110110100', '100110111000', '100111001011', '101000001011', '101000011100', '101000100000', '101001111000', '101010100000', '101011001000', '101011010011', '101011110100', '101100011011', '101101001100', '101101101000', '101101110000', '101110010000', '101110101100', '101110110000', '101111000011', '110000001100', '110000011011', '110000110000', '110001101000', '110010110000', '110011000011', '110011011100', '110011100000', '110100001011', '110101010000', '110101101100', '110101111000', '110110000100', '110110100000', '110110111000', '110111010011', '111000010011', '111000010100', '111000101000', '111001100000', '111010111000', '111011001011', '111011011000', '111011100100', '111100000011', '111101001100', '111101110000', '111101110000', '111110000100', '111110101011', '111110111000', '111111011000')", "outcome": "rejected", "statement": "a binary (12, 128, 4) code", "witness": null, "certificate": null, "key": "9b0cc2ed04e52769", "latency_s": 6.232, "usage": {"in": 79, "out": 649, "usd": 0.003324}}
{"family": "code", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(16, 6, 256)", "proposal_raw": "```json\n[\n  \"0000000000000000\",\n  \"0000000011111111\",\n  \"0000111100001111\",\n  \"0000111111110000\",\n  \"0011000000110011\",\n  \"0011000011001100\",\n  \"0011111100110011\",\n  \"0011111111001100\",\n  \"0100000001010101\",\n  \"0100000010101010\",\n  \"0100111101010101\",\n  \"0100111110101010\",\n  \"0111000001100110\",\n  \"0111000010011001\",\n  \"0111111101100110\",\n  \"0111111110011001\",\n  \"1000000000101010\",\n  \"1000000011010101\",\n  \"1000111100101010\",\n  \"1000111111010101\",\n  \"1011000000011001\",\n  \"1011000011100110\",\n  \"1011111100011001\",\n  \"1011111111100110\",\n  \"1100000001111100\",\n  \"1100000010000011\",\n  \"1100111101111100\",\n  \"1100111110000011\",\n  \"1111000001001001\",\n  \"1111000010110110\",\n  \"1111111101001001\",\n  \"1111111110110110\",\n  \"0000000101010101\",\n  \"0000000110101010\",\n  \"0000111001010101\",\n  \"0000111010101010\",\n  \"0011000101100110\",\n  \"0011000110011001\",\n  \"0011111001100110\",\n  \"0011111010011001\",\n  \"0100000100101010\",\n  \"0100000111010101\",\n  \"0100111000101010\",\n  \"0100111011010101\",\n  \"0111000100011001\",\n  \"0111000111100110\",\n  \"0111111000011001\",\n  \"0111111011100110\",\n  \"1000000101111100\",\n  \"1000000110000011\",\n  \"1000111001111100\",\n  \"1000111010000011\",\n  \"1011000100001001\",\n  \"1011000111110110\",\n  \"1011111000001001\",\n  \"1011111011110110\",\n  \"1100000100001111\",\n  \"1100000111110000\",\n  \"1100111000001111\",\n  \"1100111011110000\",\n  \"1111000100110000\",\n  \"1111000111001111\",\n  \"1111111000110000\",\n  \"1111111011001111\",\n  \"0000101000000000\",\n  \"0000101011111111\",\n  \"0000010100001111\",\n  \"0000010111110000\",\n  \"0011101000110011\",\n  \"0011101011001100\",\n  \"0011010100110011\",\n  \"0011010111001100\",\n  \"0100101001010101\",\n  \"0100101010101010\",\n  \"0100010101010101\",\n  \"0100010110101010\",\n  \"0111101001100110\",\n  \"0111101010011001\",\n  \"0111010101100110\",\n  \"0111010110011001\",\n  \"1000101000101010\",\n  \"1000101011010101\",\n  \"1000010100101010\",\n  \"1000010111010101\",\n  \"1011101000011001\",\n  \"1011101011100110\",\n  \"1011010100011001\",\n  \"1011010111100110\",\n  \"1100101001111100\",\n  \"1100101010000011\",\n  \"1100010101111100\",\n  \"1100010110000011\",\n  \"1111101001001001\",\n  \"1111101010110110\",\n  \"1111010101001001\",\n  \"1111010110110110\",\n  \"0000101101010101\",\n  \"0000101110101010\",\n  \"0000010001010101\",\n  \"0000010010101010\",\n  \"0011101101100110\",\n  \"0011101110011001\",\n  \"0011010001100110\",\n  \"0011010010011001\",\n  \"0100101100101010\",\n  \"0100101111010101\",\n  \"0100010000101010\",\n  \"0100010011010101\",\n  \"0111101100011001\",\n  \"0111101111100110\",\n  \"0111010000011001\",\n  \"0111010011100110\",\n  \"1000101101111100\",\n  \"1000101110000011\",\n  \"1000010001111100\",\n  \"1000010010000011\",\n  \"1011101101001001\",\n  \"1011101110110110\",\n  \"1011010001001001\",\n  \"1011010010110110\",\n  \"1100101100001111\",\n  \"1100101111110000\",\n  \"1100010000001111\",\n  \"1100010011110000\",\n  \"1111101100110000\",\n  \"1111101111001111\",\n  \"1111010000110000\",\n  \"1111010011001111\",\n  \"0101000000000000\",\n  \"0101000011111111\",\n  \"0101111100001111\",\n  \"0101111111110000\",\n  \"0110000000110011\",\n  \"0110000011001100\",\n  \"0110111100110011\",\n  \"0110111111001100\",\n  \"0001000001010101\",\n  \"0001000010101010\",\n  \"0001111101010101\",\n  \"0001111110101010\",\n  \"0010000001100110\",\n  \"0010000010011001\",\n  \"0010111101100110\",\n  \"0010111110011001\",\n  \"1101000000101010\",\n  \"1101000011010101\",\n  \"1101111100101010\",\n  \"1101111111010101\",\n  \"1110000000011001\",\n  \"1110000011100110\",\n  \"1110111100011001\",\n  \"1110111111100110\",\n  \"1001000001111100\",\n  \"1001000010000011\",\n  \"1001111101111100\",\n  \"1001111110000011\",\n  \"1010000001001001\",\n  \"1010000010110110\",\n  \"1010111101001001\",\n  \"1010111110110110\",\n  \"0101000101010101\",\n  \"0101000110101010\",\n  \"0101111001010101\",\n  \"0101111010101010\",\n  \"0110000101100110\",\n  \"0110000110011001\",\n  \"0110111001100110\",\n  \"0110111010011001\",\n  \"0001000100101010\",\n  \"0001000111010101\",\n  \"0001111000101010\",\n  \"0001111011010101\",\n  \"0010000100011001\",\n  \"0010000111100110\",\n  \"0010111000011001\",\n  \"0010111011100110\",\n  \"1101000101111100\",\n  \"1101000110000011\",\n  \"1101111001111100\",\n  \"1101111010000011\",\n  \"1110000100001001\",\n  \"1110000111110110\",\n  \"1110111000001001\",\n  \"1110111011110110\",\n  \"1001000100001111\",\n  \"1001000111110000\",\n  \"1001111000001111\",\n  \"1001111011110000\",\n  \"1010000100110000\",\n  \"1010000111001111\",\n  \"1010111000110000\",\n  \"1010111011001111\",\n  \"0101101000000000\",\n  \"0101101011111111\",\n  \"0101010100001111\",\n  \"0101010111110000\",\n  \"0110101000110011\",\n  \"0110101011001100\",\n  \"0110010100110011\",\n  \"0110010111001100\",\n  \"0001101001010101\",\n  \"0001101010101010\",\n  \"0001010101010101\",\n  \"0001010110101010\",\n  \"0010101001100110\",\n  \"0010101010011001\",\n  \"0010010101100110\",\n  \"0010010110011001\",\n  \"1101101000101010\",\n  \"1101101011010101\",\n  \"1101010100101010\",\n  \"1101010111010101\",\n  \"1110101000011001\",\n  \"1110101011100110\",\n  \"1110010100011001\",\n  \"1110010111100110\",\n  \"1001101001111100\",\n  \"1001101010000011\",\n  \"1001010101111100\",\n  \"1001010110000011\",\n  \"1010101001001001\",\n  \"1010101010110110\",\n  \"1010010101001001\",\n  \"1010010110110110\",\n  \"0101101101010101\",\n  \"0101101110101010\",\n  \"0101010001010101\",\n  \"0101010010101010\",\n  \"0110101101100110\",\n  \"0110101110011001\",\n  \"0110010001100110\",\n  \"0110010010011001\",\n  \"0001101100101010\",\n  \"0001101111010101\",\n  \"0001010000101010\",\n  \"0001010011010101\",\n  \"0010101100011001\",\n  \"0010101111100110\",\n  \"0010010000011001\",\n  \"0010010011100110\",\n  \"1101101101111100\",\n  \"1101101110000011\",\n  \"1101010001111100\",\n  \"1101010010000011\",\n  \"1110101101001001\",\n  \"1110101110110110\",\n  \"1110010001001001\",\n  \"1110010010110110\",\n  \"1001101100001111\",\n  \"1001101111110000\",\n  \"1001010000001111\",\n  \"1001010011110000\",\n  \"1010101100110000\",\n  \"1010101111001111\",\n  \"1010010000110000\",\n  \"1010010011001111\"\n]\n```", "obj": "('0000000000000000', '0000000011111111', '0000000101010101', '0000000110101010', '0000010001010101', '0000010010101010', '0000010100001111', '0000010111110000', '0000101000000000', '0000101011111111', '0000101101010101', '0000101110101010', '0000111001010101', '0000111010101010', '0000111100001111', '0000111111110000', '0001000001010101', '0001000010101010', '0001000100101010', '0001000111010101', '0001010000101010', '0001010011010101', '0001010101010101', '0001010110101010', '0001101001010101', '0001101010101010', '0001101100101010', '0001101111010101', '0001111000101010', '0001111011010101', '0001111101010101', '0001111110101010', '0010000001100110', '0010000010011001', '0010000100011001', '0010000111100110', '0010010000011001', '0010010011100110', '0010010101100110', '0010010110011001', '0010101001100110', '0010101010011001', '0010101100011001', '0010101111100110', '0010111000011001', '0010111011100110', '0010111101100110', '0010111110011001', '0011000000110011', '0011000011001100', '0011000101100110', '0011000110011001', '0011010001100110', '0011010010011001', '0011010100110011', '0011010111001100', '0011101000110011', '0011101011001100', '0011101101100110', '0011101110011001', '0011111001100110', '0011111010011001', '0011111100110011', '0011111111001100', '0100000001010101', '0100000010101010', '0100000100101010', '0100000111010101', '0100010000101010', '0100010011010101', '0100010101010101', '0100010110101010', '0100101001010101', '0100101010101010', '0100101100101010', '0100101111010101', '0100111000101010', '0100111011010101', '0100111101010101', '0100111110101010', '0101000000000000', '0101000011111111', '0101000101010101', '0101000110101010', '0101010001010101', '0101010010101010', '0101010100001111', '0101010111110000', '0101101000000000', '0101101011111111', '0101101101010101', '0101101110101010', '0101111001010101', '0101111010101010', '0101111100001111', '0101111111110000', '0110000000110011', '0110000011001100', '0110000101100110', '0110000110011001', '0110010001100110', '0110010010011001', '0110010100110011', '0110010111001100', '0110101000110011', '0110101011001100', '0110101101100110', '0110101110011001', '0110111001100110', '0110111010011001', '0110111100110011', '0110111111001100', '0111000001100110', '0111000010011001', '0111000100011001', '0111000111100110', '0111010000011001', '0111010011100110', '0111010101100110', '0111010110011001', '0111101001100110', '0111101010011001', '0111101100011001', '0111101111100110', '0111111000011001', '0111111011100110', '0111111101100110', '0111111110011001', '1000000000101010', '1000000011010101', '1000000101111100', '1000000110000011', '1000010001111100', '1000010010000011', '1000010100101010', '1000010111010101', '1000101000101010', '1000101011010101', '1000101101111100', '1000101110000011', '1000111001111100', '1000111010000011', '1000111100101010', '1000111111010101', '1001000001111100', '1001000010000011', '1001000100001111', '1001000111110000', '1001010000001111', '1001010011110000', '1001010101111100', '1001010110000011', '1001101001111100', '1001101010000011', '1001101100001111', '1001101111110000', '1001111000001111', '1001111011110000', '1001111101111100', '1001111110000011', '1010000001001001', '1010000010110110', '1010000100110000', '1010000111001111', '1010010000110000', '1010010011001111', '1010010101001001', '1010010110110110', '1010101001001001', '1010101010110110', '1010101100110000', '1010101111001111', '1010111000110000', '1010111011001111', '1010111101001001', '1010111110110110', '1011000000011001', '1011000011100110', '1011000100001001', '1011000111110110', '1011010001001001', '1011010010110110', '1011010100011001', '1011010111100110', '1011101000011001', '1011101011100110', '1011101101001001', '1011101110110110', '1011111000001001', '1011111011110110', '1011111100011001', '1011111111100110', '1100000001111100', '1100000010000011', '1100000100001111', '1100000111110000', '1100010000001111', '1100010011110000', '1100010101111100', '1100010110000011', '1100101001111100', '1100101010000011', '1100101100001111', '1100101111110000', '1100111000001111', '1100111011110000', '1100111101111100', '1100111110000011', '1101000000101010', '1101000011010101', '1101000101111100', '1101000110000011', '1101010001111100', '1101010010000011', '1101010100101010', '1101010111010101', '1101101000101010', '1101101011010101', '1101101101111100', '1101101110000011', '1101111001111100', '1101111010000011', '1101111100101010', '1101111111010101', '1110000000011001', '1110000011100110', '1110000100001001', '1110000111110110', '1110010001001001', '1110010010110110', '1110010100011001', '1110010111100110', '1110101000011001', '1110101011100110', '1110101101001001', '1110101110110110', '1110111000001001', '1110111011110110', '1110111100011001', '1110111111100110', '1111000001001001', '1111000010110110', '1111000100110000', '1111000111001111', '1111010000110000', '1111010011001111', '1111010101001001', '1111010110110110', '1111101001001001', '1111101010110110', '1111101100110000', '1111101111001111', '1111111000110000', '1111111011001111', '1111111101001001', '1111111110110110')", "outcome": "refuted", "statement": "a binary (16, 256, 6) code", "witness": "256 words, minimum distance 2", "certificate": {"words": ["0000000000000000", "0000000011111111", "0000000101010101", "0000000110101010", "0000010001010101", "0000010010101010", "0000010100001111", "0000010111110000", "0000101000000000", "0000101011111111", "0000101101010101", "0000101110101010", "0000111001010101", "0000111010101010", "0000111100001111", "0000111111110000", "0001000001010101", "0001000010101010", "0001000100101010", "0001000111010101", "0001010000101010", "0001010011010101", "0001010101010101", "0001010110101010", "0001101001010101", "0001101010101010", "0001101100101010", "0001101111010101", "0001111000101010", "0001111011010101", "0001111101010101", "0001111110101010", "0010000001100110", "0010000010011001", "0010000100011001", "0010000111100110", "0010010000011001", "0010010011100110", "0010010101100110", "0010010110011001", "0010101001100110", "0010101010011001", "0010101100011001", "0010101111100110", "0010111000011001", "0010111011100110", "0010111101100110", "0010111110011001", "0011000000110011", "0011000011001100", "0011000101100110", "0011000110011001", "0011010001100110", "0011010010011001", "0011010100110011", "0011010111001100", "0011101000110011", "0011101011001100", "0011101101100110", "0011101110011001", "0011111001100110", "0011111010011001", "0011111100110011", "0011111111001100", "0100000001010101", "0100000010101010", "0100000100101010", "0100000111010101", "0100010000101010", "0100010011010101", "0100010101010101", "0100010110101010", "0100101001010101", "0100101010101010", "0100101100101010", "0100101111010101", "0100111000101010", "0100111011010101", "0100111101010101", "0100111110101010", "0101000000000000", "0101000011111111", "0101000101010101", "0101000110101010", "0101010001010101", "0101010010101010", "0101010100001111", "0101010111110000", "0101101000000000", "0101101011111111", "0101101101010101", "0101101110101010", "0101111001010101", "0101111010101010", "0101111100001111", "0101111111110000", "0110000000110011", "0110000011001100", "0110000101100110", "0110000110011001", "0110010001100110", "0110010010011001", "0110010100110011", "0110010111001100", "0110101000110011", "0110101011001100", "0110101101100110", "0110101110011001", "0110111001100110", "0110111010011001", "0110111100110011", "0110111111001100", "0111000001100110", "0111000010011001", "0111000100011001", "0111000111100110", "0111010000011001", "0111010011100110", "0111010101100110", "0111010110011001", "0111101001100110", "0111101010011001", "0111101100011001", "0111101111100110", "0111111000011001", "0111111011100110", "0111111101100110", "0111111110011001", "1000000000101010", "1000000011010101", "1000000101111100", "1000000110000011", "1000010001111100", "1000010010000011", "1000010100101010", "1000010111010101", "1000101000101010", "1000101011010101", "1000101101111100", "1000101110000011", "1000111001111100", "1000111010000011", "1000111100101010", "1000111111010101", "1001000001111100", "1001000010000011", "1001000100001111", "1001000111110000", "1001010000001111", "1001010011110000", "1001010101111100", "1001010110000011", "1001101001111100", "1001101010000011", "1001101100001111", "1001101111110000", "1001111000001111", "1001111011110000", "1001111101111100", "1001111110000011", "1010000001001001", "1010000010110110", "1010000100110000", "1010000111001111", "1010010000110000", "1010010011001111", "1010010101001001", "1010010110110110", "1010101001001001", "1010101010110110", "1010101100110000", "1010101111001111", "1010111000110000", "1010111011001111", "1010111101001001", "1010111110110110", "1011000000011001", "1011000011100110", "1011000100001001", "1011000111110110", "1011010001001001", "1011010010110110", "1011010100011001", "1011010111100110", "1011101000011001", "1011101011100110", "1011101101001001", "1011101110110110", "1011111000001001", "1011111011110110", "1011111100011001", "1011111111100110", "1100000001111100", "1100000010000011", "1100000100001111", "1100000111110000", "1100010000001111", "1100010011110000", "1100010101111100", "1100010110000011", "1100101001111100", "1100101010000011", "1100101100001111", "1100101111110000", "1100111000001111", "1100111011110000", "1100111101111100", "1100111110000011", "1101000000101010", "1101000011010101", "1101000101111100", "1101000110000011", "1101010001111100", "1101010010000011", "1101010100101010", "1101010111010101", "1101101000101010", "1101101011010101", "1101101101111100", "1101101110000011", "1101111001111100", "1101111010000011", "1101111100101010", "1101111111010101", "1110000000011001", "1110000011100110", "1110000100001001", "1110000111110110", "1110010001001001", "1110010010110110", "1110010100011001", "1110010111100110", "1110101000011001", "1110101011100110", "1110101101001001", "1110101110110110", "1110111000001001", "1110111011110110", "1110111100011001", "1110111111100110", "1111000001001001", "1111000010110110", "1111000100110000", "1111000111001111", "1111010000110000", "1111010011001111", "1111010101001001", "1111010110110110", "1111101001001001", "1111101010110110", "1111101100110000", "1111101111001111", "1111111000110000", "1111111011001111", "1111111101001001", "1111111110110110"], "minDistance": 2, "closestPair": ["0000000000000000", "0000101000000000"]}, "key": "8c5555151e304784", "latency_s": 20.066, "usage": {"in": 79, "out": 2571, "usd": 0.012934}}
{"family": "code", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(10, 3, 73)", "proposal_raw": "```json\n[\n  \"0000000000\",\n  \"0000111111\",\n  \"0011001111\",\n  \"0011110000\",\n  \"0101010111\",\n  \"0101101000\",\n  \"0110100101\",\n  \"0110011010\",\n  \"1000011011\",\n  \"1000100100\",\n  \"1001001010\",\n  \"1001110101\",\n  \"1010001100\",\n  \"1010110011\",\n  \"1100010110\",\n  \"1100101001\",\n  \"1101000011\",\n  \"1101111100\",\n  \"1110011101\",\n  \"1110100010\",\n  \"0001011101\",\n  \"0001100010\",\n  \"0010010011\",\n  \"0010101100\",\n  \"0100011010\",\n  \"0100100101\",\n  \"0111000100\",\n  \"0111111011\",\n  \"1001100110\",\n  \"1001011001\",\n  \"1010100010\",\n  \"1010011101\",\n  \"1100100011\",\n  \"1100011100\",\n  \"1111011000\",\n  \"1111100111\",\n  \"0000000111\",\n  \"0000111000\",\n  \"0011000110\",\n  \"0011111001\",\n  \"0101011010\",\n  \"0101100101\",\n  \"0110101100\",\n  \"0110010011\",\n  \"1000010100\",\n  \"1000101011\",\n  \"1001000001\",\n  \"1001111110\",\n  \"1010000011\",\n  \"1010111100\",\n  \"1100001101\",\n  \"1100110010\",\n  \"1101011100\",\n  \"1101100011\",\n  \"1110010010\",\n  \"1110101101\",\n  \"0001010010\",\n  \"0001101101\",\n  \"0010011100\",\n  \"0010100011\",\n  \"0100010001\",\n  \"0100101110\",\n  \"0111001111\",\n  \"0111110000\",\n  \"1001101001\",\n  \"1001010110\",\n  \"1010101001\",\n  \"1010010110\",\n  \"1100101100\",\n  \"1100010011\",\n  \"1111010111\",\n  \"1111101000\",\n  \"0000011010\",\n  \"0011100101\",\n  \"1111111111\"\n]\n```", "obj": "('0000000000', '0000000111', '0000011010', '0000111000', '0000111111', '0001010010', '0001011101', '0001100010', '0001101101', '0010010011', '0010011100', '0010100011', '0010101100', '0011000110', '0011001111', '0011100101', '0011110000', '0011111001', '0100010001', '0100011010', '0100100101', '0100101110', '0101010111', '0101011010', '0101100101', '0101101000', '0110010011', '0110011010', '0110100101', '0110101100', '0111000100', '0111001111', '0111110000', '0111111011', '1000010100', '1000011011', '1000100100', '1000101011', '1001000001', '1001001010', '1001010110', '1001011001', '1001100110', '1001101001', '1001110101', '1001111110', '1010000011', '1010001100', '1010010110', '1010011101', '1010100010', '1010101001', '1010110011', '1010111100', '1100001101', '1100010011', '1100010110', '1100011100', '1100100011', '1100101001', '1100101100', '1100110010', '1101000011', '1101011100', '1101100011', '1101111100', '1110010010', '1110011101', '1110100010', '1110101101', '1111010111', '1111011000', '1111100111', '1111101000', '1111111111')", "outcome": "refuted", "statement": "a binary (10, 75, 3) code", "witness": "75 words, minimum distance 1", "certificate": {"words": ["0000000000", "0000000111", "0000011010", "0000111000", "0000111111", "0001010010", "0001011101", "0001100010", "0001101101", "0010010011", "0010011100", "0010100011", "0010101100", "0011000110", "0011001111", "0011100101", "0011110000", "0011111001", "0100010001", "0100011010", "0100100101", "0100101110", "0101010111", "0101011010", "0101100101", "0101101000", "0110010011", "0110011010", "0110100101", "0110101100", "0111000100", "0111001111", "0111110000", "0111111011", "1000010100", "1000011011", "1000100100", "1000101011", "1001000001", "1001001010", "1001010110", "1001011001", "1001100110", "1001101001", "1001110101", "1001111110", "1010000011", "1010001100", "1010010110", "1010011101", "1010100010", "1010101001", "1010110011", "1010111100", "1100001101", "1100010011", "1100010110", "1100011100", "1100100011", "1100101001", "1100101100", "1100110010", "1101000011", "1101011100", "1101100011", "1101111100", "1110010010", "1110011101", "1110100010", "1110101101", "1111010111", "1111011000", "1111100111", "1111101000", "1111111111"], "minDistance": 1, "closestPair": ["0000011010", "0100011010"]}, "key": "d78fc9267f66f8b2", "latency_s": 6.159, "usage": {"in": 79, "out": 611, "usd": 0.003134}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 4, 8)", "proposal_raw": "```json\n{\"n\": 8, \"circulant\": [1, 2, 4]}\n```", "obj": "('circulant', 8, (1, 2, 4))", "outcome": "refuted", "statement": "R(3,4) > 8", "witness": "8 vertices; clique of size 3: yes; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 8, "data": [1, 2, 4]}, "cliqueFound": true, "independentFound": false}, "key": "e33e80717c08c100", "latency_s": 0.986, "usage": {"in": 140, "out": 28, "usd": 0.00028}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 5, 13)", "proposal_raw": "```json\n{\n  \"n\": 13,\n  \"circulant\": [1, 2, 3, 4]\n}\n```", "obj": "('circulant', 13, (1, 2, 3, 4))", "outcome": "refuted", "statement": "R(3,5) > 13", "witness": "13 vertices; clique of size 3: yes; independent set of size 5: no", "certificate": {"graph": {"kind": "circulant", "n": 13, "data": [1, 2, 3, 4]}, "cliqueFound": true, "independentFound": false}, "key": "2334a1b6f9429282", "latency_s": 0.932, "usage": {"in": 140, "out": 38, "usd": 0.00033}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(4, 4, 17)", "proposal_raw": "```json\n{\n  \"n\": 17,\n  \"circulant\": [1, 2, 4, 8]\n}\n```", "obj": "('circulant', 17, (1, 2, 4, 8))", "outcome": "certified", "statement": "R(4,4) > 17", "witness": "17 vertices; clique of size 4: no; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8]}, "cliqueFound": false, "independentFound": false}, "key": "456fd0ac5d4ee40b", "latency_s": 0.803, "usage": {"in": 140, "out": 38, "usd": 0.00033}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 6, 17)", "proposal_raw": "```json\n{\"n\": 17, \"circulant\": [1, 2, 4, 8]}\n```", "obj": "('circulant', 17, (1, 2, 4, 8))", "outcome": "refuted", "statement": "R(3,6) > 17", "witness": "17 vertices; clique of size 3: yes; independent set of size 6: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8]}, "cliqueFound": true, "independentFound": false}, "key": "456fd0ac5d4ee40b", "latency_s": 1.124, "usage": {"in": 140, "out": 31, "usd": 0.000295}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(4, 5, 24)", "proposal_raw": "```json\n{\n  \"n\": 24,\n  \"circulant\": [1, 2, 3, 4, 8, 12]\n}\n```", "obj": "('circulant', 24, (1, 2, 3, 4, 8, 12))", "outcome": "refuted", "statement": "R(4,5) > 24", "witness": "24 vertices; clique of size 4: yes; independent set of size 5: no", "certificate": {"graph": {"kind": "circulant", "n": 24, "data": [1, 2, 3, 4, 8, 12]}, "cliqueFound": true, "independentFound": false}, "key": "76673d0923d5050c", "latency_s": 0.892, "usage": {"in": 140, "out": 44, "usd": 0.00036}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 9, 35)", "proposal_raw": "```json\n{\"n\": 35, \"circulant\": [1, 2, 3, 4, 5, 6, 7, 8, 16, 17]}\n```", "obj": "('circulant', 35, (1, 2, 3, 4, 5, 6, 7, 8, 16, 17))", "outcome": "refuted", "statement": "R(3,9) > 35", "witness": "35 vertices; clique of size 3: yes; independent set of size 9: no", "certificate": {"graph": {"kind": "circulant", "n": 35, "data": [1, 2, 3, 4, 5, 6, 7, 8, 16, 17]}, "cliqueFound": true, "independentFound": false}, "key": "c8472c6fe8e4b401", "latency_s": 1.173, "usage": {"in": 140, "out": 49, "usd": 0.000385}}
{"family": "ramsey", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(4, 6, 36)", "proposal_raw": "```json\n{\n  \"n\": 36,\n  \"circulant\": [1, 2, 3, 4, 8, 9, 10, 13]\n}\n```", "obj": "('circulant', 36, (1, 2, 3, 4, 8, 9, 10, 13))", "outcome": "refuted", "statement": "R(4,6) > 36", "witness": "36 vertices; clique of size 4: yes; independent set of size 6: yes", "certificate": {"graph": {"kind": "circulant", "n": 36, "data": [1, 2, 3, 4, 8, 9, 10, 13]}, "cliqueFound": true, "independentFound": true}, "key": "72df827bd155c137", "latency_s": 1.171, "usage": {"in": 140, "out": 50, "usd": 0.00039}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.6", "proposal_raw": "```json\n[\n  [0, 0, 45],\n  [0, 1, 12],\n  [0, 2, 8],\n  [1, 0, 12],\n  [1, 1, 20],\n  [1, 2, 5],\n  [2, 0, 8],\n  [2, 1, 5],\n  [2, 2, 3],\n  [0, 3, 5],\n  [3, 0, 5],\n  [1, 3, 2],\n  [3, 1, 2],\n  [3, 3, 1],\n  [0, 4, 3],\n  [4, 0, 3],\n  [2, 3, 1],\n  [3, 2, 1],\n  [0, 5, 2],\n  [5, 0, 2],\n  [1, 4, 1],\n  [4, 1, 1],\n  [0, 6, 1],\n  [6, 0, 1]\n]\n```", "obj": "((0, 0, 45), (0, 1, 12), (0, 2, 8), (0, 3, 5), (0, 4, 3), (0, 5, 2), (0, 6, 1), (1, 0, 12), (1, 1, 20), (1, 2, 5), (1, 3, 2), (1, 4, 1), (2, 0, 8), (2, 1, 5), (2, 2, 3), (2, 3, 1), (3, 0, 5), (3, 1, 2), (3, 2, 1), (3, 3, 1), (4, 0, 3), (4, 1, 1), (5, 0, 2), (6, 0, 1))", "outcome": "refuted", "statement": "C3b >= 1.6 from a 24-point law", "witness": "ratio in [1.06507103212129503919, 1.06507103212129503919]", "certificate": {"law": [[0, 0, 45], [0, 1, 12], [0, 2, 8], [0, 3, 5], [0, 4, 3], [0, 5, 2], [0, 6, 1], [1, 0, 12], [1, 1, 20], [1, 2, 5], [1, 3, 2], [1, 4, 1], [2, 0, 8], [2, 1, 5], [2, 2, 3], [2, 3, 1], [3, 0, 5], [3, 1, 2], [3, 2, 1], [3, 3, 1], [4, 0, 3], [4, 1, 1], [5, 0, 2], [6, 0, 1]], "ratioLo": "1.065071032121295039199331462102579142568408", "ratioHi": "1.065071032121295039199331462102579142568408"}, "key": "62b04877bac9b761", "latency_s": 1.958, "usage": {"in": 122, "out": 275, "usd": 0.001497}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.7", "proposal_raw": "```json\n[\n  [0, 0, 45],\n  [1, 0, 32],\n  [2, 0, 23],\n  [3, 0, 16],\n  [4, 0, 11],\n  [5, 0, 8],\n  [0, 1, 32],\n  [1, 1, 23],\n  [2, 1, 16],\n  [3, 1, 11],\n  [4, 1, 8],\n  [0, 2, 23],\n  [1, 2, 16],\n  [2, 2, 11],\n  [3, 2, 8],\n  [0, 3, 16],\n  [1, 3, 11],\n  [2, 3, 8],\n  [0, 4, 11],\n  [1, 4, 8],\n  [0, 5, 8],\n  [-1, 0, 32],\n  [-2, 0, 23],\n  [-3, 0, 16],\n  [-4, 0, 11],\n  [-5, 0, 8],\n  [0, -1, 32],\n  [1, -1, 23],\n  [2, -1, 16],\n  [3, -1, 11],\n  [4, -1, 8],\n  [0, -2, 23],\n  [1, -2, 16],\n  [2, -2, 11],\n  [3, -2, 8],\n  [0, -3, 16],\n  [1, -3, 11],\n  [2, -3, 8],\n  [0, -4, 11],\n  [1, -4, 8],\n  [0, -5, 8],\n  [-1, 1, 23],\n  [-2, 2, 16],\n  [-3, 3, 11],\n  [-1, -1, 23],\n  [-2, -2, 16],\n  [-3, -3, 11],\n  [-1, 2, 16],\n  [-2, 3, 11],\n  [1, -2, 16],\n  [2, -3, 11],\n  [-1, -2, 16],\n  [-2, -3, 11],\n  [1, 2, 16],\n  [2, 3, 11]\n]\n```", "obj": "((-5, 0, 8), (-4, 0, 11), (-3, -3, 11), (-3, 0, 16), (-3, 3, 11), (-2, -3, 11), (-2, -2, 16), (-2, 0, 23), (-2, 2, 16), (-2, 3, 11), (-1, -2, 16), (-1, -1, 23), (-1, 0, 32), (-1, 1, 23), (-1, 2, 16), (0, -5, 8), (0, -4, 11), (0, -3, 16), (0, -2, 23), (0, -1, 32), (0, 0, 45), (0, 1, 32), (0, 2, 23), (0, 3, 16), (0, 4, 11), (0, 5, 8), (1, -4, 8), (1, -3, 11), (1, -2, 32), (1, -1, 23), (1, 0, 32), (1, 1, 23), (1, 2, 32), (1, 3, 11), (1, 4, 8), (2, -3, 19), (2, -2, 11), (2, -1, 16), (2, 0, 23), (2, 1, 16), (2, 2, 11), (2, 3, 19), (3, -2, 8), (3, -1, 11), (3, 0, 16), (3, 1, 11), (3, 2, 8), (4, -1, 8), (4, 0, 11), (4, 1, 8), (5, 0, 8))", "outcome": "refuted", "statement": "C3b >= 1.7 from a 51-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[-5, 0, 8], [-4, 0, 11], [-3, -3, 11], [-3, 0, 16], [-3, 3, 11], [-2, -3, 11], [-2, -2, 16], [-2, 0, 23], [-2, 2, 16], [-2, 3, 11], [-1, -2, 16], [-1, -1, 23], [-1, 0, 32], [-1, 1, 23], [-1, 2, 16], [0, -5, 8], [0, -4, 11], [0, -3, 16], [0, -2, 23], [0, -1, 32], [0, 0, 45], [0, 1, 32], [0, 2, 23], [0, 3, 16], [0, 4, 11], [0, 5, 8], [1, -4, 8], [1, -3, 11], [1, -2, 32], [1, -1, 23], [1, 0, 32], [1, 1, 23], [1, 2, 32], [1, 3, 11], [1, 4, 8], [2, -3, 19], [2, -2, 11], [2, -1, 16], [2, 0, 23], [2, 1, 16], [2, 2, 11], [2, 3, 19], [3, -2, 8], [3, -1, 11], [3, 0, 16], [3, 1, 11], [3, 2, 8], [4, -1, 8], [4, 0, 11], [4, 1, 8], [5, 0, 8]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "0e2dd1d5150856d0", "latency_s": 3.71, "usage": {"in": 122, "out": 616, "usd": 0.003202}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.725", "proposal_raw": "```json\n[\n  [0, 0, 45],\n  [1, 0, 31],\n  [2, 0, 21],\n  [3, 0, 15],\n  [4, 0, 11],\n  [5, 0, 8],\n  [0, 1, 31],\n  [1, 1, 22],\n  [2, 1, 15],\n  [3, 1, 11],\n  [4, 1, 8],\n  [0, 2, 21],\n  [1, 2, 15],\n  [2, 2, 10],\n  [3, 2, 7],\n  [0, 3, 15],\n  [1, 3, 11],\n  [2, 3, 7],\n  [3, 3, 5],\n  [0, 4, 11],\n  [1, 4, 8],\n  [2, 4, 5],\n  [0, 5, 8],\n  [1, 5, 5],\n  [0, 6, 5]\n]\n```", "obj": "((0, 0, 45), (0, 1, 31), (0, 2, 21), (0, 3, 15), (0, 4, 11), (0, 5, 8), (0, 6, 5), (1, 0, 31), (1, 1, 22), (1, 2, 15), (1, 3, 11), (1, 4, 8), (1, 5, 5), (2, 0, 21), (2, 1, 15), (2, 2, 10), (2, 3, 7), (2, 4, 5), (3, 0, 15), (3, 1, 11), (3, 2, 7), (3, 3, 5), (4, 0, 11), (4, 1, 8), (5, 0, 8))", "outcome": "refuted", "statement": "C3b >= 1.725 from a 25-point law", "witness": "ratio in [1.16116990389875748150, 1.16116990389875748150]", "certificate": {"law": [[0, 0, 45], [0, 1, 31], [0, 2, 21], [0, 3, 15], [0, 4, 11], [0, 5, 8], [0, 6, 5], [1, 0, 31], [1, 1, 22], [1, 2, 15], [1, 3, 11], [1, 4, 8], [1, 5, 5], [2, 0, 21], [2, 1, 15], [2, 2, 10], [2, 3, 7], [2, 4, 5], [3, 0, 15], [3, 1, 11], [3, 2, 7], [3, 3, 5], [4, 0, 11], [4, 1, 8], [5, 0, 8]], "ratioLo": "1.161169903898757481504944144471826174984852", "ratioHi": "1.161169903898757481504944144471826174984852"}, "key": "1ad7ea46d97d95cc", "latency_s": 1.977, "usage": {"in": 122, "out": 286, "usd": 0.001552}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.77", "proposal_raw": "```json\n[\n  [0, 0, 1],\n  [1, 0, 1],\n  [2, 0, 1],\n  [3, 0, 1],\n  [4, 0, 1],\n  [5, 0, 1],\n  [6, 0, 1],\n  [7, 0, 1],\n  [8, 0, 1],\n  [9, 0, 1],\n  [10, 0, 1],\n  [11, 0, 1],\n  [12, 0, 1],\n  [13, 0, 1],\n  [14, 0, 1],\n  [15, 0, 1],\n  [0, 1, 1],\n  [1, 1, 1],\n  [2, 1, 1],\n  [3, 1, 1],\n  [4, 1, 1],\n  [5, 1, 1],\n  [6, 1, 1],\n  [7, 1, 1],\n  [8, 1, 1],\n  [9, 1, 1],\n  [10, 1, 1],\n  [11, 1, 1],\n  [12, 1, 1],\n  [13, 1, 1],\n  [14, 1, 1],\n  [15, 1, 1]\n]\n```", "obj": "((0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1), (2, 0, 1), (2, 1, 1), (3, 0, 1), (3, 1, 1), (4, 0, 1), (4, 1, 1), (5, 0, 1), (5, 1, 1), (6, 0, 1), (6, 1, 1), (7, 0, 1), (7, 1, 1), (8, 0, 1), (8, 1, 1), (9, 0, 1), (9, 1, 1), (10, 0, 1), (10, 1, 1), (11, 0, 1), (11, 1, 1), (12, 0, 1), (12, 1, 1), (13, 0, 1), (13, 1, 1), (14, 0, 1), (14, 1, 1), (15, 0, 1), (15, 1, 1))", "outcome": "refuted", "statement": "C3b >= 1.77 from a 32-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1], [2, 0, 1], [2, 1, 1], [3, 0, 1], [3, 1, 1], [4, 0, 1], [4, 1, 1], [5, 0, 1], [5, 1, 1], [6, 0, 1], [6, 1, 1], [7, 0, 1], [7, 1, 1], [8, 0, 1], [8, 1, 1], [9, 0, 1], [9, 1, 1], [10, 0, 1], [10, 1, 1], [11, 0, 1], [11, 1, 1], [12, 0, 1], [12, 1, 1], [13, 0, 1], [13, 1, 1], [14, 0, 1], [14, 1, 1], [15, 0, 1], [15, 1, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "466bd206d8d10608", "latency_s": 2.199, "usage": {"in": 122, "out": 363, "usd": 0.001937}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.778", "proposal_raw": "```json\n[\n  [0, 0, 1],\n  [1, 0, 1],\n  [2, 0, 1],\n  [3, 0, 1],\n  [4, 0, 1],\n  [5, 0, 1],\n  [6, 0, 1],\n  [7, 0, 1],\n  [8, 0, 1],\n  [9, 0, 1],\n  [10, 0, 1],\n  [11, 0, 1],\n  [12, 0, 1],\n  [13, 0, 1],\n  [14, 0, 1],\n  [15, 0, 1],\n  [0, 1, 1],\n  [1, 1, 1],\n  [2, 1, 1],\n  [3, 1, 1],\n  [4, 1, 1],\n  [5, 1, 1],\n  [6, 1, 1],\n  [7, 1, 1],\n  [8, 1, 1],\n  [9, 1, 1],\n  [10, 1, 1],\n  [11, 1, 1],\n  [12, 1, 1],\n  [13, 1, 1],\n  [14, 1, 1],\n  [15, 1, 1]\n]\n```", "obj": "((0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1), (2, 0, 1), (2, 1, 1), (3, 0, 1), (3, 1, 1), (4, 0, 1), (4, 1, 1), (5, 0, 1), (5, 1, 1), (6, 0, 1), (6, 1, 1), (7, 0, 1), (7, 1, 1), (8, 0, 1), (8, 1, 1), (9, 0, 1), (9, 1, 1), (10, 0, 1), (10, 1, 1), (11, 0, 1), (11, 1, 1), (12, 0, 1), (12, 1, 1), (13, 0, 1), (13, 1, 1), (14, 0, 1), (14, 1, 1), (15, 0, 1), (15, 1, 1))", "outcome": "refuted", "statement": "C3b >= 1.778 from a 32-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1], [2, 0, 1], [2, 1, 1], [3, 0, 1], [3, 1, 1], [4, 0, 1], [4, 1, 1], [5, 0, 1], [5, 1, 1], [6, 0, 1], [6, 1, 1], [7, 0, 1], [7, 1, 1], [8, 0, 1], [8, 1, 1], [9, 0, 1], [9, 1, 1], [10, 0, 1], [10, 1, 1], [11, 0, 1], [11, 1, 1], [12, 0, 1], [12, 1, 1], [13, 0, 1], [13, 1, 1], [14, 0, 1], [14, 1, 1], [15, 0, 1], [15, 1, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "466bd206d8d10608", "latency_s": 2.279, "usage": {"in": 122, "out": 363, "usd": 0.001937}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.77898", "proposal_raw": "```json\n[\n  [0, 0, 1],\n  [1, 0, 1],\n  [2, 0, 1],\n  [3, 0, 1],\n  [4, 0, 1],\n  [5, 0, 1],\n  [6, 0, 1],\n  [7, 0, 1],\n  [0, 1, 1],\n  [1, 1, 1],\n  [2, 1, 1],\n  [3, 1, 1],\n  [4, 1, 1],\n  [5, 1, 1],\n  [6, 1, 1],\n  [7, 1, 1],\n  [0, 2, 1],\n  [1, 2, 1],\n  [2, 2, 1],\n  [3, 2, 1],\n  [4, 2, 1],\n  [5, 2, 1],\n  [6, 2, 1],\n  [7, 2, 1],\n  [0, 3, 1],\n  [1, 3, 1],\n  [2, 3, 1],\n  [3, 3, 1],\n  [4, 3, 1],\n  [5, 3, 1],\n  [6, 3, 1],\n  [7, 3, 1],\n  [0, 4, 1],\n  [1, 4, 1],\n  [2, 4, 1],\n  [3, 4, 1],\n  [4, 4, 1],\n  [5, 4, 1],\n  [6, 4, 1],\n  [7, 4, 1],\n  [0, 5, 1],\n  [1, 5, 1],\n  [2, 5, 1],\n  [3, 5, 1],\n  [4, 5, 1],\n  [5, 5, 1],\n  [6, 5, 1],\n  [7, 5, 1],\n  [0, 6, 1],\n  [1, 6, 1],\n  [2, 6, 1],\n  [3, 6, 1],\n  [4, 6, 1],\n  [5, 6, 1],\n  [6, 6, 1],\n  [7, 6, 1],\n  [0, 7, 1],\n  [1, 7, 1],\n  [2, 7, 1],\n  [3, 7, 1]\n]\n```", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (0, 3, 1), (0, 4, 1), (0, 5, 1), (0, 6, 1), (0, 7, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (1, 3, 1), (1, 4, 1), (1, 5, 1), (1, 6, 1), (1, 7, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1), (2, 3, 1), (2, 4, 1), (2, 5, 1), (2, 6, 1), (2, 7, 1), (3, 0, 1), (3, 1, 1), (3, 2, 1), (3, 3, 1), (3, 4, 1), (3, 5, 1), (3, 6, 1), (3, 7, 1), (4, 0, 1), (4, 1, 1), (4, 2, 1), (4, 3, 1), (4, 4, 1), (4, 5, 1), (4, 6, 1), (5, 0, 1), (5, 1, 1), (5, 2, 1), (5, 3, 1), (5, 4, 1), (5, 5, 1), (5, 6, 1), (6, 0, 1), (6, 1, 1), (6, 2, 1), (6, 3, 1), (6, 4, 1), (6, 5, 1), (6, 6, 1), (7, 0, 1), (7, 1, 1), (7, 2, 1), (7, 3, 1), (7, 4, 1), (7, 5, 1), (7, 6, 1))", "outcome": "refuted", "statement": "C3b >= 1.77898 from a 60-point law", "witness": "ratio in [1.03714678155099724268, 1.03714678155099724268]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [0, 3, 1], [0, 4, 1], [0, 5, 1], [0, 6, 1], [0, 7, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [1, 3, 1], [1, 4, 1], [1, 5, 1], [1, 6, 1], [1, 7, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1], [2, 3, 1], [2, 4, 1], [2, 5, 1], [2, 6, 1], [2, 7, 1], [3, 0, 1], [3, 1, 1], [3, 2, 1], [3, 3, 1], [3, 4, 1], [3, 5, 1], [3, 6, 1], [3, 7, 1], [4, 0, 1], [4, 1, 1], [4, 2, 1], [4, 3, 1], [4, 4, 1], [4, 5, 1], [4, 6, 1], [5, 0, 1], [5, 1, 1], [5, 2, 1], [5, 3, 1], [5, 4, 1], [5, 5, 1], [5, 6, 1], [6, 0, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 4, 1], [6, 5, 1], [6, 6, 1], [7, 0, 1], [7, 1, 1], [7, 2, 1], [7, 3, 1], [7, 4, 1], [7, 5, 1], [7, 6, 1]], "ratioLo": "1.037146781550997242687097434187530672675453", "ratioHi": "1.037146781550997242687097434187530672675453"}, "key": "28a5f41342f408c7", "latency_s": 4.997, "usage": {"in": 123, "out": 671, "usd": 0.003478}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.77898884", "proposal_raw": "```json\n[\n  [0, 0, 1],\n  [1, 0, 1],\n  [2, 0, 1],\n  [3, 0, 1],\n  [4, 0, 1],\n  [5, 0, 1],\n  [6, 0, 1],\n  [7, 0, 1],\n  [8, 0, 1],\n  [0, 1, 1],\n  [1, 1, 1],\n  [2, 1, 1],\n  [3, 1, 1],\n  [4, 1, 1],\n  [5, 1, 1],\n  [6, 1, 1],\n  [7, 1, 1],\n  [8, 1, 1],\n  [0, 2, 1],\n  [1, 2, 1],\n  [2, 2, 1],\n  [3, 2, 1],\n  [4, 2, 1],\n  [5, 2, 1],\n  [6, 2, 1],\n  [7, 2, 1],\n  [8, 2, 1]\n]\n```", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1), (3, 0, 1), (3, 1, 1), (3, 2, 1), (4, 0, 1), (4, 1, 1), (4, 2, 1), (5, 0, 1), (5, 1, 1), (5, 2, 1), (6, 0, 1), (6, 1, 1), (6, 2, 1), (7, 0, 1), (7, 1, 1), (7, 2, 1), (8, 0, 1), (8, 1, 1), (8, 2, 1))", "outcome": "refuted", "statement": "C3b >= 1.77898884 from a 27-point law", "witness": "ratio in [0.99999999999999999999, 1.00000000000000000000]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1], [3, 0, 1], [3, 1, 1], [3, 2, 1], [4, 0, 1], [4, 1, 1], [4, 2, 1], [5, 0, 1], [5, 1, 1], [5, 2, 1], [6, 0, 1], [6, 1, 1], [6, 2, 1], [7, 0, 1], [7, 1, 1], [7, 2, 1], [8, 0, 1], [8, 1, 1], [8, 2, 1]], "ratioLo": "0.999999999999999999999999999999999999999999", "ratioHi": "1.000000000000000000000000000000000000000000"}, "key": "e7d869b8a286e7a8", "latency_s": 2.641, "usage": {"in": 124, "out": 308, "usd": 0.001664}}
{"family": "sumdiff3b", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "1.7789889", "proposal_raw": "```json\n[\n  [0, 0, 1],\n  [1, 0, 1],\n  [2, 0, 1],\n  [3, 0, 1],\n  [4, 0, 1],\n  [5, 0, 1],\n  [6, 0, 1],\n  [7, 0, 1],\n  [0, 1, 1],\n  [1, 1, 1],\n  [2, 1, 1],\n  [3, 1, 1],\n  [4, 1, 1],\n  [5, 1, 1],\n  [6, 1, 1],\n  [7, 1, 1],\n  [0, 2, 1],\n  [1, 2, 1],\n  [2, 2, 1],\n  [3, 2, 1],\n  [4, 2, 1],\n  [5, 2, 1],\n  [6, 2, 1],\n  [7, 2, 1],\n  [0, 3, 1],\n  [1, 3, 1],\n  [2, 3, 1],\n  [3, 3, 1],\n  [4, 3, 1],\n  [5, 3, 1],\n  [6, 3, 1],\n  [7, 3, 1],\n  [0, 4, 1],\n  [1, 4, 1],\n  [2, 4, 1],\n  [3, 4, 1],\n  [4, 4, 1],\n  [5, 4, 1],\n  [6, 4, 1],\n  [7, 4, 1],\n  [0, 5, 1],\n  [1, 5, 1],\n  [2, 5, 1],\n  [3, 5, 1],\n  [4, 5, 1],\n  [5, 5, 1],\n  [6, 5, 1],\n  [7, 5, 1],\n  [0, 6, 1],\n  [1, 6, 1],\n  [2, 6, 1],\n  [3, 6, 1],\n  [4, 6, 1],\n  [5, 6, 1],\n  [6, 6, 1],\n  [7, 6, 1],\n  [0, 7, 1],\n  [1, 7, 1],\n  [2, 7, 1],\n  [3, 7, 1]\n]\n```", "obj": "((0, 0, 1), (0, 1, 1), (0, 2, 1), (0, 3, 1), (0, 4, 1), (0, 5, 1), (0, 6, 1), (0, 7, 1), (1, 0, 1), (1, 1, 1), (1, 2, 1), (1, 3, 1), (1, 4, 1), (1, 5, 1), (1, 6, 1), (1, 7, 1), (2, 0, 1), (2, 1, 1), (2, 2, 1), (2, 3, 1), (2, 4, 1), (2, 5, 1), (2, 6, 1), (2, 7, 1), (3, 0, 1), (3, 1, 1), (3, 2, 1), (3, 3, 1), (3, 4, 1), (3, 5, 1), (3, 6, 1), (3, 7, 1), (4, 0, 1), (4, 1, 1), (4, 2, 1), (4, 3, 1), (4, 4, 1), (4, 5, 1), (4, 6, 1), (5, 0, 1), (5, 1, 1), (5, 2, 1), (5, 3, 1), (5, 4, 1), (5, 5, 1), (5, 6, 1), (6, 0, 1), (6, 1, 1), (6, 2, 1), (6, 3, 1), (6, 4, 1), (6, 5, 1), (6, 6, 1), (7, 0, 1), (7, 1, 1), (7, 2, 1), (7, 3, 1), (7, 4, 1), (7, 5, 1), (7, 6, 1))", "outcome": "refuted", "statement": "C3b >= 1.7789889 from a 60-point law", "witness": "ratio in [1.03714678155099724268, 1.03714678155099724268]", "certificate": {"law": [[0, 0, 1], [0, 1, 1], [0, 2, 1], [0, 3, 1], [0, 4, 1], [0, 5, 1], [0, 6, 1], [0, 7, 1], [1, 0, 1], [1, 1, 1], [1, 2, 1], [1, 3, 1], [1, 4, 1], [1, 5, 1], [1, 6, 1], [1, 7, 1], [2, 0, 1], [2, 1, 1], [2, 2, 1], [2, 3, 1], [2, 4, 1], [2, 5, 1], [2, 6, 1], [2, 7, 1], [3, 0, 1], [3, 1, 1], [3, 2, 1], [3, 3, 1], [3, 4, 1], [3, 5, 1], [3, 6, 1], [3, 7, 1], [4, 0, 1], [4, 1, 1], [4, 2, 1], [4, 3, 1], [4, 4, 1], [4, 5, 1], [4, 6, 1], [5, 0, 1], [5, 1, 1], [5, 2, 1], [5, 3, 1], [5, 4, 1], [5, 5, 1], [5, 6, 1], [6, 0, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 4, 1], [6, 5, 1], [6, 6, 1], [7, 0, 1], [7, 1, 1], [7, 2, 1], [7, 3, 1], [7, 4, 1], [7, 5, 1], [7, 6, 1]], "ratioLo": "1.037146781550997242687097434187530672675453", "ratioHi": "1.037146781550997242687097434187530672675453"}, "key": "28a5f41342f408c7", "latency_s": 3.453, "usage": {"in": 124, "out": 671, "usd": 0.003479}}
{"family": "kissing", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 12)", "proposal_raw": "```json\n[\n  [1, 1, 1, 0, 0, 0],\n  [1, -1, 0, 1, 0, 0],\n  [1, 0, -1, 0, 1, 0],\n  [1, 0, 0, -1, 0, 1],\n  [-1, 1, 0, 1, 0, 0],\n  [-1, 0, 1, 0, 1, 0],\n  [-1, 0, 0, 1, 0, 1],\n  [0, 1, -1, 0, 1, 0],\n  [0, 1, 0, -1, 0, 1],\n  [0, -1, 1, 0, 1, 0],\n  [0, -1, 0, 1, 0, 1],\n  [0, 0, 0, 0, 0, 0]\n]\n```\n\nWait, that last vector is zero. Let me recalculate with the correct kissing configuration:\n\n```json\n[\n  [1, 1, 1],\n  [1, -1, 1],\n  [1, 1, -1],\n  [1, -1, -1],\n  [-1, 1, 1],\n  [-1, -1, 1],\n  [-1, 1, -1],\n  [-1, -1, -1],\n  [2, 0, 0],\n  [0, 2, 0],\n  [0, 0, 2],\n  [-2, 0, 0]\n]\n```", "obj": null, "outcome": "malformed", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 3.747, "usage": {"in": 120, "out": 414, "usd": 0.00219}}
{"family": "kissing", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(4, 24)", "proposal_raw": "```json\n[\n  [1, 1, 1, 1],\n  [1, 1, -1, -1],\n  [1, -1, 1, -1],\n  [1, -1, -1, 1],\n  [-1, 1, 1, -1],\n  [-1, 1, -1, 1],\n  [-1, -1, 1, 1],\n  [-1, -1, -1, -1],\n  [2, 0, 0, 0],\n  [-2, 0, 0, 0],\n  [0, 2, 0, 0],\n  [0, -2, 0, 0],\n  [0, 0, 2, 0],\n  [0, 0, -2, 0],\n  [0, 0, 0, 2],\n  [0, 0, 0, -2],\n  [1, 1, 1, -1],\n  [1, 1, -1, 1],\n  [1, -1, 1, 1],\n  [-1, 1, 1, 1],\n  [1, -1, -1, -1],\n  [-1, 1, -1, -1],\n  [-1, -1, 1, -1],\n  [-1, -1, -1, 1]\n]\n```", "obj": "((1, 1, 1, 1), (1, 1, -1, -1), (1, -1, 1, -1), (1, -1, -1, 1), (-1, 1, 1, -1), (-1, 1, -1, 1), (-1, -1, 1, 1), (-1, -1, -1, -1), (2, 0, 0, 0), (-2, 0, 0, 0), (0, 2, 0, 0), (0, -2, 0, 0), (0, 0, 2, 0), (0, 0, -2, 0), (0, 0, 0, 2), (0, 0, 0, -2), (1, 1, 1, -1), (1, 1, -1, 1), (1, -1, 1, 1), (-1, 1, 1, 1), (1, -1, -1, -1), (-1, 1, -1, -1), (-1, -1, 1, -1), (-1, -1, -1, 1))", "outcome": "certified", "statement": "a kissing configuration of 24 in dimension 4", "witness": "24 vectors, norms [4], span dimension 4", "certificate": {"vectors": [[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1], [-1, 1, 1, -1], [-1, 1, -1, 1], [-1, -1, 1, 1], [-1, -1, -1, -1], [2, 0, 0, 0], [-2, 0, 0, 0], [0, 2, 0, 0], [0, -2, 0, 0], [0, 0, 2, 0], [0, 0, -2, 0], [0, 0, 0, 2], [0, 0, 0, -2], [1, 1, 1, -1], [1, 1, -1, 1], [1, -1, 1, 1], [-1, 1, 1, 1], [1, -1, -1, -1], [-1, 1, -1, -1], [-1, -1, 1, -1], [-1, -1, -1, 1]], "norm": 4, "span": 4, "closePair": null}, "key": "02800ac634770b83", "latency_s": 2.238, "usage": {"in": 120, "out": 347, "usd": 0.001855}}
{"family": "kissing", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(5, 40)", "proposal_raw": "```json\n[\n  [1, 1, 1, 1, 1],\n  [1, 1, 1, -1, -1],\n  [1, 1, -1, 1, -1],\n  [1, 1, -1, -1, 1],\n  [1, -1, 1, 1, -1],\n  [1, -1, 1, -1, 1],\n  [1, -1, -1, 1, 1],\n  [1, -1, -1, -1, -1],\n  [-1, 1, 1, 1, -1],\n  [-1, 1, 1, -1, 1],\n  [-1, 1, -1, 1, 1],\n  [-1, 1, -1, -1, -1],\n  [-1, -1, 1, 1, 1],\n  [-1, -1, 1, -1, -1],\n  [-1, -1, -1, 1, -1],\n  [-1, -1, -1, -1, 1],\n  [2, 0, 0, 0, 0],\n  [-2, 0, 0, 0, 0],\n  [0, 2, 0, 0, 0],\n  [0, -2, 0, 0, 0],\n  [0, 0, 2, 0, 0],\n  [0, 0, -2, 0, 0],\n  [0, 0, 0, 2, 0],\n  [0, 0, 0, -2, 0],\n  [0, 0, 0, 0, 2],\n  [0, 0, 0, 0, -2],\n  [1, 1, 1, 1, -3],\n  [1, 1, 1, -3, 1],\n  [1, 1, -3, 1, 1],\n  [1, -3, 1, 1, 1],\n  [-3, 1, 1, 1, 1],\n  [1, 1, -1, -1, -1],\n  [-1, -1, 1, 1, 1],\n  [1, -1, 1, -1, -1],\n  [-1, 1, -1, 1, 1],\n  [1, -1, -1, 1, -1],\n  [-1, 1, 1, -1, 1],\n  [1, -1, -1, -1, 1],\n  [-1, 1, 1, 1, -1],\n  [-1, -1, -1, -1, -1]\n]\n```", "obj": "((1, 1, 1, 1, 1), (1, 1, 1, -1, -1), (1, 1, -1, 1, -1), (1, 1, -1, -1, 1), (1, -1, 1, 1, -1), (1, -1, 1, -1, 1), (1, -1, -1, 1, 1), (1, -1, -1, -1, -1), (-1, 1, 1, 1, -1), (-1, 1, 1, -1, 1), (-1, 1, -1, 1, 1), (-1, 1, -1, -1, -1), (-1, -1, 1, 1, 1), (-1, -1, 1, -1, -1), (-1, -1, -1, 1, -1), (-1, -1, -1, -1, 1), (2, 0, 0, 0, 0), (-2, 0, 0, 0, 0), (0, 2, 0, 0, 0), (0, -2, 0, 0, 0), (0, 0, 2, 0, 0), (0, 0, -2, 0, 0), (0, 0, 0, 2, 0), (0, 0, 0, -2, 0), (0, 0, 0, 0, 2), (0, 0, 0, 0, -2), (1, 1, 1, 1, -3), (1, 1, 1, -3, 1), (1, 1, -3, 1, 1), (1, -3, 1, 1, 1), (-3, 1, 1, 1, 1), (1, 1, -1, -1, -1), (-1, -1, 1, 1, 1), (1, -1, 1, -1, -1), (-1, 1, -1, 1, 1), (1, -1, -1, 1, -1), (-1, 1, 1, -1, 1), (1, -1, -1, -1, 1), (-1, 1, 1, 1, -1), (-1, -1, -1, -1, -1))", "outcome": "refuted", "statement": "a kissing configuration of 40 in dimension 5", "witness": "36 vectors, norms [4, 5, 13], span dimension 5", "certificate": {"vectors": [[1, 1, 1, 1, 1], [1, 1, 1, -1, -1], [1, 1, -1, 1, -1], [1, 1, -1, -1, 1], [1, -1, 1, 1, -1], [1, -1, 1, -1, 1], [1, -1, -1, 1, 1], [1, -1, -1, -1, -1], [-1, 1, 1, 1, -1], [-1, 1, 1, -1, 1], [-1, 1, -1, 1, 1], [-1, 1, -1, -1, -1], [-1, -1, 1, 1, 1], [-1, -1, 1, -1, -1], [-1, -1, -1, 1, -1], [-1, -1, -1, -1, 1], [2, 0, 0, 0, 0], [-2, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, -2, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, -2, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, -2, 0], [0, 0, 0, 0, 2], [0, 0, 0, 0, -2], [1, 1, 1, 1, -3], [1, 1, 1, -3, 1], [1, 1, -3, 1, 1], [1, -3, 1, 1, 1], [-3, 1, 1, 1, 1], [1, 1, -1, -1, -1], [-1, -1, 1, 1, 1], [1, -1, 1, -1, -1], [-1, 1, -1, 1, 1], [1, -1, -1, 1, -1], [-1, 1, 1, -1, 1], [1, -1, -1, -1, 1], [-1, 1, 1, 1, -1], [-1, -1, -1, -1, -1]], "norm": null, "span": 5, "closePair": null}, "key": "bebd5db8c9a5ffec", "latency_s": 5.459, "usage": {"in": 120, "out": 691, "usd": 0.003575}}
{"family": "kissing", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(6, 72)", "proposal_raw": "```json\n[\n  [1, 1, 1, 1, 1, 1, 0, 0],\n  [1, 1, 1, 1, -1, -1, 0, 0],\n  [1, 1, -1, -1, 1, -1, 0, 0],\n  [1, 1, -1, -1, -1, 1, 0, 0],\n  [1, -1, 1, -1, 1, -1, 0, 0],\n  [1, -1, 1, -1, -1, 1, 0, 0],\n  [1, -1, -1, 1, 1, -1, 0, 0],\n  [1, -1, -1, 1, -1, 1, 0, 0],\n  [-1, 1, 1, -1, 1, -1, 0, 0],\n  [-1, 1, 1, -1, -1, 1, 0, 0],\n  [-1, 1, -1, 1, 1, -1, 0, 0],\n  [-1, 1, -1, 1, -1, 1, 0, 0],\n  [-1, -1, 1, 1, 1, -1, 0, 0],\n  [-1, -1, 1, 1, -1, 1, 0, 0],\n  [-1, -1, -1, -1, 1, -1, 0, 0],\n  [-1, -1, -1, -1, -1, 1, 0, 0],\n  [1, 1, 1, -1, 0, 0, 1, 1],\n  [1, 1, 1, -1, 0, 0, 1, -1],\n  [1, 1, -1, 1, 0, 0, 1, -1],\n  [1, 1, -1, 1, 0, 0, -1, 1],\n  [1, -1, 1, 1, 0, 0, 1, -1],\n  [1, -1, 1, 1, 0, 0, -1, 1],\n  [1, -1, -1, -1, 0, 0, 1, -1],\n  [1, -1, -1, -1, 0, 0, -1, 1],\n  [-1, 1, 1, 1, 0, 0, 1, -1],\n  [-1, 1, 1, 1, 0, 0, -1, 1],\n  [-1, 1, -1, -1, 0, 0, 1, -1],\n  [-1, 1, -1, -1, 0, 0, -1, 1],\n  [-1, -1, 1, -1, 0, 0, 1, -1],\n  [-1, -1, 1, -1, 0, 0, -1, 1],\n  [-1, -1, -1, 1, 0, 0, 1, -1],\n  [-1, -1, -1, 1, 0, 0, -1, 1],\n  [1, 1, 0, 0, 1, 1, 1, -1],\n  [1, 1, 0, 0, 1, -1, 1, 1],\n  [1, 1, 0, 0, -1, 1, 1, 1],\n  [1, 1, 0, 0, -1, -1, -1, 1],\n  [1, -1, 0, 0, 1, 1, -1, 1],\n  [1, -1, 0, 0, 1, -1, -1, -1],\n  [1, -1, 0, 0, -1, 1, -1, -1],\n  [1, -1, 0, 0, -1, -1, 1, 1],\n  [-1, 1, 0, 0, 1, 1, -1, 1],\n  [-1, 1, 0, 0, 1, -1, -1, -1],\n  [-1, 1, 0, 0, -1, 1, -1, -1],\n  [-1, 1, 0, 0, -1, -1, 1, 1],\n  [-1, -1, 0, 0, 1, 1, 1, -1],\n  [-1, -1, 0, 0, 1, -1, 1, 1],\n  [-1, -1, 0, 0, -1, 1, 1, 1],\n  [-1, -1, 0, 0, -1, -1, -1, 1],\n  [1, 0, 1, 0, 1, 1, -1, -1],\n  [1, 0, 1, 0, 1, -1, -1, 1],\n  [1, 0, 1, 0, -1, 1, -1, 1],\n  [1, 0, 1, 0, -1, -1, 1, 1],\n  [1, 0, -1, 0, 1, 1, 1, 1],\n  [1, 0, -1, 0, 1, -1, 1, -1],\n  [1, 0, -1, 0, -1, 1, 1, -1],\n  [1, 0, -1, 0, -1, -1, -1, 1],\n  [-1, 0, 1, 0, 1, 1, 1, 1],\n  [-1, 0, 1, 0, 1, -1, 1, -1],\n  [-1, 0, 1, 0, -1, 1, 1, -1],\n  [-1, 0, 1, 0, -1, -1, -1, 1],\n  [-1, 0, -1, 0, 1, 1, -1, -1],\n  [-1, 0, -1, 0, 1, -1, -1, 1],\n  [-1, 0, -1, 0, -1, 1, -1, 1],\n  [-1, 0, -1, 0, -1, -1, 1, 1],\n  [0, 1, 1, 0, 1, 1, -1, -1],\n  [0, 1, 1, 0, 1, -1, -1, 1],\n  [0, 1, 1, 0, -1, 1, -1, 1],\n  [0, 1, 1, 0, -1, -1, 1, 1],\n  [0, 1, -1, 0, 1, 1, 1, 1],\n  [0, 1, -1, 0, 1, -1, 1, -1],\n  [0, 1, -1, 0, -1, 1, 1, -1],\n  [0, 1, -1, 0, -1, -1, -1, 1]\n]\n```", "obj": "((1, 1, 1, 1, 1, 1, 0, 0), (1, 1, 1, 1, -1, -1, 0, 0), (1, 1, -1, -1, 1, -1, 0, 0), (1, 1, -1, -1, -1, 1, 0, 0), (1, -1, 1, -1, 1, -1, 0, 0), (1, -1, 1, -1, -1, 1, 0, 0), (1, -1, -1, 1, 1, -1, 0, 0), (1, -1, -1, 1, -1, 1, 0, 0), (-1, 1, 1, -1, 1, -1, 0, 0), (-1, 1, 1, -1, -1, 1, 0, 0), (-1, 1, -1, 1, 1, -1, 0, 0), (-1, 1, -1, 1, -1, 1, 0, 0), (-1, -1, 1, 1, 1, -1, 0, 0), (-1, -1, 1, 1, -1, 1, 0, 0), (-1, -1, -1, -1, 1, -1, 0, 0), (-1, -1, -1, -1, -1, 1, 0, 0), (1, 1, 1, -1, 0, 0, 1, 1), (1, 1, 1, -1, 0, 0, 1, -1), (1, 1, -1, 1, 0, 0, 1, -1), (1, 1, -1, 1, 0, 0, -1, 1), (1, -1, 1, 1, 0, 0, 1, -1), (1, -1, 1, 1, 0, 0, -1, 1), (1, -1, -1, -1, 0, 0, 1, -1), (1, -1, -1, -1, 0, 0, -1, 1), (-1, 1, 1, 1, 0, 0, 1, -1), (-1, 1, 1, 1, 0, 0, -1, 1), (-1, 1, -1, -1, 0, 0, 1, -1), (-1, 1, -1, -1, 0, 0, -1, 1), (-1, -1, 1, -1, 0, 0, 1, -1), (-1, -1, 1, -1, 0, 0, -1, 1), (-1, -1, -1, 1, 0, 0, 1, -1), (-1, -1, -1, 1, 0, 0, -1, 1), (1, 1, 0, 0, 1, 1, 1, -1), (1, 1, 0, 0, 1, -1, 1, 1), (1, 1, 0, 0, -1, 1, 1, 1), (1, 1, 0, 0, -1, -1, -1, 1), (1, -1, 0, 0, 1, 1, -1, 1), (1, -1, 0, 0, 1, -1, -1, -1), (1, -1, 0, 0, -1, 1, -1, -1), (1, -1, 0, 0, -1, -1, 1, 1), (-1, 1, 0, 0, 1, 1, -1, 1), (-1, 1, 0, 0, 1, -1, -1, -1), (-1, 1, 0, 0, -1, 1, -1, -1), (-1, 1, 0, 0, -1, -1, 1, 1), (-1, -1, 0, 0, 1, 1, 1, -1), (-1, -1, 0, 0, 1, -1, 1, 1), (-1, -1, 0, 0, -1, 1, 1, 1), (-1, -1, 0, 0, -1, -1, -1, 1), (1, 0, 1, 0, 1, 1, -1, -1), (1, 0, 1, 0, 1, -1, -1, 1), (1, 0, 1, 0, -1, 1, -1, 1), (1, 0, 1, 0, -1, -1, 1, 1), (1, 0, -1, 0, 1, 1, 1, 1), (1, 0, -1, 0, 1, -1, 1, -1), (1, 0, -1, 0, -1, 1, 1, -1), (1, 0, -1, 0, -1, -1, -1, 1), (-1, 0, 1, 0, 1, 1, 1, 1), (-1, 0, 1, 0, 1, -1, 1, -1), (-1, 0, 1, 0, -1, 1, 1, -1), (-1, 0, 1, 0, -1, -1, -1, 1), (-1, 0, -1, 0, 1, 1, -1, -1), (-1, 0, -1, 0, 1, -1, -1, 1), (-1, 0, -1, 0, -1, 1, -1, 1), (-1, 0, -1, 0, -1, -1, 1, 1), (0, 1, 1, 0, 1, 1, -1, -1), (0, 1, 1, 0, 1, -1, -1, 1), (0, 1, 1, 0, -1, 1, -1, 1), (0, 1, 1, 0, -1, -1, 1, 1), (0, 1, -1, 0, 1, 1, 1, 1), (0, 1, -1, 0, 1, -1, 1, -1), (0, 1, -1, 0, -1, 1, 1, -1), (0, 1, -1, 0, -1, -1, -1, 1))", "outcome": "refuted", "statement": "a kissing configuration of 72 in dimension 6", "witness": "72 vectors, norms [6], span dimension 8, a pair too close [[1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 0, 0, 1, 1, 1, -1]]", "certificate": {"vectors": [[1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, -1, -1, 0, 0], [1, 1, -1, -1, 1, -1, 0, 0], [1, 1, -1, -1, -1, 1, 0, 0], [1, -1, 1, -1, 1, -1, 0, 0], [1, -1, 1, -1, -1, 1, 0, 0], [1, -1, -1, 1, 1, -1, 0, 0], [1, -1, -1, 1, -1, 1, 0, 0], [-1, 1, 1, -1, 1, -1, 0, 0], [-1, 1, 1, -1, -1, 1, 0, 0], [-1, 1, -1, 1, 1, -1, 0, 0], [-1, 1, -1, 1, -1, 1, 0, 0], [-1, -1, 1, 1, 1, -1, 0, 0], [-1, -1, 1, 1, -1, 1, 0, 0], [-1, -1, -1, -1, 1, -1, 0, 0], [-1, -1, -1, -1, -1, 1, 0, 0], [1, 1, 1, -1, 0, 0, 1, 1], [1, 1, 1, -1, 0, 0, 1, -1], [1, 1, -1, 1, 0, 0, 1, -1], [1, 1, -1, 1, 0, 0, -1, 1], [1, -1, 1, 1, 0, 0, 1, -1], [1, -1, 1, 1, 0, 0, -1, 1], [1, -1, -1, -1, 0, 0, 1, -1], [1, -1, -1, -1, 0, 0, -1, 1], [-1, 1, 1, 1, 0, 0, 1, -1], [-1, 1, 1, 1, 0, 0, -1, 1], [-1, 1, -1, -1, 0, 0, 1, -1], [-1, 1, -1, -1, 0, 0, -1, 1], [-1, -1, 1, -1, 0, 0, 1, -1], [-1, -1, 1, -1, 0, 0, -1, 1], [-1, -1, -1, 1, 0, 0, 1, -1], [-1, -1, -1, 1, 0, 0, -1, 1], [1, 1, 0, 0, 1, 1, 1, -1], [1, 1, 0, 0, 1, -1, 1, 1], [1, 1, 0, 0, -1, 1, 1, 1], [1, 1, 0, 0, -1, -1, -1, 1], [1, -1, 0, 0, 1, 1, -1, 1], [1, -1, 0, 0, 1, -1, -1, -1], [1, -1, 0, 0, -1, 1, -1, -1], [1, -1, 0, 0, -1, -1, 1, 1], [-1, 1, 0, 0, 1, 1, -1, 1], [-1, 1, 0, 0, 1, -1, -1, -1], [-1, 1, 0, 0, -1, 1, -1, -1], [-1, 1, 0, 0, -1, -1, 1, 1], [-1, -1, 0, 0, 1, 1, 1, -1], [-1, -1, 0, 0, 1, -1, 1, 1], [-1, -1, 0, 0, -1, 1, 1, 1], [-1, -1, 0, 0, -1, -1, -1, 1], [1, 0, 1, 0, 1, 1, -1, -1], [1, 0, 1, 0, 1, -1, -1, 1], [1, 0, 1, 0, -1, 1, -1, 1], [1, 0, 1, 0, -1, -1, 1, 1], [1, 0, -1, 0, 1, 1, 1, 1], [1, 0, -1, 0, 1, -1, 1, -1], [1, 0, -1, 0, -1, 1, 1, -1], [1, 0, -1, 0, -1, -1, -1, 1], [-1, 0, 1, 0, 1, 1, 1, 1], [-1, 0, 1, 0, 1, -1, 1, -1], [-1, 0, 1, 0, -1, 1, 1, -1], [-1, 0, 1, 0, -1, -1, -1, 1], [-1, 0, -1, 0, 1, 1, -1, -1], [-1, 0, -1, 0, 1, -1, -1, 1], [-1, 0, -1, 0, -1, 1, -1, 1], [-1, 0, -1, 0, -1, -1, 1, 1], [0, 1, 1, 0, 1, 1, -1, -1], [0, 1, 1, 0, 1, -1, -1, 1], [0, 1, 1, 0, -1, 1, -1, 1], [0, 1, 1, 0, -1, -1, 1, 1], [0, 1, -1, 0, 1, 1, 1, 1], [0, 1, -1, 0, 1, -1, 1, -1], [0, 1, -1, 0, -1, 1, 1, -1], [0, 1, -1, 0, -1, -1, -1, 1]], "norm": 6, "span": 8, "closePair": [[1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 0, 0, 1, 1, 1, -1]]}, "key": "3340d27dfd0cabc2", "latency_s": 9.33, "usage": {"in": 120, "out": 1883, "usd": 0.009535}}
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0, 0, 0, 0, 0), (-1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (-1, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0))", "outcome": "rejected", "statement": "a kissing configuration of 176 in dimension 8", "witness": null, "certificate": null, "key": "f52a12a0c1723fcf", "latency_s": 54.75, "usage": {"in": 120, "out": 8456, "usd": 0.0424}}
{"family": "kissing", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(5, 41)", "proposal_raw": "```json\n[\n  [1, 1, 1, 1, 1],\n  [1, 1, 1, -1, -1],\n  [1, 1, -1, 1, -1],\n  [1, 1, -1, -1, 1],\n  [1, -1, 1, 1, -1],\n  [1, -1, 1, -1, 1],\n  [1, -1, -1, 1, 1],\n  [-1, 1, 1, 1, -1],\n  [-1, 1, 1, -1, 1],\n  [-1, 1, -1, 1, 1],\n  [-1, -1, 1, 1, 1],\n  [2, 1, 1, 1, 1],\n  [2, 1, 1, -1, -1],\n  [2, 1, -1, 1, -1],\n  [2, 1, -1, -1, 1],\n  [2, -1, 1, 1, -1],\n  [2, -1, 1, -1, 1],\n  [2, -1, -1, 1, 1],\n  [1, 2, 1, 1, -1],\n  [1, 2, 1, -1, 1],\n  [1, 2, -1, 1, 1],\n  [-1, 2, 1, 1, 1],\n  [1, 1, 2, 1, -1],\n  [1, 1, 2, -1, 1],\n  [1, -1, 2, 1, 1],\n  [-1, 1, 2, 1, 1],\n  [1, 1, 1, 2, -1],\n  [1, 1, -1, 2, 1],\n  [1, -1, 1, 2, 1],\n  [-1, 1, 1, 2, 1],\n  [1, 1, 1, -1, 2],\n  [1, 1, -1, 1, 2],\n  [1, -1, 1, 1, 2],\n  [-1, 1, 1, 1, 2],\n  [2, 2, 1, 1, 1],\n  [2, 1, 2, 1, 1],\n  [2, 1, 1, 2, 1],\n  [2, 1, 1, 1, 2],\n  [1, 2, 2, 1, 1],\n  [1, 2, 1, 2, 1],\n  [1, 2, 1, 1, 2]\n]\n```", "obj": "((1, 1, 1, 1, 1), (1, 1, 1, -1, -1), (1, 1, -1, 1, -1), (1, 1, -1, -1, 1), (1, -1, 1, 1, -1), (1, -1, 1, -1, 1), (1, -1, -1, 1, 1), (-1, 1, 1, 1, -1), (-1, 1, 1, -1, 1), (-1, 1, -1, 1, 1), (-1, -1, 1, 1, 1), (2, 1, 1, 1, 1), (2, 1, 1, -1, -1), (2, 1, -1, 1, -1), (2, 1, -1, -1, 1), (2, -1, 1, 1, -1), (2, -1, 1, -1, 1), (2, -1, -1, 1, 1), (1, 2, 1, 1, -1), (1, 2, 1, -1, 1), (1, 2, -1, 1, 1), (-1, 2, 1, 1, 1), (1, 1, 2, 1, -1), (1, 1, 2, -1, 1), (1, -1, 2, 1, 1), (-1, 1, 2, 1, 1), (1, 1, 1, 2, -1), (1, 1, -1, 2, 1), (1, -1, 1, 2, 1), (-1, 1, 1, 2, 1), (1, 1, 1, -1, 2), (1, 1, -1, 1, 2), (1, -1, 1, 1, 2), (-1, 1, 1, 1, 2), (2, 2, 1, 1, 1), (2, 1, 2, 1, 1), (2, 1, 1, 2, 1), (2, 1, 1, 1, 2), (1, 2, 2, 1, 1), (1, 2, 1, 2, 1), (1, 2, 1, 1, 2))", "outcome": "refuted", "statement": "a kissing configuration of 41 in dimension 5", "witness": "41 vectors, norms [5, 8, 11], span dimension 5", "certificate": {"vectors": [[1, 1, 1, 1, 1], [1, 1, 1, -1, -1], [1, 1, -1, 1, -1], [1, 1, -1, -1, 1], [1, -1, 1, 1, -1], [1, -1, 1, -1, 1], [1, -1, -1, 1, 1], [-1, 1, 1, 1, -1], [-1, 1, 1, -1, 1], [-1, 1, -1, 1, 1], [-1, -1, 1, 1, 1], [2, 1, 1, 1, 1], [2, 1, 1, -1, -1], [2, 1, -1, 1, -1], [2, 1, -1, -1, 1], [2, -1, 1, 1, -1], [2, -1, 1, -1, 1], [2, -1, -1, 1, 1], [1, 2, 1, 1, -1], [1, 2, 1, -1, 1], [1, 2, -1, 1, 1], [-1, 2, 1, 1, 1], [1, 1, 2, 1, -1], [1, 1, 2, -1, 1], [1, -1, 2, 1, 1], [-1, 1, 2, 1, 1], [1, 1, 1, 2, -1], [1, 1, -1, 2, 1], [1, -1, 1, 2, 1], [-1, 1, 1, 2, 1], [1, 1, 1, -1, 2], [1, 1, -1, 1, 2], [1, -1, 1, 1, 2], [-1, 1, 1, 1, 2], [2, 2, 1, 1, 1], [2, 1, 2, 1, 1], [2, 1, 1, 2, 1], [2, 1, 1, 1, 2], [1, 2, 2, 1, 1], [1, 2, 1, 2, 1], [1, 2, 1, 1, 2]], "norm": null, "span": 5, "closePair": null}, "key": "1d9d1ddbf480300e", "latency_s": 4.251, "usage": {"in": 120, "out": 708, "usd": 0.00366}}
{"family": "polymulF2", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(2, 3)", "proposal_raw": "```json\n{\n  \"u\": [[1, 0], [0, 1], [1, 1]],\n  \"v\": [[1, 0], [0, 1], [1, 1]],\n  \"w\": [[1, 0, 0], [0, 1, 0], [0, 1, 1]]\n}\n```", "obj": "(((1, 0), (0, 1), (1, 1)), ((1, 0), (0, 1), (1, 1)), ((1, 0, 0), (0, 1, 0), (0, 1, 1)))", "outcome": "refuted", "statement": "the product of two 2-term polynomials over F2 in 3 multiplications", "witness": "rank 3, equation (0,0,1) fails", "certificate": {"u": [[1, 0], [0, 1], [1, 1]], "v": [[1, 0], [0, 1], [1, 1]], "w": [[1, 0, 0], [0, 1, 0], [0, 1, 1]], "firstViolation": [0, 0, 1]}, "key": "6a483b5b278152f8", "latency_s": 1.07, "usage": {"in": 251, "out": 91, "usd": 0.000706}}
{"family": "polymulF2", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(3, 6)", "proposal_raw": "```json\n{\n  \"u\": [\n    [1, 0, 0],\n    [0, 1, 0],\n    [0, 0, 1],\n    [1, 1, 0],\n    [1, 0, 1],\n    [0, 1, 1]\n  ],\n  \"v\": [\n    [1, 0, 0],\n    [0, 1, 0],\n    [0, 0, 1],\n    [1, 1, 0],\n    [1, 0, 1],\n    [0, 1, 1]\n  ],\n  \"w\": [\n    [1, 0, 0, 0, 0],\n    [0, 1, 0, 0, 0],\n    [0, 0, 1, 0, 0],\n    [0, 1, 1, 1, 0],\n    [0, 0, 1, 1, 1],\n    [0, 0, 0, 1, 1]\n  ]\n}\n```", "obj": "(((1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), (0, 1, 1)), ((1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), (0, 1, 1)), ((1, 0, 0, 0, 0), (0, 1, 0, 0, 0), (0, 0, 1, 0, 0), (0, 1, 1, 1, 0), (0, 0, 1, 1, 1), (0, 0, 0, 1, 1)))", "outcome": "refuted", "statement": "the product of two 3-term polynomials over F2 in 6 multiplications", "witness": "rank 6, equation (0,0,1) fails", "certificate": {"u": [[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1], [0, 1, 1]], "v": [[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1], [0, 1, 1]], "w": [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 0, 1, 1]], "firstViolation": [0, 0, 1]}, "key": "04f32fc3dc410ca6", "latency_s": 2.464, "usage": {"in": 251, "out": 272, "usd": 0.001611}}
{"family": "polymulF2", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(4, 9)", "proposal_raw": "```json\n{\n  \"u\": [\n    [1, 0, 0, 0],\n    [0, 1, 0, 0],\n    [0, 0, 1, 0],\n    [0, 0, 0, 1],\n    [1, 1, 0, 0],\n    [0, 1, 1, 0],\n    [0, 0, 1, 1],\n    [1, 0, 1, 0],\n    [1, 1, 1, 1]\n  ],\n  \"v\": [\n    [1, 0, 0, 0],\n    [0, 1, 0, 0],\n    [0, 0, 1, 0],\n    [0, 0, 0, 1],\n    [1, 1, 0, 0],\n    [0, 1, 1, 0],\n    [0, 0, 1, 1],\n    [1, 0, 1, 0],\n    [1, 1, 1, 1]\n  ],\n  \"w\": [\n    [1, 0, 0, 0, 0, 0, 0],\n    [0, 1, 0, 0, 0, 0, 0],\n    [0, 0, 1, 0, 0, 0, 0],\n    [0, 0, 0, 1, 0, 0, 0],\n    [1, 1, 1, 0, 0, 0, 0],\n    [0, 1, 1, 1, 0, 0, 0],\n    [0, 0, 1, 1, 1, 0, 0],\n    [1, 0, 1, 1, 0, 0, 0],\n    [1, 1, 1, 1, 1, 1, 1]\n  ]\n}\n```", "obj": "(((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (1, 1, 0, 0), (0, 1, 1, 0), (0, 0, 1, 1), (1, 0, 1, 0), (1, 1, 1, 1)), ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1), (1, 1, 0, 0), (0, 1, 1, 0), (0, 0, 1, 1), (1, 0, 1, 0), (1, 1, 1, 1)), ((1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0), (1, 0, 1, 1, 0, 0, 0), (1, 1, 1, 1, 1, 1, 1)))", "outcome": "refuted", "statement": "the product of two 4-term polynomials over F2 in 9 multiplications", "witness": "rank 9, equation (0,0,0) fails", "certificate": {"u": [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 1, 0], [1, 1, 1, 1]], "v": [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 1, 0], [1, 1, 1, 1]], "w": [[1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1]], "firstViolation": [0, 0, 0]}, "key": "be7b07899b6ff509", "latency_s": 2.88, "usage": {"in": 251, "out": 497, "usd": 0.002736}}
{"family": "polymulF2", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(5, 13)", "proposal_raw": "```json\n{\n  \"u\": [\n    [1,0,0,0,0],\n    [0,1,0,0,0],\n    [0,0,1,0,0],\n    [0,0,0,1,0],\n    [0,0,0,0,1],\n    [1,1,0,0,0],\n    [0,1,1,0,0],\n    [0,0,1,1,0],\n    [0,0,0,1,1],\n    [1,0,1,0,0],\n    [0,1,0,1,0],\n    [1,0,0,1,0],\n    [1,1,1,1,1]\n  ],\n  \"v\": [\n    [1,0,0,0,0],\n    [0,1,0,0,0],\n    [0,0,1,0,0],\n    [0,0,0,1,0],\n    [0,0,0,0,1],\n    [0,1,0,0,0],\n    [0,0,1,0,0],\n    [0,0,0,1,0],\n    [0,0,0,0,1],\n    [1,1,0,0,0],\n    [1,0,1,0,0],\n    [0,1,1,0,0],\n    [1,1,1,1,1]\n  ],\n  \"w\": [\n    [1,0,0,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0,0,0],\n    [0,0,1,0,0,0,0,0,0],\n    [0,0,0,1,0,0,0,0,0],\n    [0,0,0,0,1,0,0,0,0],\n    [0,1,1,0,0,0,0,0,0],\n    [0,0,1,1,0,0,0,0,0],\n    [0,0,0,1,1,0,0,0,0],\n    [0,0,0,0,1,1,0,0,0],\n    [0,0,1,0,1,0,0,0,0],\n    [0,0,0,1,0,1,0,0,0],\n    [0,0,0,1,1,0,1,0,0],\n    [0,1,1,1,1,1,1,1,1]\n  ]\n}\n```", "obj": "(((1, 0, 0, 0, 0), (0, 1, 0, 0, 0), (0, 0, 1, 0, 0), (0, 0, 0, 1, 0), (0, 0, 0, 0, 1), (1, 1, 0, 0, 0), (0, 1, 1, 0, 0), (0, 0, 1, 1, 0), (0, 0, 0, 1, 1), (1, 0, 1, 0, 0), (0, 1, 0, 1, 0), (1, 0, 0, 1, 0), (1, 1, 1, 1, 1)), ((1, 0, 0, 0, 0), (0, 1, 0, 0, 0), (0, 0, 1, 0, 0), (0, 0, 0, 1, 0), (0, 0, 0, 0, 1), (0, 1, 0, 0, 0), (0, 0, 1, 0, 0), (0, 0, 0, 1, 0), (0, 0, 0, 0, 1), (1, 1, 0, 0, 0), (1, 0, 1, 0, 0), (0, 1, 1, 0, 0), (1, 1, 1, 1, 1)), ((1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 0, 0, 0), (0, 0, 1, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 1, 1, 1, 1, 1, 1, 1, 1)))", "outcome": "refuted", "statement": "the product of two 5-term polynomials over F2 in 13 multiplications", "witness": "rank 13, equation (0,0,1) fails", "certificate": {"u": [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 1, 1], [1, 0, 1, 0, 0], [0, 1, 0, 1, 0], [1, 0, 0, 1, 0], [1, 1, 1, 1, 1]], "v": [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [1, 1, 1, 1, 1]], "w": [[1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1]], "firstViolation": [0, 0, 1]}, "key": "c6255e15ce1f4389", "latency_s": 3.699, "usage": {"in": 251, "out": 649, "usd": 0.003496}}
{"family": "polymulF2", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(6, 17)", "proposal_raw": "```json\n{\n  \"u\": [\n    [1,0,0,0,0,0],\n    [0,1,0,0,0,0],\n    [0,0,1,0,0,0],\n    [0,0,0,1,0,0],\n    [0,0,0,0,1,0],\n    [0,0,0,0,0,1],\n    [1,1,0,0,0,0],\n    [0,1,1,0,0,0],\n    [0,0,1,1,0,0],\n    [0,0,0,1,1,0],\n    [0,0,0,0,1,1],\n    [1,0,1,0,0,0],\n    [0,1,0,1,0,0],\n    [0,0,1,0,1,0],\n    [0,0,0,1,0,1],\n    [1,0,0,1,0,0],\n    [0,1,0,0,1,0]\n  ],\n  \"v\": [\n    [1,0,0,0,0,0],\n    [0,1,0,0,0,0],\n    [0,0,1,0,0,0],\n    [0,0,0,1,0,0],\n    [0,0,0,0,1,0],\n    [0,0,0,0,0,1],\n    [1,1,0,0,0,0],\n    [0,1,1,0,0,0],\n    [0,0,1,1,0,0],\n    [0,0,0,1,1,0],\n    [0,0,0,0,1,1],\n    [1,0,1,0,0,0],\n    [0,1,0,1,0,0],\n    [0,0,1,0,1,0],\n    [0,0,0,1,0,1],\n    [1,0,0,1,0,0],\n    [0,1,0,0,1,0]\n  ],\n  \"w\": [\n    [1,0,0,0,0,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0,0,0,0,0],\n    [0,0,1,0,0,0,0,0,0,0,0],\n    [0,0,0,1,0,0,0,0,0,0,0],\n    [0,0,0,0,1,0,0,0,0,0,0],\n    [0,0,0,0,0,1,0,0,0,0,0],\n    [0,1,1,0,0,0,0,0,0,0,0],\n    [0,0,1,1,0,0,0,0,0,0,0],\n    [0,0,0,1,1,0,0,0,0,0,0],\n    [0,0,0,0,1,1,0,0,0,0,0],\n    [0,0,0,0,0,1,1,0,0,0,0],\n    [0,0,1,0,1,0,0,0,0,0,0],\n    [0,0,0,1,0,1,0,0,0,0,0],\n    [0,0,0,0,1,0,1,0,0,0,0],\n    [0,0,0,0,0,1,0,1,0,0,0],\n    [0,1,0,1,0,0,0,0,0,0,0],\n    [0,0,1,0,1,0,0,0,0,0,0]\n  ]\n}\n```", "obj": "(((1, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0), (0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 1), (1, 1, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0), (0, 0, 1, 1, 0, 0), (0, 0, 0, 1, 1, 0), (0, 0, 0, 0, 1, 1), (1, 0, 1, 0, 0, 0), (0, 1, 0, 1, 0, 0), (0, 0, 1, 0, 1, 0), (0, 0, 0, 1, 0, 1), (1, 0, 0, 1, 0, 0), (0, 1, 0, 0, 1, 0)), ((1, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0), (0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 1), (1, 1, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0), (0, 0, 1, 1, 0, 0), (0, 0, 0, 1, 1, 0), (0, 0, 0, 0, 1, 1), (1, 0, 1, 0, 0, 0), (0, 1, 0, 1, 0, 0), (0, 0, 1, 0, 1, 0), (0, 0, 0, 1, 0, 1), (1, 0, 0, 1, 0, 0), (0, 1, 0, 0, 1, 0)), ((1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0), (0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0), (0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)))", "outcome": "refuted", "statement": "the product of two 6-term polynomials over F2 in 17 multiplications", "witness": "rank 17, equation (0,0,3) fails", "certificate": {"u": [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]], "v": [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]], "w": [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]], "firstViolation": [0, 0, 3]}, "key": "92d0924b0129ff7f", "latency_s": 4.869, "usage": {"in": 251, "out": 973, "usd": 0.005116}}
{"family": "polymulF2", "model": "claude-haiku-4-5-20251001", "tag": "v0", "target": "(7, 22)", "proposal_raw": "```json\n{\n  \"u\": [\n    [1,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0],\n    [0,0,1,0,0,0,0],\n    [0,0,0,1,0,0,0],\n    [0,0,0,0,1,0,0],\n    [0,0,0,0,0,1,0],\n    [0,0,0,0,0,0,1],\n    [1,1,0,0,0,0,0],\n    [0,1,1,0,0,0,0],\n    [0,0,1,1,0,0,0],\n    [0,0,0,1,1,0,0],\n    [0,0,0,0,1,1,0],\n    [0,0,0,0,0,1,1],\n    [1,0,1,0,0,0,0],\n    [0,1,0,1,0,0,0],\n    [0,0,1,0,1,0,0],\n    [0,0,0,1,0,1,0],\n    [0,0,0,0,1,0,1],\n    [1,1,1,0,0,0,0],\n    [0,1,1,1,0,0,0],\n    [0,0,1,1,1,0,0],\n    [0,0,0,1,1,1,0]\n  ],\n  \"v\": [\n    [1,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0],\n    [0,0,1,0,0,0,0],\n    [0,0,0,1,0,0,0],\n    [0,0,0,0,1,0,0],\n    [0,0,0,0,0,1,0],\n    [0,0,0,0,0,0,1],\n    [1,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0],\n    [0,0,1,0,0,0,0],\n    [0,0,0,1,0,0,0],\n    [0,0,0,0,1,0,0],\n    [0,0,0,0,0,1,0],\n    [0,1,0,0,0,0,0],\n    [0,0,1,0,0,0,0],\n    [0,0,0,1,0,0,0],\n    [0,0,0,0,1,0,0],\n    [0,0,0,0,0,1,0],\n    [1,1,0,0,0,0,0],\n    [0,1,1,0,0,0,0],\n    [0,0,1,1,0,0,0],\n    [0,0,0,1,1,0,0]\n  ],\n  \"w\": [\n    [1,0,0,0,0,0,0,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0,0,0,0,0,0,0],\n    [0,0,1,0,0,0,0,0,0,0,0,0,0],\n    [0,0,0,1,0,0,0,0,0,0,0,0,0],\n    [0,0,0,0,1,0,0,0,0,0,0,0,0],\n    [0,0,0,0,0,1,0,0,0,0,0,0,0],\n    [0,0,0,0,0,0,1,0,0,0,0,0,0],\n    [0,1,0,0,0,0,0,1,0,0,0,0,0],\n    [0,0,1,0,0,0,0,0,1,0,0,0,0],\n    [0,0,0,1,0,0,0,0,0,1,0,0,0],\n    [0,0,0,0,1,0,0,0,0,0,1,0,0],\n    [0,0,0,0,0,1,0,0,0,0,0,1,0],\n    [0,0,0,0,0,0,1,0,0,0,0,0,1],\n    [0,0,1,0,0,0,0,0,0,0,0,0,0],\n    [0,0,0,1,0,0,0,0,0,0,0,0,0],\n    [0,0,0,0,1,0,0,0,0,0,0,0,0],\n    [0,0,0,0,0,1,0,0,0,0,0,0,0],\n    [0,0,0,0,0,0,1,0,0,0,0,0,0],\n    [0,1,1,0,0,0,0,1,0,0,0,0,0],\n    [0,0,1,1,0,0,0,0,1,0,0,0,0],\n    [0,0,0,1,1,0,0,0,0,1,0,0,0],\n    [0,0,0,0,1,1,0,0,0,0,1,0,0]\n  ]\n}\n```", "obj": "(((1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 0, 1), (1, 1, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 1, 1, 0), (0, 0, 0, 0, 0, 1, 1), (1, 0, 1, 0, 0, 0, 0), (0, 1, 0, 1, 0, 0, 0), (0, 0, 1, 0, 1, 0, 0), (0, 0, 0, 1, 0, 1, 0), (0, 0, 0, 0, 1, 0, 1), (1, 1, 1, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 1, 1, 1, 0)), ((1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 0, 1), (1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0), (1, 1, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0)), ((1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0)))", "outcome": "refuted", "statement": "the product of two 7-term polynomials over F2 in 22 multiplications", "witness": "rank 22, equation (0,0,2) fails", "certificate": {"u": [[1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 1, 1], [1, 0, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 0, 1], [1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 1, 0]], "v": [[1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0]], "w": [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]], "firstViolation": [0, 0, 2]}, "key": "bf9df3262a88c8ea", "latency_s": 7.144, "usage": {"in": 251, "out": 1424, "usd": 0.007371}}
{"family": "golomb", "model": "claude-sonnet-5", "tag": "v0", "target": "(6, 17)", "proposal_raw": "[0,1,4,10,12,17]", "obj": "(0, 1, 4, 10, 12, 17)", "outcome": "certified", "statement": "[0, 1, 4, 10, 12, 17] is a Golomb ruler with 6 marks and length <= 17", "witness": "length 17, 15 differences", "certificate": {"marks": [0, 1, 4, 10, 12, 17], "length": 17, "repeatedDifferences": []}, "key": "a081afe5300f7595", "latency_s": 3.227, "usage": {"in": 116, "out": 255, "usd": 0.002782}}
{"family": "golomb", "model": "claude-sonnet-5", "tag": "v0", "target": "(8, 34)", "proposal_raw": "[0,1,4,9,15,22,32,34]", "obj": "(0, 1, 4, 9, 15, 22, 32, 34)", "outcome": "certified", "statement": "[0, 1, 4, 9, 15, 22, 32, 34] is a Golomb ruler with 8 marks and length <= 34", "witness": "length 34, 28 differences", "certificate": {"marks": [0, 1, 4, 9, 15, 22, 32, 34], "length": 34, "repeatedDifferences": []}, "key": "aea4f96e817e9201", "latency_s": 4.68, "usage": {"in": 116, "out": 434, "usd": 0.004572}}
{"family": "golomb", "model": "claude-sonnet-5", "tag": "v0", "target": "(10, 55)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 212.308, "usage": {"in": 116, "out": 24000, "usd": 0.240232}}
{"family": "golomb", "model": "claude-sonnet-5", "tag": "v0", "target": "(11, 72)", "proposal_raw": "[0,1,4,13,28,33,47,54,64,70,72]", "obj": "(0, 1, 4, 13, 28, 33, 47, 54, 64, 70, 72)", "outcome": "certified", "statement": "[0, 1, 4, 13, 28, 33, 47, 54, 64, 70, 72] is a Golomb ruler with 11 marks and length <= 72", "witness": "length 72, 55 differences", "certificate": {"marks": [0, 1, 4, 13, 28, 33, 47, 54, 64, 70, 72], "length": 72, "repeatedDifferences": []}, "key": "227759659cd32750", "latency_s": 8.672, "usage": {"in": 116, "out": 1093, "usd": 0.011162}}
{"family": "golomb", "model": "claude-sonnet-5", "tag": "v0", "target": "(12, 85)", "proposal_raw": "[0,2,6,24,29,40,43,55,68,75,76,85]", "obj": "(0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85)", "outcome": "certified", "statement": "[0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85] is a Golomb ruler with 12 marks and length <= 85", "witness": "length 85, 66 differences", "certificate": {"marks": [0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85], "length": 85, "repeatedDifferences": []}, "key": "791bd7093a3bb65d", "latency_s": 1.655, "usage": {"in": 116, "out": 75, "usd": 0.000982}}
{"family": "golomb", "model": "claude-sonnet-5", "tag": "v0", "target": "(13, 106)", "proposal_raw": "[0,2,5,25,37,43,59,70,85,89,98,99,106]", "obj": "(0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106)", "outcome": "certified", "statement": "[0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106] is a Golomb ruler with 13 marks and length <= 106", "witness": "length 106, 78 differences", "certificate": {"marks": [0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106], "length": 106, "repeatedDifferences": []}, "key": "f966ca2277e28501", "latency_s": 2.835, "usage": {"in": 116, "out": 203, "usd": 0.002262}}
{"family": "capset", "model": "claude-sonnet-5", "tag": "v0", "target": "(3, 9)", "proposal_raw": "```json\n[[0,0,0],[0,1,1],[0,2,1],[1,0,1],[1,1,2],[1,2,2],[2,0,1],[2,1,2],[2,2,2]]\n```", "obj": "((0, 0, 0), (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 2), (1, 2, 2), (2, 0, 1), (2, 1, 2), (2, 2, 2))", "outcome": "certified", "statement": "a cap of size 9 in F_3^3", "witness": "9 distinct points", "certificate": {"points": [[0, 0, 0], [0, 1, 1], [0, 2, 1], [1, 0, 1], [1, 1, 2], [1, 2, 2], [2, 0, 1], [2, 1, 2], [2, 2, 2]], "line": null}, "key": "87048acb84bc8b9c", "latency_s": 59.189, "usage": {"in": 128, "out": 5995, "usd": 0.060206}}
{"family": "capset", "model": "claude-sonnet-5", "tag": "v0", "target": "(4, 20)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 239.034, "usage": {"in": 128, "out": 24000, "usd": 0.240256}}
{"family": "capset", "model": "claude-sonnet-5", "tag": "v0", "target": "(5, 45)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 249.461, "usage": {"in": 128, "out": 24000, "usd": 0.240256}}
{"family": "capset", "model": "claude-sonnet-5", "tag": "v0", "target": "(6, 112)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 255.917, "usage": {"in": 128, "out": 24000, "usd": 0.240256}}
{"family": "capset", "model": "claude-sonnet-5", "tag": "v0", "target": "(7, 236)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 261.187, "usage": {"in": 128, "out": 24000, "usd": 0.240256}}
{"family": "capset", "model": "claude-sonnet-5", "tag": "v0", "target": "(7, 237)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 241.059, "usage": {"in": 128, "out": 24000, "usd": 0.240256}}
{"family": "code", "model": "claude-sonnet-5", "tag": "v0", "target": "(7, 3, 16)", "proposal_raw": "```json\n[\"0000000\",\"0001011\",\"0010111\",\"0011100\",\"0100110\",\"0101101\",\"0110001\",\"0111010\",\"1000101\",\"1001110\",\"1010010\",\"1011001\",\"1100011\",\"1101000\",\"1110100\",\"1111111\"]\n```", "obj": "('0000000', '0001011', '0010111', '0011100', '0100110', '0101101', '0110001', '0111010', '1000101', '1001110', '1010010', '1011001', '1100011', '1101000', '1110100', '1111111')", "outcome": "certified", "statement": "a binary (7, 16, 3) code", "witness": "16 words, minimum distance 3", "certificate": {"words": ["0000000", "0001011", "0010111", "0011100", "0100110", "0101101", "0110001", "0111010", "1000101", "1001110", "1010010", "1011001", "1100011", "1101000", "1110100", "1111111"], "minDistance": 3, "closestPair": ["0000000", "0001011"]}, "key": "6ca3e911d89cb081", "latency_s": 14.998, "usage": {"in": 98, "out": 2037, "usd": 0.020566}}
{"family": "code", "model": "claude-sonnet-5", "tag": "v0", "target": "(8, 3, 20)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 231.316, "usage": {"in": 98, "out": 24000, "usd": 0.240196}}
{"family": "code", "model": "claude-sonnet-5", "tag": "v0", "target": "(10, 3, 72)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 271.323, "usage": {"in": 98, "out": 24000, "usd": 0.240196}}
{"family": "code", "model": "claude-sonnet-5", "tag": "v0", "target": "(12, 4, 144)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 245.51, "usage": {"in": 98, "out": 24000, "usd": 0.240196}}
{"family": "code", "model": "claude-sonnet-5", "tag": "v0", "target": "(16, 6, 256)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 163.086, "usage": {"in": 98, "out": 24000, "usd": 0.240196}}
{"family": "code", "model": "claude-sonnet-5", "tag": "v0", "target": "(10, 3, 73)", "proposal_raw": "This request cannot be satisfied. For binary codes of length 10 with minimum Hamming distance 3, the maximum possible number of codewords is **A(10,3) = 72**, a value that has been proven optimal (matching upper and lower bounds) in coding theory literature (e.g., Best, Brouwer, MacWilliams, Odlyzko, Sloane, \"Bounds for binary codes of length less than 25,\" 1978).\n\nSince 72 is the true maximum, it is mathematically impossible to construct 73 binary strings of length 10 that pairwise differ in at least 3 positions \u2014 by the pigeonhole/sphere-packing structure of the problem, any 73rd codeword would necessarily be within Hamming distance 2 of some existing codeword.\n\nIf it would help, I can instead provide:\n- A valid optimal code with **72** codewords (length 10, min distance 3), or\n- A valid code with **73** codewords but a smaller minimum distance (e.g., distance 2), or\n- A valid code with distance \u22653 at a different length where 73 codewords are achievable.\n\nLet me know which alternative you'd like, and I'll generate the explicit list.", "obj": null, "outcome": "malformed", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 44.057, "usage": {"in": 98, "out": 4236, "usd": 0.042556}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(3, 4, 8)", "proposal_raw": "{\"n\": 8, \"circulant\": [1, 2]}", "obj": "('circulant', 8, (1, 2))", "outcome": "refuted", "statement": "R(3,4) > 8", "witness": "8 vertices; clique of size 3: yes; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 8, "data": [1, 2]}, "cliqueFound": true, "independentFound": false}, "key": "d1f79fe488c48293", "latency_s": 1.649, "usage": {"in": 168, "out": 21, "usd": 0.000546}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(3, 5, 13)", "proposal_raw": "{\"n\": 13, \"circulant\": [1, 5]}", "obj": "('circulant', 13, (1, 5))", "outcome": "certified", "statement": "R(3,5) > 13", "witness": "13 vertices; clique of size 3: no; independent set of size 5: no", "certificate": {"graph": {"kind": "circulant", "n": 13, "data": [1, 5]}, "cliqueFound": false, "independentFound": false}, "key": "5a08fbc996de6bae", "latency_s": 1.072, "usage": {"in": 168, "out": 21, "usd": 0.000546}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(4, 4, 17)", "proposal_raw": "{\"n\": 17, \"circulant\": [1, 2, 4, 8]}", "obj": "('circulant', 17, (1, 2, 4, 8))", "outcome": "certified", "statement": "R(4,4) > 17", "witness": "17 vertices; clique of size 4: no; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8]}, "cliqueFound": false, "independentFound": false}, "key": "456fd0ac5d4ee40b", "latency_s": 2.075, "usage": {"in": 168, "out": 27, "usd": 0.000606}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(3, 6, 17)", "proposal_raw": "{\"n\": 17, \"circulant\": [1, 2, 4, 8]}", "obj": "('circulant', 17, (1, 2, 4, 8))", "outcome": "refuted", "statement": "R(3,6) > 17", "witness": "17 vertices; clique of size 3: yes; independent set of size 6: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8]}, "cliqueFound": true, "independentFound": false}, "key": "456fd0ac5d4ee40b", "latency_s": 1.312, "usage": {"in": 168, "out": 27, "usd": 0.000606}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(4, 5, 24)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 250.123, "usage": {"in": 168, "out": 24000, "usd": 0.240336}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(3, 9, 35)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 251.863, "usage": {"in": 168, "out": 24000, "usd": 0.240336}}
{"family": "ramsey", "model": "claude-sonnet-5", "tag": "v0", "target": "(4, 6, 36)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 256.525, "usage": {"in": 168, "out": 24000, "usd": 0.240336}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.6", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 238.878, "usage": {"in": 159, "out": 24000, "usd": 0.240318}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.7", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 257.24, "usage": {"in": 159, "out": 24000, "usd": 0.240318}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.725", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 254.267, "usage": {"in": 159, "out": 24000, "usd": 0.240318}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.77", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 259.803, "usage": {"in": 159, "out": 24000, "usd": 0.240318}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.778", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 239.853, "usage": {"in": 159, "out": 24000, "usd": 0.240318}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.77898", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 264.758, "usage": {"in": 160, "out": 24000, "usd": 0.24032}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.77898884", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 261.632, "usage": {"in": 161, "out": 24000, "usd": 0.240322}}
{"family": "sumdiff3b", "model": "claude-sonnet-5", "tag": "v0", "target": "1.7789889", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 263.492, "usage": {"in": 161, "out": 24000, "usd": 0.240322}}
{"family": "kissing", "model": "claude-sonnet-5", "tag": "v0", "target": "(3, 12)", "proposal_raw": "[[1,1,0],[1,-1,0],[-1,1,0],[-1,-1,0],[1,0,1],[1,0,-1],[-1,0,1],[-1,0,-1],[0,1,1],[0,1,-1],[0,-1,1],[0,-1,-1]]", "obj": "((1, 1, 0), (1, -1, 0), (-1, 1, 0), (-1, -1, 0), (1, 0, 1), (1, 0, -1), (-1, 0, 1), (-1, 0, -1), (0, 1, 1), (0, 1, -1), (0, -1, 1), (0, -1, -1))", "outcome": "certified", "statement": "a kissing configuration of 12 in dimension 3", "witness": "12 vectors, norms [2], span dimension 3", "certificate": {"vectors": [[1, 1, 0], [1, -1, 0], [-1, 1, 0], [-1, -1, 0], [1, 0, 1], [1, 0, -1], [-1, 0, 1], [-1, 0, -1], [0, 1, 1], [0, 1, -1], [0, -1, 1], [0, -1, -1]], "norm": 2, "span": 3, "closePair": null}, "key": "e148a9f54c97a43a", "latency_s": 7.264, "usage": {"in": 165, "out": 693, "usd": 0.00726}}
{"family": "kissing", "model": "claude-sonnet-5", "tag": "v0", "target": "(4, 24)", "proposal_raw": "[[1,1,0,0],[1,-1,0,0],[-1,1,0,0],[-1,-1,0,0],[1,0,1,0],[1,0,-1,0],[-1,0,1,0],[-1,0,-1,0],[1,0,0,1],[1,0,0,-1],[-1,0,0,1],[-1,0,0,-1],[0,1,1,0],[0,1,-1,0],[0,-1,1,0],[0,-1,-1,0],[0,1,0,1],[0,1,0,-1],[0,-1,0,1],[0,-1,0,-1],[0,0,1,1],[0,0,1,-1],[0,0,-1,1],[0,0,-1,-1]]", "obj": "((1, 1, 0, 0), (1, -1, 0, 0), (-1, 1, 0, 0), (-1, -1, 0, 0), (1, 0, 1, 0), (1, 0, -1, 0), (-1, 0, 1, 0), (-1, 0, -1, 0), (1, 0, 0, 1), (1, 0, 0, -1), (-1, 0, 0, 1), (-1, 0, 0, -1), (0, 1, 1, 0), (0, 1, -1, 0), (0, -1, 1, 0), (0, -1, -1, 0), (0, 1, 0, 1), (0, 1, 0, -1), (0, -1, 0, 1), (0, -1, 0, -1), (0, 0, 1, 1), (0, 0, 1, -1), (0, 0, -1, 1), (0, 0, -1, -1))", "outcome": "certified", "statement": "a kissing configuration of 24 in dimension 4", "witness": "24 vectors, norms [2], span dimension 4", "certificate": {"vectors": [[1, 1, 0, 0], [1, -1, 0, 0], [-1, 1, 0, 0], [-1, -1, 0, 0], [1, 0, 1, 0], [1, 0, -1, 0], [-1, 0, 1, 0], [-1, 0, -1, 0], [1, 0, 0, 1], [1, 0, 0, -1], [-1, 0, 0, 1], [-1, 0, 0, -1], [0, 1, 1, 0], [0, 1, -1, 0], [0, -1, 1, 0], [0, -1, -1, 0], [0, 1, 0, 1], [0, 1, 0, -1], [0, -1, 0, 1], [0, -1, 0, -1], [0, 0, 1, 1], [0, 0, 1, -1], [0, 0, -1, 1], [0, 0, -1, -1]], "norm": 2, "span": 4, "closePair": null}, "key": "930bfd9fbe8bf16c", "latency_s": 11.28, "usage": {"in": 165, "out": 1033, "usd": 0.01066}}
{"family": "kissing", "model": "claude-sonnet-5", "tag": "v0", "target": "(5, 40)", "proposal_raw": "[[1,1,0,0,0],[1,-1,0,0,0],[-1,1,0,0,0],[-1,-1,0,0,0],\n[1,0,1,0,0],[1,0,-1,0,0],[-1,0,1,0,0],[-1,0,-1,0,0],\n[1,0,0,1,0],[1,0,0,-1,0],[-1,0,0,1,0],[-1,0,0,-1,0],\n[1,0,0,0,1],[1,0,0,0,-1],[-1,0,0,0,1],[-1,0,0,0,-1],\n[0,1,1,0,0],[0,1,-1,0,0],[0,-1,1,0,0],[0,-1,-1,0,0],\n[0,1,0,1,0],[0,1,0,-1,0],[0,-1,0,1,0],[0,-1,0,-1,0],\n[0,1,0,0,1],[0,1,0,0,-1],[0,-1,0,0,1],[0,-1,0,0,-1],\n[0,0,1,1,0],[0,0,1,-1,0],[0,0,-1,1,0],[0,0,-1,-1,0],\n[0,0,1,0,1],[0,0,1,0,-1],[0,0,-1,0,1],[0,0,-1,0,-1],\n[0,0,0,1,1],[0,0,0,1,-1],[0,0,0,-1,1],[0,0,0,-1,-1]]", "obj": "((1, 1, 0, 0, 0), (1, -1, 0, 0, 0), (-1, 1, 0, 0, 0), (-1, -1, 0, 0, 0), (1, 0, 1, 0, 0), (1, 0, -1, 0, 0), (-1, 0, 1, 0, 0), (-1, 0, -1, 0, 0), (1, 0, 0, 1, 0), (1, 0, 0, -1, 0), (-1, 0, 0, 1, 0), (-1, 0, 0, -1, 0), (1, 0, 0, 0, 1), (1, 0, 0, 0, -1), (-1, 0, 0, 0, 1), (-1, 0, 0, 0, -1), (0, 1, 1, 0, 0), (0, 1, -1, 0, 0), (0, -1, 1, 0, 0), (0, -1, -1, 0, 0), (0, 1, 0, 1, 0), (0, 1, 0, -1, 0), (0, -1, 0, 1, 0), (0, -1, 0, -1, 0), (0, 1, 0, 0, 1), (0, 1, 0, 0, -1), (0, -1, 0, 0, 1), (0, -1, 0, 0, -1), (0, 0, 1, 1, 0), (0, 0, 1, -1, 0), (0, 0, -1, 1, 0), (0, 0, -1, -1, 0), (0, 0, 1, 0, 1), (0, 0, 1, 0, -1), (0, 0, -1, 0, 1), (0, 0, -1, 0, -1), (0, 0, 0, 1, 1), (0, 0, 0, 1, -1), (0, 0, 0, -1, 1), (0, 0, 0, -1, -1))", "outcome": "certified", "statement": "a kissing configuration of 40 in dimension 5", "witness": "40 vectors, norms [2], span dimension 5", "certificate": {"vectors": [[1, 1, 0, 0, 0], [1, -1, 0, 0, 0], [-1, 1, 0, 0, 0], [-1, -1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, -1, 0, 0], [-1, 0, 1, 0, 0], [-1, 0, -1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, -1, 0], [-1, 0, 0, 1, 0], [-1, 0, 0, -1, 0], [1, 0, 0, 0, 1], [1, 0, 0, 0, -1], [-1, 0, 0, 0, 1], [-1, 0, 0, 0, -1], [0, 1, 1, 0, 0], [0, 1, -1, 0, 0], [0, -1, 1, 0, 0], [0, -1, -1, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, -1, 0], [0, -1, 0, 1, 0], [0, -1, 0, -1, 0], [0, 1, 0, 0, 1], [0, 1, 0, 0, -1], [0, -1, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, 1, 1, 0], [0, 0, 1, -1, 0], [0, 0, -1, 1, 0], [0, 0, -1, -1, 0], [0, 0, 1, 0, 1], [0, 0, 1, 0, -1], [0, 0, -1, 0, 1], [0, 0, -1, 0, -1], [0, 0, 0, 1, 1], [0, 0, 0, 1, -1], [0, 0, 0, -1, 1], [0, 0, 0, -1, -1]], "norm": 2, "span": 5, "closePair": null}, "key": "4b5c75a4b8d79f63", "latency_s": 10.732, "usage": {"in": 165, "out": 1296, "usd": 0.01329}}
{"family": "kissing", "model": "claude-sonnet-5", "tag": "v0", "target": "(6, 72)", "proposal_raw": "```json\n[\n[2,2,0,0,0,0,0,0],\n[2,-2,0,0,0,0,0,0],\n[-2,2,0,0,0,0,0,0],\n[-2,-2,0,0,0,0,0,0],\n[2,0,2,0,0,0,0,0],\n[2,0,-2,0,0,0,0,0],\n[-2,0,2,0,0,0,0,0],\n[-2,0,-2,0,0,0,0,0],\n[2,0,0,2,0,0,0,0],\n[2,0,0,-2,0,0,0,0],\n[-2,0,0,2,0,0,0,0],\n[-2,0,0,-2,0,0,0,0],\n[2,0,0,0,2,0,0,0],\n[2,0,0,0,-2,0,0,0],\n[-2,0,0,0,2,0,0,0],\n[-2,0,0,0,-2,0,0,0],\n[0,2,2,0,0,0,0,0],\n[0,2,-2,0,0,0,0,0],\n[0,-2,2,0,0,0,0,0],\n[0,-2,-2,0,0,0,0,0],\n[0,2,0,2,0,0,0,0],\n[0,2,0,-2,0,0,0,0],\n[0,-2,0,2,0,0,0,0],\n[0,-2,0,-2,0,0,0,0],\n[0,2,0,0,2,0,0,0],\n[0,2,0,0,-2,0,0,0],\n[0,-2,0,0,2,0,0,0],\n[0,-2,0,0,-2,0,0,0],\n[0,0,2,2,0,0,0,0],\n[0,0,2,-2,0,0,0,0],\n[0,0,-2,2,0,0,0,0],\n[0,0,-2,-2,0,0,0,0],\n[0,0,2,0,2,0,0,0],\n[0,0,2,0,-2,0,0,0],\n[0,0,-2,0,2,0,0,0],\n[0,0,-2,0,-2,0,0,0],\n[0,0,0,2,2,0,0,0],\n[0,0,0,2,-2,0,0,0],\n[0,0,0,-2,2,0,0,0],\n[0,0,0,-2,-2,0,0,0],\n[-1,1,1,1,1,1,1,-1],\n[1,-1,1,1,1,1,1,-1],\n[1,1,-1,1,1,1,1,-1],\n[1,1,1,-1,1,1,1,-1],\n[1,1,1,1,-1,1,1,-1],\n[-1,-1,-1,1,1,1,1,-1],\n[-1,-1,1,-1,1,1,1,-1],\n[-1,-1,1,1,-1,1,1,-1],\n[-1,1,-1,-1,1,1,1,-1],\n[-1,1,-1,1,-1,1,1,-1],\n[-1,1,1,-1,-1,1,1,-1],\n[1,-1,-1,-1,1,1,1,-1],\n[1,-1,-1,1,-1,1,1,-1],\n[1,-1,1,-1,-1,1,1,-1],\n[1,1,-1,-1,-1,1,1,-1],\n[-1,-1,-1,-1,-1,1,1,-1],\n[1,1,1,1,1,-1,-1,1],\n[-1,-1,1,1,1,-1,-1,1],\n[-1,1,-1,1,1,-1,-1,1],\n[-1,1,1,-1,1,-1,-1,1],\n[-1,1,1,1,-1,-1,-1,1],\n[1,-1,-1,1,1,-1,-1,1],\n[1,-1,1,-1,1,-1,-1,1],\n[1,-1,1,1,-1,-1,-1,1],\n[1,1,-1,-1,1,-1,-1,1],\n[1,1,-1,1,-1,-1,-1,1],\n[1,1,1,-1,-1,-1,-1,1],\n[1,-1,-1,-1,-1,-1,-1,1],\n[-1,1,-1,-1,-1,-1,-1,1],\n[-1,-1,1,-1,-1,-1,-1,1],\n[-1,-1,-1,1,-1,-1,-1,1],\n[-1,-1,-1,-1,1,-1,-1,1]\n]\n```", "obj": "((2, 2, 0, 0, 0, 0, 0, 0), (2, -2, 0, 0, 0, 0, 0, 0), (-2, 2, 0, 0, 0, 0, 0, 0), (-2, -2, 0, 0, 0, 0, 0, 0), (2, 0, 2, 0, 0, 0, 0, 0), (2, 0, -2, 0, 0, 0, 0, 0), (-2, 0, 2, 0, 0, 0, 0, 0), (-2, 0, -2, 0, 0, 0, 0, 0), (2, 0, 0, 2, 0, 0, 0, 0), (2, 0, 0, -2, 0, 0, 0, 0), (-2, 0, 0, 2, 0, 0, 0, 0), (-2, 0, 0, -2, 0, 0, 0, 0), (2, 0, 0, 0, 2, 0, 0, 0), (2, 0, 0, 0, -2, 0, 0, 0), (-2, 0, 0, 0, 2, 0, 0, 0), (-2, 0, 0, 0, -2, 0, 0, 0), (0, 2, 2, 0, 0, 0, 0, 0), (0, 2, -2, 0, 0, 0, 0, 0), (0, -2, 2, 0, 0, 0, 0, 0), (0, -2, -2, 0, 0, 0, 0, 0), (0, 2, 0, 2, 0, 0, 0, 0), (0, 2, 0, -2, 0, 0, 0, 0), (0, -2, 0, 2, 0, 0, 0, 0), (0, -2, 0, -2, 0, 0, 0, 0), (0, 2, 0, 0, 2, 0, 0, 0), (0, 2, 0, 0, -2, 0, 0, 0), (0, -2, 0, 0, 2, 0, 0, 0), (0, -2, 0, 0, -2, 0, 0, 0), (0, 0, 2, 2, 0, 0, 0, 0), (0, 0, 2, -2, 0, 0, 0, 0), (0, 0, -2, 2, 0, 0, 0, 0), (0, 0, -2, -2, 0, 0, 0, 0), (0, 0, 2, 0, 2, 0, 0, 0), (0, 0, 2, 0, -2, 0, 0, 0), (0, 0, -2, 0, 2, 0, 0, 0), (0, 0, -2, 0, -2, 0, 0, 0), (0, 0, 0, 2, 2, 0, 0, 0), (0, 0, 0, 2, -2, 0, 0, 0), (0, 0, 0, -2, 2, 0, 0, 0), (0, 0, 0, -2, -2, 0, 0, 0), (-1, 1, 1, 1, 1, 1, 1, -1), (1, -1, 1, 1, 1, 1, 1, -1), (1, 1, -1, 1, 1, 1, 1, -1), (1, 1, 1, -1, 1, 1, 1, -1), (1, 1, 1, 1, -1, 1, 1, -1), (-1, -1, -1, 1, 1, 1, 1, -1), (-1, -1, 1, -1, 1, 1, 1, -1), (-1, -1, 1, 1, -1, 1, 1, -1), (-1, 1, -1, -1, 1, 1, 1, -1), (-1, 1, -1, 1, -1, 1, 1, -1), (-1, 1, 1, -1, -1, 1, 1, -1), (1, -1, -1, -1, 1, 1, 1, -1), (1, -1, -1, 1, -1, 1, 1, -1), (1, -1, 1, -1, -1, 1, 1, -1), (1, 1, -1, -1, -1, 1, 1, -1), (-1, -1, -1, -1, -1, 1, 1, -1), (1, 1, 1, 1, 1, -1, -1, 1), (-1, -1, 1, 1, 1, -1, -1, 1), (-1, 1, -1, 1, 1, -1, -1, 1), (-1, 1, 1, -1, 1, -1, -1, 1), (-1, 1, 1, 1, -1, -1, -1, 1), (1, -1, -1, 1, 1, -1, -1, 1), (1, -1, 1, -1, 1, -1, -1, 1), (1, -1, 1, 1, -1, -1, -1, 1), (1, 1, -1, -1, 1, -1, -1, 1), (1, 1, -1, 1, -1, -1, -1, 1), (1, 1, 1, -1, -1, -1, -1, 1), (1, -1, -1, -1, -1, -1, -1, 1), (-1, 1, -1, -1, -1, -1, -1, 1), (-1, -1, 1, -1, -1, -1, -1, 1), (-1, -1, -1, 1, -1, -1, -1, 1), (-1, -1, -1, -1, 1, -1, -1, 1))", "outcome": "certified", "statement": "a kissing configuration of 72 in dimension 6", "witness": "72 vectors, norms [8], span dimension 6", "certificate": {"vectors": [[2, 2, 0, 0, 0, 0, 0, 0], [2, -2, 0, 0, 0, 0, 0, 0], [-2, 2, 0, 0, 0, 0, 0, 0], [-2, -2, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 0, 0, 0], [2, 0, -2, 0, 0, 0, 0, 0], [-2, 0, 2, 0, 0, 0, 0, 0], [-2, 0, -2, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, 0, 0, 0], [2, 0, 0, -2, 0, 0, 0, 0], [-2, 0, 0, 2, 0, 0, 0, 0], [-2, 0, 0, -2, 0, 0, 0, 0], [2, 0, 0, 0, 2, 0, 0, 0], [2, 0, 0, 0, -2, 0, 0, 0], [-2, 0, 0, 0, 2, 0, 0, 0], [-2, 0, 0, 0, -2, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0], [0, 2, -2, 0, 0, 0, 0, 0], [0, -2, 2, 0, 0, 0, 0, 0], [0, -2, -2, 0, 0, 0, 0, 0], [0, 2, 0, 2, 0, 0, 0, 0], [0, 2, 0, -2, 0, 0, 0, 0], [0, -2, 0, 2, 0, 0, 0, 0], [0, -2, 0, -2, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0, 0, 0], [0, 2, 0, 0, -2, 0, 0, 0], [0, -2, 0, 0, 2, 0, 0, 0], [0, -2, 0, 0, -2, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0], [0, 0, 2, -2, 0, 0, 0, 0], [0, 0, -2, 2, 0, 0, 0, 0], [0, 0, -2, -2, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0], [0, 0, 2, 0, -2, 0, 0, 0], [0, 0, -2, 0, 2, 0, 0, 0], [0, 0, -2, 0, -2, 0, 0, 0], [0, 0, 0, 2, 2, 0, 0, 0], [0, 0, 0, 2, -2, 0, 0, 0], [0, 0, 0, -2, 2, 0, 0, 0], [0, 0, 0, -2, -2, 0, 0, 0], [-1, 1, 1, 1, 1, 1, 1, -1], [1, -1, 1, 1, 1, 1, 1, -1], [1, 1, -1, 1, 1, 1, 1, -1], [1, 1, 1, -1, 1, 1, 1, -1], [1, 1, 1, 1, -1, 1, 1, -1], [-1, -1, -1, 1, 1, 1, 1, -1], [-1, -1, 1, -1, 1, 1, 1, -1], [-1, -1, 1, 1, -1, 1, 1, -1], [-1, 1, -1, -1, 1, 1, 1, -1], [-1, 1, -1, 1, -1, 1, 1, -1], [-1, 1, 1, -1, -1, 1, 1, -1], [1, -1, -1, -1, 1, 1, 1, -1], [1, -1, -1, 1, -1, 1, 1, -1], [1, -1, 1, -1, -1, 1, 1, -1], [1, 1, -1, -1, -1, 1, 1, -1], [-1, -1, -1, -1, -1, 1, 1, -1], [1, 1, 1, 1, 1, -1, -1, 1], [-1, -1, 1, 1, 1, -1, -1, 1], [-1, 1, -1, 1, 1, -1, -1, 1], [-1, 1, 1, -1, 1, -1, -1, 1], [-1, 1, 1, 1, -1, -1, -1, 1], [1, -1, -1, 1, 1, -1, -1, 1], [1, -1, 1, -1, 1, -1, -1, 1], [1, -1, 1, 1, -1, -1, -1, 1], [1, 1, -1, -1, 1, -1, -1, 1], [1, 1, -1, 1, -1, -1, -1, 1], [1, 1, 1, -1, -1, -1, -1, 1], [1, -1, -1, -1, -1, -1, -1, 1], [-1, 1, -1, -1, -1, -1, -1, 1], [-1, -1, 1, -1, -1, -1, -1, 1], [-1, -1, -1, 1, -1, -1, -1, 1], [-1, -1, -1, -1, 1, -1, -1, 1]], "norm": 8, "span": 6, "closePair": null}, "key": "aa84331d4b0fa53c", "latency_s": 135.284, "usage": {"in": 165, "out": 15912, "usd": 0.15945}}
{"family": "kissing", "model": "claude-sonnet-5", "tag": "v0", "target": "(7, 126)", "proposal_raw": "```json\n[[0,0,2,2,0,0,0,0],[0,0,2,-2,0,0,0,0],[0,0,-2,2,0,0,0,0],[0,0,-2,-2,0,0,0,0],\n[0,0,2,0,2,0,0,0],[0,0,2,0,-2,0,0,0],[0,0,-2,0,2,0,0,0],[0,0,-2,0,-2,0,0,0],\n[0,0,2,0,0,2,0,0],[0,0,2,0,0,-2,0,0],[0,0,-2,0,0,2,0,0],[0,0,-2,0,0,-2,0,0],\n[0,0,2,0,0,0,2,0],[0,0,2,0,0,0,-2,0],[0,0,-2,0,0,0,2,0],[0,0,-2,0,0,0,-2,0],\n[0,0,2,0,0,0,0,2],[0,0,2,0,0,0,0,-2],[0,0,-2,0,0,0,0,2],[0,0,-2,0,0,0,0,-2],\n[0,0,0,2,2,0,0,0],[0,0,0,2,-2,0,0,0],[0,0,0,-2,2,0,0,0],[0,0,0,-2,-2,0,0,0],\n[0,0,0,2,0,2,0,0],[0,0,0,2,0,-2,0,0],[0,0,0,-2,0,2,0,0],[0,0,0,-2,0,-2,0,0],\n[0,0,0,2,0,0,2,0],[0,0,0,2,0,0,-2,0],[0,0,0,-2,0,0,2,0],[0,0,0,-2,0,0,-2,0],\n[0,0,0,2,0,0,0,2],[0,0,0,2,0,0,0,-2],[0,0,0,-2,0,0,0,2],[0,0,0,-2,0,0,0,-2],\n[0,0,0,0,2,2,0,0],[0,0,0,0,2,-2,0,0],[0,0,0,0,-2,2,0,0],[0,0,0,0,-2,-2,0,0],\n[0,0,0,0,2,0,2,0],[0,0,0,0,2,0,-2,0],[0,0,0,0,-2,0,2,0],[0,0,0,0,-2,0,-2,0],\n[0,0,0,0,2,0,0,2],[0,0,0,0,2,0,0,-2],[0,0,0,0,-2,0,0,2],[0,0,0,0,-2,0,0,-2],\n[0,0,0,0,0,2,2,0],[0,0,0,0,0,2,-2,0],[0,0,0,0,0,-2,2,0],[0,0,0,0,0,-2,-2,0],\n[0,0,0,0,0,2,0,2],[0,0,0,0,0,2,0,-2],[0,0,0,0,0,-2,0,2],[0,0,0,0,0,-2,0,-2],\n[0,0,0,0,0,0,2,2],[0,0,0,0,0,0,2,-2],[0,0,0,0,0,0,-2,2],[0,0,0,0,0,0,-2,-2],\n[2,-2,0,0,0,0,0,0],[-2,2,0,0,0,0,0,0],\n[1,-1,-1,1,1,1,1,1],[1,-1,1,-1,1,1,1,1],[1,-1,1,1,-1,1,1,1],[1,-1,1,1,1,-1,1,1],\n[1,-1,1,1,1,1,-1,1],[1,-1,1,1,1,1,1,-1],[1,-1,-1,-1,-1,1,1,1],[1,-1,-1,-1,1,-1,1,1],\n[1,-1,-1,-1,1,1,-1,1],[1,-1,-1,-1,1,1,1,-1],[1,-1,-1,1,-1,-1,1,1],[1,-1,-1,1,-1,1,-1,1],\n[1,-1,-1,1,-1,1,1,-1],[1,-1,-1,1,1,-1,-1,1],[1,-1,-1,1,1,-1,1,-1],[1,-1,-1,1,1,1,-1,-1],\n[1,-1,1,-1,-1,-1,1,1],[1,-1,1,-1,-1,1,-1,1],[1,-1,1,-1,-1,1,1,-1],[1,-1,1,-1,1,-1,-1,1],\n[1,-1,1,-1,1,-1,1,-1],[1,-1,1,-1,1,1,-1,-1],[1,-1,1,1,-1,-1,-1,1],[1,-1,1,1,-1,-1,1,-1],\n[1,-1,1,1,-1,1,-1,-1],[1,-1,1,1,1,-1,-1,-1],[1,-1,1,-1,-1,-1,-1,-1],[1,-1,-1,1,-1,-1,-1,-1],\n[1,-1,-1,-1,1,-1,-1,-1],[1,-1,-1,-1,-1,1,-1,-1],[1,-1,-1,-1,-1,-1,1,-1],[1,-1,-1,-1,-1,-1,-1,1],\n[-1,1,-1,1,1,1,1,1],[-1,1,1,-1,1,1,1,1],[-1,1,1,1,-1,1,1,1],[-1,1,1,1,1,-1,1,1],\n[-1,1,1,1,1,1,-1,1],[-1,1,1,1,1,1,1,-1],[-1,1,-1,-1,-1,1,1,1],[-1,1,-1,-1,1,-1,1,1],\n[-1,1,-1,-1,1,1,-1,1],[-1,1,-1,-1,1,1,1,-1],[-1,1,-1,1,-1,-1,1,1],[-1,1,-1,1,-1,1,-1,1],\n[-1,1,-1,1,-1,1,1,-1],[-1,1,-1,1,1,-1,-1,1],[-1,1,-1,1,1,-1,1,-1],[-1,1,-1,1,1,1,-1,-1],\n[-1,1,1,-1,-1,-1,1,1],[-1,1,1,-1,-1,1,-1,1],[-1,1,1,-1,-1,1,1,-1],[-1,1,1,-1,1,-1,-1,1],\n[-1,1,1,-1,1,-1,1,-1],[-1,1,1,-1,1,1,-1,-1],[-1,1,1,1,-1,-1,-1,1],[-1,1,1,1,-1,-1,1,-1],\n[-1,1,1,1,-1,1,-1,-1],[-1,1,1,1,1,-1,-1,-1],[-1,1,1,-1,-1,-1,-1,-1],[-1,1,-1,1,-1,-1,-1,-1],\n[-1,1,-1,-1,1,-1,-1,-1],[-1,1,-1,-1,-1,1,-1,-1],[-1,1,-1,-1,-1,-1,1,-1],[-1,1,-1,-1,-1,-1,-1,1]]\n```", "obj": "((0, 0, 2, 2, 0, 0, 0, 0), (0, 0, 2, -2, 0, 0, 0, 0), (0, 0, -2, 2, 0, 0, 0, 0), (0, 0, -2, -2, 0, 0, 0, 0), (0, 0, 2, 0, 2, 0, 0, 0), (0, 0, 2, 0, -2, 0, 0, 0), (0, 0, -2, 0, 2, 0, 0, 0), (0, 0, -2, 0, -2, 0, 0, 0), (0, 0, 2, 0, 0, 2, 0, 0), (0, 0, 2, 0, 0, -2, 0, 0), (0, 0, -2, 0, 0, 2, 0, 0), (0, 0, -2, 0, 0, -2, 0, 0), (0, 0, 2, 0, 0, 0, 2, 0), (0, 0, 2, 0, 0, 0, -2, 0), (0, 0, -2, 0, 0, 0, 2, 0), (0, 0, -2, 0, 0, 0, -2, 0), (0, 0, 2, 0, 0, 0, 0, 2), (0, 0, 2, 0, 0, 0, 0, -2), (0, 0, -2, 0, 0, 0, 0, 2), (0, 0, -2, 0, 0, 0, 0, -2), (0, 0, 0, 2, 2, 0, 0, 0), (0, 0, 0, 2, -2, 0, 0, 0), (0, 0, 0, -2, 2, 0, 0, 0), (0, 0, 0, -2, -2, 0, 0, 0), (0, 0, 0, 2, 0, 2, 0, 0), (0, 0, 0, 2, 0, -2, 0, 0), (0, 0, 0, -2, 0, 2, 0, 0), (0, 0, 0, -2, 0, -2, 0, 0), (0, 0, 0, 2, 0, 0, 2, 0), (0, 0, 0, 2, 0, 0, -2, 0), (0, 0, 0, -2, 0, 0, 2, 0), (0, 0, 0, -2, 0, 0, -2, 0), (0, 0, 0, 2, 0, 0, 0, 2), (0, 0, 0, 2, 0, 0, 0, -2), (0, 0, 0, -2, 0, 0, 0, 2), (0, 0, 0, -2, 0, 0, 0, -2), (0, 0, 0, 0, 2, 2, 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-1, 1, -1, 1, 1, -1), (-1, 1, -1, 1, 1, -1, -1, 1), (-1, 1, -1, 1, 1, -1, 1, -1), (-1, 1, -1, 1, 1, 1, -1, -1), (-1, 1, 1, -1, -1, -1, 1, 1), (-1, 1, 1, -1, -1, 1, -1, 1), (-1, 1, 1, -1, -1, 1, 1, -1), (-1, 1, 1, -1, 1, -1, -1, 1), (-1, 1, 1, -1, 1, -1, 1, -1), (-1, 1, 1, -1, 1, 1, -1, -1), (-1, 1, 1, 1, -1, -1, -1, 1), (-1, 1, 1, 1, -1, -1, 1, -1), (-1, 1, 1, 1, -1, 1, -1, -1), (-1, 1, 1, 1, 1, -1, -1, -1), (-1, 1, 1, -1, -1, -1, -1, -1), (-1, 1, -1, 1, -1, -1, -1, -1), (-1, 1, -1, -1, 1, -1, -1, -1), (-1, 1, -1, -1, -1, 1, -1, -1), (-1, 1, -1, -1, -1, -1, 1, -1), (-1, 1, -1, -1, -1, -1, -1, 1))", "outcome": "certified", "statement": "a kissing configuration of 126 in dimension 7", "witness": "126 vectors, norms [8], span dimension 7", "certificate": {"vectors": [[0, 0, 2, 2, 0, 0, 0, 0], [0, 0, 2, -2, 0, 0, 0, 0], [0, 0, -2, 2, 0, 0, 0, 0], [0, 0, -2, -2, 0, 0, 0, 0], [0, 0, 2, 0, 2, 0, 0, 0], [0, 0, 2, 0, -2, 0, 0, 0], [0, 0, -2, 0, 2, 0, 0, 0], [0, 0, -2, 0, -2, 0, 0, 0], [0, 0, 2, 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1, 1, -1, 1, -1, 1, -1], [-1, 1, 1, -1, 1, 1, -1, -1], [-1, 1, 1, 1, -1, -1, -1, 1], [-1, 1, 1, 1, -1, -1, 1, -1], [-1, 1, 1, 1, -1, 1, -1, -1], [-1, 1, 1, 1, 1, -1, -1, -1], [-1, 1, 1, -1, -1, -1, -1, -1], [-1, 1, -1, 1, -1, -1, -1, -1], [-1, 1, -1, -1, 1, -1, -1, -1], [-1, 1, -1, -1, -1, 1, -1, -1], [-1, 1, -1, -1, -1, -1, 1, -1], [-1, 1, -1, -1, -1, -1, -1, 1]], "norm": 8, "span": 7, "closePair": null}, "key": "e1e078e0e4dc2b27", "latency_s": 118.449, "usage": {"in": 165, "out": 16165, "usd": 0.16198}}
{"family": "kissing", "model": "claude-sonnet-5", "tag": "v0", "target": "(8, 240)", "proposal_raw": "```json\n[\n[2,2,0,0,0,0,0,0],[2,-2,0,0,0,0,0,0],[-2,2,0,0,0,0,0,0],[-2,-2,0,0,0,0,0,0],\n[2,0,2,0,0,0,0,0],[2,0,-2,0,0,0,0,0],[-2,0,2,0,0,0,0,0],[-2,0,-2,0,0,0,0,0],\n[2,0,0,2,0,0,0,0],[2,0,0,-2,0,0,0,0],[-2,0,0,2,0,0,0,0],[-2,0,0,-2,0,0,0,0],\n[2,0,0,0,2,0,0,0],[2,0,0,0,-2,0,0,0],[-2,0,0,0,2,0,0,0],[-2,0,0,0,-2,0,0,0],\n[2,0,0,0,0,2,0,0],[2,0,0,0,0,-2,0,0],[-2,0,0,0,0,2,0,0],[-2,0,0,0,0,-2,0,0],\n[2,0,0,0,0,0,2,0],[2,0,0,0,0,0,-2,0],[-2,0,0,0,0,0,2,0],[-2,0,0,0,0,0,-2,0],\n[2,0,0,0,0,0,0,2],[2,0,0,0,0,0,0,-2],[-2,0,0,0,0,0,0,2],[-2,0,0,0,0,0,0,-2],\n[0,2,2,0,0,0,0,0],[0,2,-2,0,0,0,0,0],[0,-2,2,0,0,0,0,0],[0,-2,-2,0,0,0,0,0],\n[0,2,0,2,0,0,0,0],[0,2,0,-2,0,0,0,0],[0,-2,0,2,0,0,0,0],[0,-2,0,-2,0,0,0,0],\n[0,2,0,0,2,0,0,0],[0,2,0,0,-2,0,0,0],[0,-2,0,0,2,0,0,0],[0,-2,0,0,-2,0,0,0],\n[0,2,0,0,0,2,0,0],[0,2,0,0,0,-2,0,0],[0,-2,0,0,0,2,0,0],[0,-2,0,0,0,-2,0,0],\n[0,2,0,0,0,0,2,0],[0,2,0,0,0,0,-2,0],[0,-2,0,0,0,0,2,0],[0,-2,0,0,0,0,-2,0],\n[0,2,0,0,0,0,0,2],[0,2,0,0,0,0,0,-2],[0,-2,0,0,0,0,0,2],[0,-2,0,0,0,0,0,-2],\n[0,0,2,2,0,0,0,0],[0,0,2,-2,0,0,0,0],[0,0,-2,2,0,0,0,0],[0,0,-2,-2,0,0,0,0],\n[0,0,2,0,2,0,0,0],[0,0,2,0,-2,0,0,0],[0,0,-2,0,2,0,0,0],[0,0,-2,0,-2,0,0,0],\n[0,0,2,0,0,2,0,0],[0,0,2,0,0,-2,0,0],[0,0,-2,0,0,2,0,0],[0,0,-2,0,0,-2,0,0],\n[0,0,2,0,0,0,2,0],[0,0,2,0,0,0,-2,0],[0,0,-2,0,0,0,2,0],[0,0,-2,0,0,0,-2,0],\n[0,0,2,0,0,0,0,2],[0,0,2,0,0,0,0,-2],[0,0,-2,0,0,0,0,2],[0,0,-2,0,0,0,0,-2],\n[0,0,0,2,2,0,0,0],[0,0,0,2,-2,0,0,0],[0,0,0,-2,2,0,0,0],[0,0,0,-2,-2,0,0,0],\n[0,0,0,2,0,2,0,0],[0,0,0,2,0,-2,0,0],[0,0,0,-2,0,2,0,0],[0,0,0,-2,0,-2,0,0],\n[0,0,0,2,0,0,2,0],[0,0,0,2,0,0,-2,0],[0,0,0,-2,0,0,2,0],[0,0,0,-2,0,0,-2,0],\n[0,0,0,2,0,0,0,2],[0,0,0,2,0,0,0,-2],[0,0,0,-2,0,0,0,2],[0,0,0,-2,0,0,0,-2],\n[0,0,0,0,2,2,0,0],[0,0,0,0,2,-2,0,0],[0,0,0,0,-2,2,0,0],[0,0,0,0,-2,-2,0,0],\n[0,0,0,0,2,0,2,0],[0,0,0,0,2,0,-2,0],[0,0,0,0,-2,0,2,0],[0,0,0,0,-2,0,-2,0],\n[0,0,0,0,2,0,0,2],[0,0,0,0,2,0,0,-2],[0,0,0,0,-2,0,0,2],[0,0,0,0,-2,0,0,-2],\n[0,0,0,0,0,2,2,0],[0,0,0,0,0,2,-2,0],[0,0,0,0,0,-2,2,0],[0,0,0,0,0,-2,-2,0],\n[0,0,0,0,0,2,0,2],[0,0,0,0,0,2,0,-2],[0,0,0,0,0,-2,0,2],[0,0,0,0,0,-2,0,-2],\n[0,0,0,0,0,0,2,2],[0,0,0,0,0,0,2,-2],[0,0,0,0,0,0,-2,2],[0,0,0,0,0,0,-2,-2],\n[1,1,1,1,1,1,1,1],\n[-1,-1,1,1,1,1,1,1],[-1,1,-1,1,1,1,1,1],[-1,1,1,-1,1,1,1,1],[-1,1,1,1,-1,1,1,1],[-1,1,1,1,1,-1,1,1],[-1,1,1,1,1,1,-1,1],[-1,1,1,1,1,1,1,-1],\n[1,-1,-1,1,1,1,1,1],[1,-1,1,-1,1,1,1,1],[1,-1,1,1,-1,1,1,1],[1,-1,1,1,1,-1,1,1],[1,-1,1,1,1,1,-1,1],[1,-1,1,1,1,1,1,-1],\n[1,1,-1,-1,1,1,1,1],[1,1,-1,1,-1,1,1,1],[1,1,-1,1,1,-1,1,1],[1,1,-1,1,1,1,-1,1],[1,1,-1,1,1,1,1,-1],\n[1,1,1,-1,-1,1,1,1],[1,1,1,-1,1,-1,1,1],[1,1,1,-1,1,1,-1,1],[1,1,1,-1,1,1,1,-1],\n[1,1,1,1,-1,-1,1,1],[1,1,1,1,-1,1,-1,1],[1,1,1,1,-1,1,1,-1],\n[1,1,1,1,1,-1,-1,1],[1,1,1,1,1,-1,1,-1],\n[1,1,1,1,1,1,-1,-1],\n[1,1,-1,-1,-1,-1,-1,-1],[-1,1,1,-1,-1,-1,-1,-1],[-1,-1,1,1,-1,-1,-1,-1],[-1,-1,-1,1,1,-1,-1,-1],\n[-1,-1,-1,-1,1,1,-1,-1],[-1,-1,-1,-1,-1,1,1,-1],[-1,-1,-1,-1,-1,-1,1,1],\n[1,-1,1,-1,-1,-1,-1,-1],[1,-1,-1,1,-1,-1,-1,-1],[1,-1,-1,-1,1,-1,-1,-1],[1,-1,-1,-1,-1,1,-1,-1],\n[1,-1,-1,-1,-1,-1,1,-1],[1,-1,-1,-1,-1,-1,-1,1],\n[-1,1,-1,1,-1,-1,-1,-1],[-1,1,-1,-1,1,-1,-1,-1],[-1,1,-1,-1,-1,1,-1,-1],[-1,1,-1,-1,-1,-1,1,-1],[-1,1,-1,-1,-1,-1,-1,1],\n[-1,-1,1,-1,1,-1,-1,-1],[-1,-1,1,-1,-1,1,-1,-1],[-1,-1,1,-1,-1,-1,1,-1],[-1,-1,1,-1,-1,-1,-1,1],\n[-1,-1,-1,1,-1,1,-1,-1],[-1,-1,-1,1,-1,-1,1,-1],[-1,-1,-1,1,-1,-1,-1,1],\n[-1,-1,-1,-1,1,-1,1,-1],[-1,-1,-1,-1,1,-1,-1,1],\n[-1,-1,-1,-1,-1,1,-1,1],\n[-1,-1,-1,-1,-1,-1,-1,-1],\n[-1,-1,-1,-1,1,1,1,1],[-1,-1,-1,1,-1,1,1,1],[-1,-1,-1,1,1,-1,1,1],[-1,-1,-1,1,1,1,-1,1],[-1,-1,-1,1,1,1,1,-1],\n[-1,-1,1,-1,-1,1,1,1],[-1,-1,1,-1,1,-1,1,1],[-1,-1,1,-1,1,1,-1,1],[-1,-1,1,-1,1,1,1,-1],\n[-1,-1,1,1,-1,-1,1,1],[-1,-1,1,1,-1,1,-1,1],[-1,-1,1,1,-1,1,1,-1],\n[-1,-1,1,1,1,-1,-1,1],[-1,-1,1,1,1,-1,1,-1],\n[-1,-1,1,1,1,1,-1,-1],\n[-1,1,-1,-1,-1,1,1,1],[-1,1,-1,-1,1,-1,1,1],[-1,1,-1,-1,1,1,-1,1],[-1,1,-1,-1,1,1,1,-1],\n[-1,1,-1,1,-1,-1,1,1],[-1,1,-1,1,-1,1,-1,1],[-1,1,-1,1,-1,1,1,-1],\n[-1,1,-1,1,1,-1,-1,1],[-1,1,-1,1,1,-1,1,-1],\n[-1,1,-1,1,1,1,-1,-1],\n[-1,1,1,-1,-1,-1,1,1],[-1,1,1,-1,-1,1,-1,1],[-1,1,1,-1,-1,1,1,-1],\n[-1,1,1,-1,1,-1,-1,1],[-1,1,1,-1,1,-1,1,-1],\n[-1,1,1,-1,1,1,-1,-1],\n[-1,1,1,1,-1,-1,-1,1],[-1,1,1,1,-1,-1,1,-1],\n[-1,1,1,1,-1,1,-1,-1],\n[-1,1,1,1,1,-1,-1,-1],\n[1,-1,-1,-1,-1,1,1,1],[1,-1,-1,-1,1,-1,1,1],[1,-1,-1,-1,1,1,-1,1],[1,-1,-1,-1,1,1,1,-1],\n[1,-1,-1,1,-1,-1,1,1],[1,-1,-1,1,-1,1,-1,1],[1,-1,-1,1,-1,1,1,-1],\n[1,-1,-1,1,1,-1,-1,1],[1,-1,-1,1,1,-1,1,-1],\n[1,-1,-1,1,1,1,-1,-1],\n[1,-1,1,-1,-1,-1,1,1],[1,-1,1,-1,-1,1,-1,1],[1,-1,1,-1,-1,1,1,-1],\n[1,-1,1,-1,1,-1,-1,1],[1,-1,1,-1,1,-1,1,-1],\n[1,-1,1,-1,1,1,-1,-1],\n[1,-1,1,1,-1,-1,-1,1],[1,-1,1,1,-1,-1,1,-1],\n[1,-1,1,1,-1,1,-1,-1],\n[1,-1,1,1,1,-1,-1,-1],\n[1,1,-1,-1,-1,-1,1,1],[1,1,-1,-1,-1,1,-1,1],[1,1,-1,-1,-1,1,1,-1],\n[1,1,-1,-1,1,-1,-1,1],[1,1,-1,-1,1,-1,1,-1],\n[1,1,-1,-1,1,1,-1,-1],\n[1,1,-1,1,-1,-1,-1,1],[1,1,-1,1,-1,-1,1,-1],\n[1,1,-1,1,-1,1,-1,-1],\n[1,1,-1,1,1,-1,-1,-1],\n[1,1,1,-1,-1,-1,-1,1],[1,1,1,-1,-1,-1,1,-1],\n[1,1,1,-1,-1,1,-1,-1],\n[1,1,1,-1,1,-1,-1,-1],\n[1,1,1,1,-1,-1,-1,-1]\n]\n```", "obj": "((2, 2, 0, 0, 0, 0, 0, 0), (2, -2, 0, 0, 0, 0, 0, 0), (-2, 2, 0, 0, 0, 0, 0, 0), (-2, -2, 0, 0, 0, 0, 0, 0), (2, 0, 2, 0, 0, 0, 0, 0), (2, 0, -2, 0, 0, 0, 0, 0), (-2, 0, 2, 0, 0, 0, 0, 0), (-2, 0, -2, 0, 0, 0, 0, 0), (2, 0, 0, 2, 0, 0, 0, 0), (2, 0, 0, -2, 0, 0, 0, 0), (-2, 0, 0, 2, 0, 0, 0, 0), (-2, 0, 0, -2, 0, 0, 0, 0), (2, 0, 0, 0, 2, 0, 0, 0), (2, 0, 0, 0, -2, 0, 0, 0), (-2, 0, 0, 0, 2, 0, 0, 0), (-2, 0, 0, 0, -2, 0, 0, 0), (2, 0, 0, 0, 0, 2, 0, 0), (2, 0, 0, 0, 0, -2, 0, 0), (-2, 0, 0, 0, 0, 2, 0, 0), (-2, 0, 0, 0, 0, -2, 0, 0), (2, 0, 0, 0, 0, 0, 2, 0), (2, 0, 0, 0, 0, 0, -2, 0), (-2, 0, 0, 0, 0, 0, 2, 0), (-2, 0, 0, 0, 0, 0, -2, 0), (2, 0, 0, 0, 0, 0, 0, 2), (2, 0, 0, 0, 0, 0, 0, -2), (-2, 0, 0, 0, 0, 0, 0, 2), (-2, 0, 0, 0, 0, 0, 0, -2), (0, 2, 2, 0, 0, 0, 0, 0), (0, 2, -2, 0, 0, 0, 0, 0), (0, -2, 2, 0, 0, 0, 0, 0), (0, -2, -2, 0, 0, 0, 0, 0), (0, 2, 0, 2, 0, 0, 0, 0), (0, 2, 0, -2, 0, 0, 0, 0), (0, -2, 0, 2, 0, 0, 0, 0), (0, -2, 0, -2, 0, 0, 0, 0), (0, 2, 0, 0, 2, 0, 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0, 0), (0, 0, 0, -2, 2, 0, 0, 0), (0, 0, 0, -2, -2, 0, 0, 0), (0, 0, 0, 2, 0, 2, 0, 0), (0, 0, 0, 2, 0, -2, 0, 0), (0, 0, 0, -2, 0, 2, 0, 0), (0, 0, 0, -2, 0, -2, 0, 0), (0, 0, 0, 2, 0, 0, 2, 0), (0, 0, 0, 2, 0, 0, -2, 0), (0, 0, 0, -2, 0, 0, 2, 0), (0, 0, 0, -2, 0, 0, -2, 0), (0, 0, 0, 2, 0, 0, 0, 2), (0, 0, 0, 2, 0, 0, 0, -2), (0, 0, 0, -2, 0, 0, 0, 2), (0, 0, 0, -2, 0, 0, 0, -2), (0, 0, 0, 0, 2, 2, 0, 0), (0, 0, 0, 0, 2, -2, 0, 0), (0, 0, 0, 0, -2, 2, 0, 0), (0, 0, 0, 0, -2, -2, 0, 0), (0, 0, 0, 0, 2, 0, 2, 0), (0, 0, 0, 0, 2, 0, -2, 0), (0, 0, 0, 0, -2, 0, 2, 0), (0, 0, 0, 0, -2, 0, -2, 0), (0, 0, 0, 0, 2, 0, 0, 2), (0, 0, 0, 0, 2, 0, 0, -2), (0, 0, 0, 0, -2, 0, 0, 2), (0, 0, 0, 0, -2, 0, 0, -2), (0, 0, 0, 0, 0, 2, 2, 0), (0, 0, 0, 0, 0, 2, -2, 0), (0, 0, 0, 0, 0, -2, 2, 0), (0, 0, 0, 0, 0, -2, -2, 0), (0, 0, 0, 0, 0, 2, 0, 2), (0, 0, 0, 0, 0, 2, 0, -2), (0, 0, 0, 0, 0, -2, 0, 2), (0, 0, 0, 0, 0, -2, 0, -2), (0, 0, 0, 0, 0, 0, 2, 2), (0, 0, 0, 0, 0, 0, 2, -2), (0, 0, 0, 0, 0, 0, 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1), (1, -1, -1, 1, -1, 1, 1, -1), (1, -1, -1, 1, 1, -1, -1, 1), (1, -1, -1, 1, 1, -1, 1, -1), (1, -1, -1, 1, 1, 1, -1, -1), (1, -1, 1, -1, -1, -1, 1, 1), (1, -1, 1, -1, -1, 1, -1, 1), (1, -1, 1, -1, -1, 1, 1, -1), (1, -1, 1, -1, 1, -1, -1, 1), (1, -1, 1, -1, 1, -1, 1, -1), (1, -1, 1, -1, 1, 1, -1, -1), (1, -1, 1, 1, -1, -1, -1, 1), (1, -1, 1, 1, -1, -1, 1, -1), (1, -1, 1, 1, -1, 1, -1, -1), (1, -1, 1, 1, 1, -1, -1, -1), (1, 1, -1, -1, -1, -1, 1, 1), (1, 1, -1, -1, -1, 1, -1, 1), (1, 1, -1, -1, -1, 1, 1, -1), (1, 1, -1, -1, 1, -1, -1, 1), (1, 1, -1, -1, 1, -1, 1, -1), (1, 1, -1, -1, 1, 1, -1, -1), (1, 1, -1, 1, -1, -1, -1, 1), (1, 1, -1, 1, -1, -1, 1, -1), (1, 1, -1, 1, -1, 1, -1, -1), (1, 1, -1, 1, 1, -1, -1, -1), (1, 1, 1, -1, -1, -1, -1, 1), (1, 1, 1, -1, -1, -1, 1, -1), (1, 1, 1, -1, -1, 1, -1, -1), (1, 1, 1, -1, 1, -1, -1, -1), (1, 1, 1, 1, -1, -1, -1, -1))", "outcome": "certified", "statement": "a kissing configuration of 240 in dimension 8", "witness": "240 vectors, norms [8], 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-1, 1, 1], [1, -1, -1, 1, -1, 1, -1, 1], [1, -1, -1, 1, -1, 1, 1, -1], [1, -1, -1, 1, 1, -1, -1, 1], [1, -1, -1, 1, 1, -1, 1, -1], [1, -1, -1, 1, 1, 1, -1, -1], [1, -1, 1, -1, -1, -1, 1, 1], [1, -1, 1, -1, -1, 1, -1, 1], [1, -1, 1, -1, -1, 1, 1, -1], [1, -1, 1, -1, 1, -1, -1, 1], [1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1, 1, 1, -1, -1], [1, -1, 1, 1, -1, -1, -1, 1], [1, -1, 1, 1, -1, -1, 1, -1], [1, -1, 1, 1, -1, 1, -1, -1], [1, -1, 1, 1, 1, -1, -1, -1], [1, 1, -1, -1, -1, -1, 1, 1], [1, 1, -1, -1, -1, 1, -1, 1], [1, 1, -1, -1, -1, 1, 1, -1], [1, 1, -1, -1, 1, -1, -1, 1], [1, 1, -1, -1, 1, -1, 1, -1], [1, 1, -1, -1, 1, 1, -1, -1], [1, 1, -1, 1, -1, -1, -1, 1], [1, 1, -1, 1, -1, -1, 1, -1], [1, 1, -1, 1, -1, 1, -1, -1], [1, 1, -1, 1, 1, -1, -1, -1], [1, 1, 1, -1, -1, -1, -1, 1], [1, 1, 1, -1, -1, -1, 1, -1], [1, 1, 1, -1, -1, 1, -1, -1], [1, 1, 1, -1, 1, -1, -1, -1], [1, 1, 1, 1, -1, -1, -1, -1]], "norm": 8, "span": 8, "closePair": null}, "key": "2a8f6a05bc2ee05b", "latency_s": 111.908, "usage": {"in": 165, "out": 16574, "usd": 0.16607}}
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{"family": "polymulF2", "model": "claude-sonnet-5", "tag": "v0", "target": "(2, 3)", "proposal_raw": "{\"u\": [[1,0],[0,1],[1,1]], \"v\": [[1,0],[0,1],[1,1]], \"w\": [[1,1,0],[0,1,1],[0,1,0]]}", "obj": "(((1, 0), (0, 1), (1, 1)), ((1, 0), (0, 1), (1, 1)), ((1, 1, 0), (0, 1, 1), (0, 1, 0)))", "outcome": "certified", "statement": "the product of two 2-term polynomials over F2 in 3 multiplications", "witness": "rank 3", "certificate": {"u": [[1, 0], [0, 1], [1, 1]], "v": [[1, 0], [0, 1], [1, 1]], "w": [[1, 1, 0], [0, 1, 1], [0, 1, 0]], "firstViolation": null}, "key": "6087c552f4ddf3ed", "latency_s": 7.417, "usage": {"in": 287, "out": 810, "usd": 0.008674}}
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{"family": "polymulF2", "model": "claude-sonnet-5", "tag": "v0", "target": "(5, 13)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 219.947, "usage": {"in": 287, "out": 24000, "usd": 0.240574}}
{"family": "polymulF2", "model": "claude-sonnet-5", "tag": "v0", "target": "(6, 17)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 252.567, "usage": {"in": 287, "out": 24000, "usd": 0.240574}}
{"family": "polymulF2", "model": "claude-sonnet-5", "tag": "v0", "target": "(7, 22)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 255.75, "usage": {"in": 287, "out": 24000, "usd": 0.240574}}
{"family": "golomb", "model": "claude-opus-5", "tag": "v0", "target": "(6, 17)", "proposal_raw": "[0,1,4,10,12,17]", "obj": "(0, 1, 4, 10, 12, 17)", "outcome": "certified", "statement": "[0, 1, 4, 10, 12, 17] is a Golomb ruler with 6 marks and length <= 17", "witness": "length 17, 15 differences", "certificate": {"marks": [0, 1, 4, 10, 12, 17], "length": 17, "repeatedDifferences": []}, "key": "a081afe5300f7595", "latency_s": 4.618, "usage": {"in": 116, "out": 267, "usd": 0.007255}}
{"family": "golomb", "model": "claude-opus-5", "tag": "v0", "target": "(8, 34)", "proposal_raw": "[0,1,4,9,15,22,32,34]", "obj": "(0, 1, 4, 9, 15, 22, 32, 34)", "outcome": "certified", "statement": "[0, 1, 4, 9, 15, 22, 32, 34] is a Golomb ruler with 8 marks and length <= 34", "witness": "length 34, 28 differences", "certificate": {"marks": [0, 1, 4, 9, 15, 22, 32, 34], "length": 34, "repeatedDifferences": []}, "key": "aea4f96e817e9201", "latency_s": 4.716, "usage": {"in": 116, "out": 371, "usd": 0.009855}}
{"family": "golomb", "model": "claude-opus-5", "tag": "v0", "target": "(10, 55)", "proposal_raw": "[0,1,6,10,23,26,34,41,53,55]", "obj": "(0, 1, 6, 10, 23, 26, 34, 41, 53, 55)", "outcome": "certified", "statement": "[0, 1, 6, 10, 23, 26, 34, 41, 53, 55] is a Golomb ruler with 10 marks and length <= 55", "witness": "length 55, 45 differences", "certificate": {"marks": [0, 1, 6, 10, 23, 26, 34, 41, 53, 55], "length": 55, "repeatedDifferences": []}, "key": "f6cbb15c637c5874", "latency_s": 6.496, "usage": {"in": 116, "out": 493, "usd": 0.012905}}
{"family": "golomb", "model": "claude-opus-5", "tag": "v0", "target": "(11, 72)", "proposal_raw": "[0,1,4,13,28,33,47,54,64,70,72]", "obj": "(0, 1, 4, 13, 28, 33, 47, 54, 64, 70, 72)", "outcome": "certified", "statement": "[0, 1, 4, 13, 28, 33, 47, 54, 64, 70, 72] is a Golomb ruler with 11 marks and length <= 72", "witness": "length 72, 55 differences", "certificate": {"marks": [0, 1, 4, 13, 28, 33, 47, 54, 64, 70, 72], "length": 72, "repeatedDifferences": []}, "key": "227759659cd32750", "latency_s": 10.313, "usage": {"in": 116, "out": 872, "usd": 0.02238}}
{"family": "golomb", "model": "claude-opus-5", "tag": "v0", "target": "(12, 85)", "proposal_raw": "[0,2,6,24,29,40,43,55,68,75,76,85]", "obj": "(0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85)", "outcome": "certified", "statement": "[0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85] is a Golomb ruler with 12 marks and length <= 85", "witness": "length 85, 66 differences", "certificate": {"marks": [0, 2, 6, 24, 29, 40, 43, 55, 68, 75, 76, 85], "length": 85, "repeatedDifferences": []}, "key": "791bd7093a3bb65d", "latency_s": 8.312, "usage": {"in": 116, "out": 644, "usd": 0.01668}}
{"family": "golomb", "model": "claude-opus-5", "tag": "v0", "target": "(13, 106)", "proposal_raw": "[0,2,5,25,37,43,59,70,85,89,98,99,106]", "obj": "(0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106)", "outcome": "certified", "statement": "[0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106] is a Golomb ruler with 13 marks and length <= 106", "witness": "length 106, 78 differences", "certificate": {"marks": [0, 2, 5, 25, 37, 43, 59, 70, 85, 89, 98, 99, 106], "length": 106, "repeatedDifferences": []}, "key": "f966ca2277e28501", "latency_s": 15.752, "usage": {"in": 116, "out": 1440, "usd": 0.03658}}
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{"family": "capset", "model": "claude-opus-5", "tag": "v0", "target": "(7, 236)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 298.75, "usage": {"in": 128, "out": 24000, "usd": 0.60064}}
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{"family": "code", "model": "claude-opus-5", "tag": "v0", "target": "(10, 3, 72)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 310.085, "usage": {"in": 98, "out": 24000, "usd": 0.60049}}
{"family": "code", "model": "claude-opus-5", "tag": "v0", "target": "(12, 4, 144)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 237.692, "usage": {"in": 98, "out": 24000, "usd": 0.60049}}
{"family": "code", "model": "claude-opus-5", "tag": "v0", "target": "(16, 6, 256)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 197.009, "usage": {"in": 98, "out": 24000, "usd": 0.60049}}
{"family": "code", "model": "claude-opus-5", "tag": "v0", "target": "(10, 3, 73)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 297.853, "usage": {"in": 98, "out": 24000, "usd": 0.60049}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(3, 4, 8)", "proposal_raw": "{\"n\": 8, \"circulant\": [1, 4]}", "obj": "('circulant', 8, (1, 4))", "outcome": "certified", "statement": "R(3,4) > 8", "witness": "8 vertices; clique of size 3: no; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 8, "data": [1, 4]}, "cliqueFound": false, "independentFound": false}, "key": "903552cff478b32a", "latency_s": 10.94, "usage": {"in": 168, "out": 796, "usd": 0.02074}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(3, 5, 13)", "proposal_raw": "{\"n\": 13, \"circulant\": [1, 5]}", "obj": "('circulant', 13, (1, 5))", "outcome": "certified", "statement": "R(3,5) > 13", "witness": "13 vertices; clique of size 3: no; independent set of size 5: no", "certificate": {"graph": {"kind": "circulant", "n": 13, "data": [1, 5]}, "cliqueFound": false, "independentFound": false}, "key": "5a08fbc996de6bae", "latency_s": 22.954, "usage": {"in": 168, "out": 1956, "usd": 0.04974}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(4, 4, 17)", "proposal_raw": "{\"n\": 17, \"circulant\": [1, 2, 4, 8]}", "obj": "('circulant', 17, (1, 2, 4, 8))", "outcome": "certified", "statement": "R(4,4) > 17", "witness": "17 vertices; clique of size 4: no; independent set of size 4: no", "certificate": {"graph": {"kind": "circulant", "n": 17, "data": [1, 2, 4, 8]}, "cliqueFound": false, "independentFound": false}, "key": "456fd0ac5d4ee40b", "latency_s": 3.116, "usage": {"in": 168, "out": 100, "usd": 0.00334}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(3, 6, 17)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 273.662, "usage": {"in": 168, "out": 24000, "usd": 0.60084}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(4, 5, 24)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 293.39, "usage": {"in": 168, "out": 24000, "usd": 0.60084}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(3, 9, 35)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 254.597, "usage": {"in": 168, "out": 24000, "usd": 0.60084}}
{"family": "ramsey", "model": "claude-opus-5", "tag": "v0", "target": "(4, 6, 36)", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 288.419, "usage": {"in": 168, "out": 24000, "usd": 0.60084}}
{"family": "sumdiff3b", "model": "claude-opus-5", "tag": "v0", "target": "1.6", "proposal_raw": "", "obj": null, "outcome": "budget-exhausted", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 294.865, "usage": {"in": 159, "out": 24000, "usd": 0.600795}}
{"family": "sumdiff3b", "model": "claude-opus-5", "tag": "v0", "target": "1.7", "proposal_raw": "", "obj": null, "outcome": "malformed", "statement": null, "witness": null, "certificate": null, "key": null, "latency_s": 76.487, "usage": {"in": 159, "out": 4, "usd": 0.000895}}
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