{
 "description": "single-valued depth-three MZVs zsv(a,b,c), a,b,c odd >=3, weights 11-21, as 2*zeta(a,b,c) + correction",
 "convention": {
  "mzv": "ascending: zeta(n1,...,nr) = sum_{0<k1<...<kr} prod k_i^(-n_i)",
  "even_zeta": "powers of zeta(2)",
  "coefficient": "c_k = (sum_i num_i * monomial_i) / den, integers as computed (not reduced)",
  "monomial_syntax": "zeta(n), zeta(2)^j, zeta(n1,n2), zeta(n1,n2,n3) joined by *; '1' = rational"
 },
 "generated": "2026-09-28T16:39:13Z",
 "formulas": {
  "3,3,5": {
   "weight": 11,
   "label": "extracted",
   "leading": "2*zeta(3,3,5)",
   "correction": {
    "zeta(2)*zeta(9)": "90",
    "zeta(2)^2*zeta(7)": "12/5",
    "zeta(2)^3*zeta(5)": "-8/7",
    "zeta(3)^2*zeta(5)": "-5"
   }
  },
  "3,5,3": {
   "weight": 11,
   "label": "extracted",
   "leading": "2*zeta(3,5,3)",
   "correction": {
    "zeta(3)*zeta(3,5)": "-2",
    "zeta(3)^2*zeta(5)": "-10"
   }
  },
  "5,3,3": {
   "weight": 11,
   "label": "extracted",
   "leading": "2*zeta(5,3,3)",
   "correction": {
    "zeta(2)*zeta(9)": "-90",
    "zeta(2)^2*zeta(7)": "-12/5",
    "zeta(2)^3*zeta(5)": "48/35",
    "zeta(2)^4*zeta(3)": "48/175",
    "zeta(3)*zeta(3,5)": "2",
    "zeta(3)^2*zeta(5)": "18"
   }
  },
  "3,3,7": {
   "weight": 13,
   "label": "extracted",
   "leading": "2*zeta(3,3,7)",
   "correction": {
    "zeta(2)*zeta(11)": "407",
    "zeta(2)^2*zeta(9)": "112/5",
    "zeta(2)^3*zeta(7)": "-64/35",
    "zeta(3)*zeta(5)^2": "60",
    "zeta(5)*zeta(3,5)": "12",
    "zeta(3)^2*zeta(7)": "-14"
   }
  },
  "3,5,5": {
   "weight": 13,
   "label": "extracted",
   "leading": "2*zeta(3,5,5)",
   "correction": {
    "zeta(2)*zeta(11)": "275",
    "zeta(2)^2*zeta(9)": "20",
    "zeta(3)*zeta(5)^2": "50",
    "zeta(5)*zeta(3,5)": "10"
   }
  },
  "3,7,3": {
   "weight": 13,
   "label": "extracted",
   "leading": "2*zeta(3,7,3)",
   "correction": {
    "zeta(2)^4*zeta(5)": "-288/175",
    "zeta(3)*zeta(3,7)": "-2",
    "zeta(3)*zeta(5)^2": "-144",
    "zeta(5)*zeta(3,5)": "-24",
    "zeta(3)^2*zeta(7)": "-28"
   }
  },
  "5,3,5": {
   "weight": 13,
   "label": "extracted",
   "leading": "2*zeta(5,3,5)",
   "correction": {
    "zeta(2)^4*zeta(5)": "-48/35",
    "zeta(3)*zeta(5)^2": "-120",
    "zeta(5)*zeta(3,5)": "-22"
   }
  },
  "5,5,3": {
   "weight": 13,
   "label": "extracted",
   "leading": "2*zeta(5,5,3)",
   "correction": {
    "zeta(2)*zeta(11)": "-275",
    "zeta(2)^2*zeta(9)": "-20",
    "zeta(2)^4*zeta(5)": "288/175",
    "zeta(2)^5*zeta(3)": "32/385",
    "zeta(3)*zeta(5)^2": "73",
    "zeta(5)*zeta(3,5)": "12"
   }
  },
  "7,3,3": {
   "weight": 13,
   "label": "extracted",
   "leading": "2*zeta(7,3,3)",
   "correction": {
    "zeta(2)*zeta(11)": "-407",
    "zeta(2)^2*zeta(9)": "-112/5",
    "zeta(2)^3*zeta(7)": "72/35",
    "zeta(2)^4*zeta(5)": "288/175",
    "zeta(2)^5*zeta(3)": "64/385",
    "zeta(3)*zeta(3,7)": "2",
    "zeta(3)*zeta(5)^2": "84",
    "zeta(5)*zeta(3,5)": "12",
    "zeta(3)^2*zeta(7)": "45"
   }
  },
  "3,3,9": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(3,3,9)",
   "correction": {
    "zeta(2)*zeta(13)": "1209",
    "zeta(2)^2*zeta(11)": "504/5",
    "zeta(2)^3*zeta(9)": "232/35",
    "zeta(2)^4*zeta(7)": "144/175",
    "zeta(5)^3": "72",
    "zeta(5)*zeta(3,7)": "12",
    "zeta(3)*zeta(5)*zeta(7)": "318",
    "zeta(7)*zeta(3,5)": "30",
    "zeta(3)^2*zeta(9)": "-27"
   }
  },
  "3,5,7": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(3,5,7)",
   "correction": {
    "zeta(2)*zeta(13)": "1638",
    "zeta(2)^2*zeta(11)": "114",
    "zeta(2)^3*zeta(9)": "64/35",
    "zeta(5)^3": "72",
    "zeta(5)*zeta(3,7)": "12",
    "zeta(3)*zeta(5)*zeta(7)": "308",
    "zeta(7)*zeta(3,5)": "28",
    "zeta(3)^2*zeta(9)": "-42"
   }
  },
  "3,7,5": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(3,7,5)",
   "correction": {
    "zeta(2)*zeta(13)": "637",
    "zeta(2)^2*zeta(11)": "70",
    "zeta(2)^3*zeta(9)": "48/5",
    "zeta(2)^5*zeta(5)": "-192/385",
    "zeta(5)^3": "-18",
    "zeta(5)*zeta(3,7)": "-2",
    "zeta(3)*zeta(5)*zeta(7)": "-28",
    "zeta(3)^2*zeta(9)": "42"
   }
  },
  "3,9,3": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(3,9,3)",
   "correction": {
    "zeta(2)^4*zeta(7)": "-144/35",
    "zeta(2)^5*zeta(5)": "-384/385",
    "zeta(3)*zeta(3,9)": "-2",
    "zeta(5)^3": "-144",
    "zeta(5)*zeta(3,7)": "-24",
    "zeta(3)*zeta(5)*zeta(7)": "-720",
    "zeta(7)*zeta(3,5)": "-60",
    "zeta(3)^2*zeta(9)": "-54"
   }
  },
  "5,3,7": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(5,3,7)",
   "correction": {
    "zeta(2)*zeta(13)": "1001",
    "zeta(2)^2*zeta(11)": "44",
    "zeta(2)^3*zeta(9)": "-272/35",
    "zeta(2)^4*zeta(7)": "-96/25",
    "zeta(2)^5*zeta(5)": "-192/385",
    "zeta(5)^3": "-78",
    "zeta(5)*zeta(3,7)": "-12",
    "zeta(3)*zeta(5)*zeta(7)": "-336",
    "zeta(7)*zeta(3,5)": "-28"
   }
  },
  "5,5,5": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(5,5,5)",
   "correction": {
    "zeta(2)^5*zeta(5)": "32/385",
    "zeta(5)^3": "1"
   }
  },
  "5,7,3": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(5,7,3)",
   "correction": {
    "zeta(2)*zeta(13)": "-637",
    "zeta(2)^2*zeta(11)": "-70",
    "zeta(2)^3*zeta(9)": "-48/5",
    "zeta(2)^5*zeta(5)": "192/385",
    "zeta(2)^6*zeta(3)": "1552448/1576575",
    "zeta(3)*zeta(3,9)": "-28/9",
    "zeta(5)^3": "6",
    "zeta(3)*zeta(5)*zeta(7)": "-140/3",
    "zeta(3)^2*zeta(9)": "-126"
   }
  },
  "7,3,5": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(7,3,5)",
   "correction": {
    "zeta(2)*zeta(13)": "-1001",
    "zeta(2)^2*zeta(11)": "-44",
    "zeta(2)^3*zeta(9)": "272/35",
    "zeta(2)^5*zeta(5)": "-128/385",
    "zeta(5)^3": "-54",
    "zeta(5)*zeta(3,7)": "-10",
    "zeta(3)*zeta(5)*zeta(7)": "-300",
    "zeta(7)*zeta(3,5)": "-30"
   }
  },
  "7,5,3": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(7,5,3)",
   "correction": {
    "zeta(2)*zeta(13)": "-1638",
    "zeta(2)^2*zeta(11)": "-114",
    "zeta(2)^3*zeta(9)": "-64/35",
    "zeta(2)^4*zeta(7)": "144/35",
    "zeta(2)^5*zeta(5)": "384/385",
    "zeta(2)^6*zeta(3)": "-6966208/7882875",
    "zeta(3)*zeta(3,9)": "28/9",
    "zeta(5)^3": "72",
    "zeta(5)*zeta(3,7)": "12",
    "zeta(3)*zeta(5)*zeta(7)": "1226/3",
    "zeta(7)*zeta(3,5)": "30",
    "zeta(3)^2*zeta(9)": "126"
   }
  },
  "9,3,3": {
   "weight": 15,
   "label": "extracted",
   "leading": "2*zeta(9,3,3)",
   "correction": {
    "zeta(2)*zeta(13)": "-1209",
    "zeta(2)^2*zeta(11)": "-504/5",
    "zeta(2)^3*zeta(9)": "-32/5",
    "zeta(2)^4*zeta(7)": "576/175",
    "zeta(2)^5*zeta(5)": "384/385",
    "zeta(2)^6*zeta(3)": "88448/875875",
    "zeta(3)*zeta(3,9)": "2",
    "zeta(5)^3": "72",
    "zeta(5)*zeta(3,7)": "12",
    "zeta(3)*zeta(5)*zeta(7)": "402",
    "zeta(7)*zeta(3,5)": "30",
    "zeta(3)^2*zeta(9)": "84"
   }
  },
  "3,3,11": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(3,3,11)",
   "correction": {
    "zeta(3)^2*zeta(11)": "-44",
    "zeta(2)*zeta(15)": "2898",
    "zeta(2)^2*zeta(13)": "1584/5",
    "zeta(2)^3*zeta(11)": "1664/35",
    "zeta(2)^4*zeta(9)": "192/25",
    "zeta(2)^5*zeta(7)": "192/385",
    "zeta(5)*zeta(3,9)": "12",
    "zeta(5)^2*zeta(7)": "432",
    "zeta(3)*zeta(7)^2": "420",
    "zeta(7)*zeta(3,7)": "30",
    "zeta(3)*zeta(5)*zeta(9)": "604",
    "zeta(9)*zeta(3,5)": "56"
   }
  },
  "3,5,9": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(3,5,9)",
   "correction": {
    "zeta(3)^2*zeta(11)": "-165",
    "zeta(2)*zeta(15)": "6330",
    "zeta(2)^2*zeta(13)": "2442/5",
    "zeta(2)^3*zeta(11)": "192/7",
    "zeta(2)^4*zeta(9)": "48/7",
    "zeta(5)*zeta(3,9)": "12",
    "zeta(5)^2*zeta(7)": "432",
    "zeta(3)*zeta(7)^2": "420",
    "zeta(7)*zeta(3,7)": "30",
    "zeta(3)*zeta(5)*zeta(9)": "1014",
    "zeta(9)*zeta(3,5)": "138"
   }
  },
  "3,7,7": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(3,7,7)",
   "correction": {
    "zeta(2)*zeta(15)": "4900",
    "zeta(2)^2*zeta(13)": "2156/5",
    "zeta(2)^3*zeta(11)": "40",
    "zeta(2)^6*zeta(5)": "-3104896/525525",
    "zeta(5)*zeta(3,9)": "56/3",
    "zeta(5)^2*zeta(7)": "448",
    "zeta(3)*zeta(7)^2": "392",
    "zeta(7)*zeta(3,7)": "28",
    "zeta(3)*zeta(5)*zeta(9)": "504"
   }
  },
  "3,9,5": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(3,9,5)",
   "correction": {
    "zeta(3)^2*zeta(11)": "165",
    "zeta(2)*zeta(15)": "1260",
    "zeta(2)^2*zeta(13)": "882/5",
    "zeta(2)^3*zeta(11)": "264/7",
    "zeta(2)^5*zeta(7)": "-96/77",
    "zeta(2)^6*zeta(5)": "13932416/2627625",
    "zeta(5)*zeta(3,9)": "-62/3",
    "zeta(5)^2*zeta(7)": "-529",
    "zeta(3)*zeta(7)^2": "-420",
    "zeta(7)*zeta(3,7)": "-30",
    "zeta(3)*zeta(5)*zeta(9)": "-978",
    "zeta(9)*zeta(3,5)": "-84"
   }
  },
  "3,11,3": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(3,11,3)",
   "correction": {
    "zeta(3)^2*zeta(11)": "-88",
    "zeta(2)^4*zeta(9)": "-192/25",
    "zeta(2)^5*zeta(7)": "-192/77",
    "zeta(2)^6*zeta(5)": "-530688/875875",
    "zeta(3)*zeta(3,11)": "-2",
    "zeta(5)*zeta(3,9)": "-24",
    "zeta(5)^2*zeta(7)": "-864",
    "zeta(3)*zeta(7)^2": "-900",
    "zeta(7)*zeta(3,7)": "-60",
    "zeta(3)*zeta(5)*zeta(9)": "-1344",
    "zeta(9)*zeta(3,5)": "-112"
   }
  },
  "5,3,9": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(5,3,9)",
   "correction": {
    "zeta(2)*zeta(15)": "5070",
    "zeta(2)^2*zeta(13)": "312",
    "zeta(2)^3*zeta(11)": "-72/7",
    "zeta(2)^4*zeta(9)": "-2112/175",
    "zeta(2)^5*zeta(7)": "-96/77",
    "zeta(2)^6*zeta(5)": "-3104896/525525",
    "zeta(5)*zeta(3,9)": "20/3",
    "zeta(5)^2*zeta(7)": "13",
    "zeta(3)*zeta(5)*zeta(9)": "-144",
    "zeta(9)*zeta(3,5)": "-54"
   }
  },
  "5,5,7": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(5,5,7)",
   "correction": {
    "zeta(2)*zeta(15)": "3640",
    "zeta(2)^2*zeta(13)": "1274/5",
    "zeta(2)^3*zeta(11)": "16/7",
    "zeta(2)^4*zeta(9)": "-288/25",
    "zeta(2)^5*zeta(7)": "-64/55",
    "zeta(5)^2*zeta(7)": "-14",
    "zeta(3)*zeta(5)*zeta(9)": "-504",
    "zeta(9)*zeta(3,5)": "-84"
   }
  },
  "5,7,5": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(5,7,5)",
   "correction": {
    "zeta(2)^4*zeta(9)": "288/25",
    "zeta(2)^6*zeta(5)": "1552448/1576575",
    "zeta(5)*zeta(3,9)": "-28/9",
    "zeta(5)^2*zeta(7)": "-140/3",
    "zeta(3)*zeta(5)*zeta(9)": "840",
    "zeta(9)*zeta(3,5)": "168"
   }
  },
  "5,9,3": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(5,9,3)",
   "correction": {
    "zeta(3)^2*zeta(11)": "-495",
    "zeta(2)*zeta(15)": "-1260",
    "zeta(2)^2*zeta(13)": "-882/5",
    "zeta(2)^3*zeta(11)": "-264/7",
    "zeta(2)^4*zeta(9)": "-288/25",
    "zeta(2)^5*zeta(7)": "-96/77",
    "zeta(2)^6*zeta(5)": "3104896/525525",
    "zeta(3)*zeta(5,9)": "-2",
    "zeta(5)*zeta(3,9)": "-56/3",
    "zeta(5)^2*zeta(7)": "-445",
    "zeta(3)*zeta(7)^2": "-480",
    "zeta(7)*zeta(3,7)": "-30",
    "zeta(3)*zeta(5)*zeta(9)": "-1146",
    "zeta(9)*zeta(3,5)": "-84"
   }
  },
  "7,3,7": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(7,3,7)",
   "correction": {
    "zeta(2)^5*zeta(7)": "-128/55",
    "zeta(2)^6*zeta(5)": "4208128/375375",
    "zeta(5)*zeta(3,9)": "-112/3",
    "zeta(5)^2*zeta(7)": "-920",
    "zeta(3)*zeta(7)^2": "-840",
    "zeta(7)*zeta(3,7)": "-58",
    "zeta(3)*zeta(5)*zeta(9)": "-1008"
   }
  },
  "7,5,5": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(7,5,5)",
   "correction": {
    "zeta(2)*zeta(15)": "-3640",
    "zeta(2)^2*zeta(13)": "-1274/5",
    "zeta(2)^3*zeta(11)": "-16/7",
    "zeta(2)^5*zeta(7)": "96/77",
    "zeta(2)^6*zeta(5)": "-6966208/7882875",
    "zeta(5)*zeta(3,9)": "28/9",
    "zeta(5)^2*zeta(7)": "191/3",
    "zeta(3)*zeta(5)*zeta(9)": "-336",
    "zeta(9)*zeta(3,5)": "-84"
   }
  },
  "7,7,3": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(7,7,3)",
   "correction": {
    "zeta(2)*zeta(15)": "-4900",
    "zeta(2)^2*zeta(13)": "-2156/5",
    "zeta(2)^3*zeta(11)": "-40",
    "zeta(2)^5*zeta(7)": "192/77",
    "zeta(2)^6*zeta(5)": "-13932416/2627625",
    "zeta(2)^7*zeta(3)": "768/25025",
    "zeta(5)*zeta(3,9)": "56/3",
    "zeta(5)^2*zeta(7)": "472",
    "zeta(3)*zeta(7)^2": "451",
    "zeta(7)*zeta(3,7)": "30",
    "zeta(3)*zeta(5)*zeta(9)": "504"
   }
  },
  "9,3,5": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(9,3,5)",
   "correction": {
    "zeta(2)*zeta(15)": "-5070",
    "zeta(2)^2*zeta(13)": "-312",
    "zeta(2)^3*zeta(11)": "72/7",
    "zeta(2)^4*zeta(9)": "816/175",
    "zeta(2)^5*zeta(7)": "96/77",
    "zeta(2)^6*zeta(5)": "-15259136/2627625",
    "zeta(5)*zeta(3,9)": "26/3",
    "zeta(5)^2*zeta(7)": "97",
    "zeta(3)*zeta(5)*zeta(9)": "-56",
    "zeta(9)*zeta(3,5)": "-56"
   }
  },
  "9,5,3": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(9,5,3)",
   "correction": {
    "zeta(3)^2*zeta(11)": "495",
    "zeta(2)*zeta(15)": "-6330",
    "zeta(2)^2*zeta(13)": "-2442/5",
    "zeta(2)^3*zeta(11)": "-192/7",
    "zeta(2)^4*zeta(9)": "432/35",
    "zeta(2)^5*zeta(7)": "192/77",
    "zeta(2)^6*zeta(5)": "530688/875875",
    "zeta(2)^7*zeta(3)": "1536/25025",
    "zeta(3)*zeta(5,9)": "2",
    "zeta(5)*zeta(3,9)": "12",
    "zeta(5)^2*zeta(7)": "432",
    "zeta(3)*zeta(7)^2": "480",
    "zeta(7)*zeta(3,7)": "30",
    "zeta(3)*zeta(5)*zeta(9)": "1316",
    "zeta(9)*zeta(3,5)": "140"
   }
  },
  "11,3,3": {
   "weight": 17,
   "label": "extracted",
   "leading": "2*zeta(11,3,3)",
   "correction": {
    "zeta(3)^2*zeta(11)": "135",
    "zeta(2)*zeta(15)": "-2898",
    "zeta(2)^2*zeta(13)": "-1584/5",
    "zeta(2)^3*zeta(11)": "-1656/35",
    "zeta(2)^5*zeta(7)": "768/385",
    "zeta(2)^6*zeta(5)": "530688/875875",
    "zeta(2)^7*zeta(3)": "1536/25025",
    "zeta(3)*zeta(3,11)": "2",
    "zeta(5)*zeta(3,9)": "12",
    "zeta(5)^2*zeta(7)": "432",
    "zeta(3)*zeta(7)^2": "480",
    "zeta(7)*zeta(3,7)": "30",
    "zeta(3)*zeta(5)*zeta(9)": "740",
    "zeta(9)*zeta(3,5)": "56"
   }
  },
  "3,3,13": {
   "weight": 19,
   "label": "extracted",
   "leading": "2*zeta(3,3,13)",
   "correction": {
    "zeta(3)*zeta(5)*zeta(11)": "-208698/17",
    "zeta(11)*zeta(3,5)": "90",
    "zeta(3)^2*zeta(13)": "-65",
    "zeta(19)": "81716/17",
    "zeta(2)*zeta(17)": "9182/3",
    "zeta(2)^2*zeta(15)": "-26488/3",
    "zeta(2)^3*zeta(13)": "-195528/85",
    "zeta(2)^4*zeta(11)": "93144/85",
    "zeta(2)^5*zeta(9)": "348928/255",
    "zeta(2)^6*zeta(7)": "14912/51",
    "zeta(2)^7*zeta(5)": "-4608/85",
    "zeta(2)^8*zeta(3)": "61824/85",
    "zeta(3)*zeta(3,13)": "-150935/51",
    "zeta(3)*zeta(5,11)": "11949/17",
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 }
}