{
 "title": "Boundary master integrals of the dissipative crossed family PX2 at 5PM-2SF: definitions, computed values, and the flow-free relations",
 "paper": "M. D. Schwartz, Memory back-reaction in black-hole scattering at fifth post-Minkowskian order: Sec. 5 (response matrices, boundary constants of PX2, relations among boundary constants), Tables 3, 4 and 5; equation numbers below as in the revised manuscript that this package accompanies",
 "conventions": {
  "family": "pm5_2SF_PX2_diss (kira/integralfamilies.yaml, families_dissipative.json)",
  "propagators_D1_to_D22": [
   "2*k1*u1",
   "2*k2*u1",
   "2*k3*u2",
   "2*k4*u2",
   "2*k1*u2",
   "2*k1*u2-2*k2*u2",
   "2*k3*u1",
   "2*k3*u1-2*k4*u1",
   "(k1-k2)^2",
   "(k1-k3)^2",
   "(k1-k4)^2",
   "(k2-k3)^2",
   "(k2-k4)^2",
   "(k3-k4)^2",
   "(k1+q)^2",
   "(k2+q)^2",
   "(k3+q)^2",
   "(k4+q)^2",
   "k1^2",
   "k2^2",
   "k3^2",
   "k4^2"
  ],
  "cut": "D1..D4 are cut: 2 pi delta(2 k_i.u) each",
  "measure": "prod_i d^D k_i / (i pi^(D/2)), D = 4 - 2 eps, no exp(gammaE eps) factor",
  "kinematic_point": {
   "gamma": "5/4",
   "q^2": "-1",
   "u1^2": "1",
   "u2^2": "1",
   "u_i.q": "0"
  },
  "index_vector": "n_i = exponent of D_i; negative n_i = numerator power; kira_sector = sum of 2^(i-1) over D_i with n_i > 0",
  "sectors": {
   "S1": 1077759,
   "S2": 1091071,
   "S3": 599551
  },
  "graviton_i0": "keys fey / conj / pv: Feynman (+i0) on every graviton propagator / the complex-conjugate assignment / their average.  All values in this file are boundary data with Feynman-type graviton propagators; no in-in (retarded) boundary values are given.",
  "linearized_i0": "for integrals with an uncut linearized worldline propagator 1/(D_j + i sigma 0) the value is given at sigma = +1; which sign of sigma corresponds to retarded boundary conditions is not fixed here",
  "laurent": "keys '-2','-1','0','1','2' = coefficient of eps^k; 're','im' decimal strings as produced (digits beyond 'correct_digits' are not significant); 'exact' closed forms use pi, ln2 = log 2, gammaE = Euler's constant, i"
 },
 "counts": {
  "support_rows": 31,
  "distinct_integrals_at_most": 25,
  "computed_distinct": [
   "I_0",
   "I_2",
   "I_3",
   "I_r1",
   "I_r4",
   "I_r5",
   "I_r6",
   "I_r7",
   "Itilde_1",
   "Itilde_5",
   "Itilde_6",
   "Itilde_7"
  ],
  "n_computed_distinct": 12,
  "identically_zero": [
   "I_r1",
   "Itilde_1"
  ],
  "note": "I_r0, I_r2, I_r3 and Itilde_0, Itilde_2, Itilde_3 are relabelings of I_0, I_3, I_2; Itilde_5,6,7 equal I_r5,6,7 in value"
 },
 "masters": [
  {
   "name": "I_0",
   "sector": "S1",
   "top_sector_label": 1077759,
   "response_matrix_row": 0,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    0,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1077519,
   "uncut_denominators": [
    "D9",
    "D13",
    "D14",
    "D15",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [],
   "class": "radiative corner",
   "status": "computed",
   "values": {
    "graviton_i0": {
     "fey": {
      "-1": {
       "re": "26.88409537992407336529551453260998562542",
       "im": "11.3340623994548686393607892608679854252",
       "exact_re": "pi^4*(80*log(2)-48)/27",
       "exact_im": "pi^5/27",
       "correct_digits": 32
      },
      "0": {
       "re": "388.8416383979840135592604872635651201957",
       "im": "161.9427314980753499103669332391881456479",
       "correct_digits": 28
      }
     },
     "conj": {
      "-1": {
       "re": "26.88409537992407336529551453260998562542",
       "im": "-11.3340623994548686393607892608679854252",
       "exact_re": "pi^4*(80*log(2)-48)/27",
       "exact_im": "-(pi^5/27)",
       "correct_digits": 32
      },
      "0": {
       "re": "388.8416383979840135592604872635651201957",
       "im": "-161.9427314980753499103669332391881456479",
       "correct_digits": 28
      }
     },
     "pv": {
      "-1": {
       "re": "26.88409537992407336529551453260998562542",
       "im": "0.0",
       "exact_re": "pi^4*(80*log(2)-48)/27",
       "exact_im": "0",
       "correct_digits": 32
      },
      "0": {
       "re": "388.8416383979840135592604872635651201957",
       "im": "0.0",
       "correct_digits": 28
      }
     }
    },
    "note": "orders eps^-1 (exact and numerical) and eps^0 (numerical); correct_digits = number of leading significant digits established by two independent evaluations"
   }
  },
  {
   "name": "I_2",
   "sector": "S1",
   "top_sector_label": 1077759,
   "response_matrix_row": 2,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,-1,0,0,1,1,1,0,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    -1,
    0,
    0,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1077519,
   "uncut_denominators": [
    "D9",
    "D13",
    "D14",
    "D15",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D10"
   ],
   "class": "radiative corner, numerator",
   "status": "computed",
   "values": {
    "graviton_i0": {
     "fey": {
      "-1": {
       "re": "-8.991868272122910263602443172207386303432",
       "im": "-2.479326149880752514860172650814871811762",
       "exact_re": "pi^4*(150-220*log(2))/27",
       "exact_im": "-7*pi^5/864",
       "correct_digits": 30
      },
      "0": {
       "re": "-131.6922906709016052922584138525323324664",
       "im": "-35.15238209960831752412489636759280285351",
       "correct_digits": 26
      }
     },
     "conj": {
      "-1": {
       "re": "-8.991868272122910263602443172207386303432",
       "im": "2.479326149880752514860172650814871811762",
       "exact_re": "pi^4*(150-220*log(2))/27",
       "exact_im": "-(-7*pi^5/864)",
       "correct_digits": 30
      },
      "0": {
       "re": "-131.6922906709016052922584138525323324664",
       "im": "35.15238209960831752412489636759280285351",
       "correct_digits": 26
      }
     },
     "pv": {
      "-1": {
       "re": "-8.991868272122910263602443172207386303432",
       "im": "0.0",
       "exact_re": "pi^4*(150-220*log(2))/27",
       "exact_im": "0",
       "correct_digits": 30
      },
      "0": {
       "re": "-131.6922906709016052922584138525323324664",
       "im": "0.0",
       "correct_digits": 26
      }
     }
    },
    "note": "orders eps^-1 (exact and numerical) and eps^0 (numerical); correct_digits = number of leading significant digits established by two independent evaluations"
   }
  },
  {
   "name": "I_3",
   "sector": "S1",
   "top_sector_label": 1077759,
   "response_matrix_row": 3,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,-1,0,1,1,1,0,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    -1,
    0,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1077519,
   "uncut_denominators": [
    "D9",
    "D13",
    "D14",
    "D15",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D11"
   ],
   "class": "radiative corner, numerator",
   "status": "computed",
   "values": {
    "graviton_i0": {
     "fey": {
      "-1": {
       "re": "-3.51208923412190800676403039763823466548",
       "im": "-0.3148350666515241288711330350241107062555",
       "exact_re": "pi^4*(1128-1640*log(2))/243",
       "exact_im": "-pi^5/972",
       "correct_digits": 30
      },
      "0": {
       "re": "-52.25287419669298022213073111948182795981",
       "im": "-4.256106616639279480827641220212752033664",
       "correct_digits": 26
      }
     },
     "conj": {
      "-1": {
       "re": "-3.51208923412190800676403039763823466548",
       "im": "0.3148350666515241288711330350241107062555",
       "exact_re": "pi^4*(1128-1640*log(2))/243",
       "exact_im": "-(-pi^5/972)",
       "correct_digits": 30
      },
      "0": {
       "re": "-52.25287419669298022213073111948182795981",
       "im": "4.256106616639279480827641220212752033664",
       "correct_digits": 26
      }
     },
     "pv": {
      "-1": {
       "re": "-3.51208923412190800676403039763823466548",
       "im": "0.0",
       "exact_re": "pi^4*(1128-1640*log(2))/243",
       "exact_im": "0",
       "correct_digits": 30
      },
      "0": {
       "re": "-52.25287419669298022213073111948182795981",
       "im": "0.0",
       "correct_digits": 26
      }
     }
    },
    "note": "orders eps^-1 (exact and numerical) and eps^0 (numerical); correct_digits = number of leading significant digits established by two independent evaluations"
   }
  },
  {
   "name": "I_r0",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 0,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090831,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [],
   "class": "radiative corner (relabeling of I_0)",
   "status": "computed (identical to an S_1 integral by the relabeling k1 <-> k2 of loop momenta)",
   "equal_to": "I_0"
  },
  {
   "name": "I_r1",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 1,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,-1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    -1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090831,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D5"
   ],
   "class": "odd numerator, no linearized denominator: vanishes",
   "status": "computed",
   "values": {
    "exact": "0",
    "note": "vanishes identically, all orders in eps, any i0 assignment (reflection of the two uncut worldline frequency components)"
   }
  },
  {
   "name": "I_r2",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 2,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,-1,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    -1,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090831,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D10"
   ],
   "class": "radiative corner, numerator (relabeling of I_3)",
   "status": "computed (identical to an S_1 integral by the relabeling k1 <-> k2 of loop momenta)",
   "equal_to": "I_3"
  },
  {
   "name": "I_r3",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 3,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,1,-1,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    -1,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090831,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D12"
   ],
   "class": "radiative corner, numerator (relabeling of I_2)",
   "status": "computed (identical to an S_1 integral by the relabeling k1 <-> k2 of loop momenta)",
   "equal_to": "I_2"
  },
  {
   "name": "I_r4",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 4,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,1,0,0,2,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    2,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090831,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [
    "D14"
   ],
   "numerators": [],
   "class": "radiative corner, dotted graviton propagator",
   "status": "computed",
   "values": {
    "graviton_i0": {
     "fey": {
      "-1": {
       "re": "97.40909103400243723644033268870511124973",
       "im": "1.574814671885801716967282977206801776543e-120"
      },
      "0": {
       "re": "614.8577298822660234593791791516525551807",
       "im": "-204.0131231901876355084942066956237376535"
      }
     },
     "conj": "complex conjugate of fey (only the radiation-cone layer is complex)",
     "pv": "real part of fey"
    },
    "exact": {
     "-1": "pi^4",
     "0": "pi^4*(4 + (20/3)*ln2 - 4*gammaE) - (2/3)*i*pi^5"
    },
    "exact_identification": {
     "-1": "integer relation over (pi^4, pi^4 ln2, pi^5), re-verified to 3.86e-152",
     "0": "integer relation at 40 digits (re parts over pi^4(1, ln2, gammaE): ['4', '20/3', '-4']; im part over pi^5: -2/3), residuals 8.46e-40, 3.38e-38"
    },
    "correct_digits": {
     "-1": "exact",
     "0": 38
    },
    "note": "order eps^1 not computed"
   }
  },
  {
   "name": "I_r5",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 5,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090847,
   "uncut_denominators": [
    "D5",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5"
   ],
   "dotted": [],
   "numerators": [],
   "class": "static slice (one uncut linearized propagator)",
   "status": "computed",
   "values": {
    "linearized_i0": "value at sigma = +1 for the uncut linearized propagator 1/(D5 + i sigma 0); sigma = -1 reverses the sign; the principal-value part is zero",
    "graviton_i0": "independent of the graviton i0 assignment (static slice, radiation cone not crossed)",
    "exact": {
     "-1": "0",
     "0": "(-16/3)*i*pi^5",
     "1": "((-128) + (160/3)*ln2 + (64/3)*gammaE)*i*pi^5"
    },
    "exact_identification": {
     "0": "integer relation, re-verified to 5.51e-151",
     "1": "integer relation over i pi^5 (1, ln2, gammaE), re-verified to 4.21e-150"
    },
    "numerical_sigma_plus": {
     "0": {
      "re": "-3.446606804215893262808047263624853144337e-119",
      "im": "-1632.104985521501084067953653564989901228"
     },
     "1": {
      "re": "7.528318682467074722358251551108667991677e-118",
      "im": "-24089.32370396783800485458665371166696987"
     },
     "2": {
      "re": "-1.371826959916222504963059171535357278483e-116",
      "im": "-311453.9229622015993068010973351811968433"
     }
    },
    "note": "purely imaginary; the listed real parts are numerical zeros of the evaluation; order eps^2 numerical only"
   }
  },
  {
   "name": "I_r6",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 6,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,0,1,0,1,-1,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    -1,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090847,
   "uncut_denominators": [
    "D5",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5"
   ],
   "dotted": [],
   "numerators": [
    "D12"
   ],
   "class": "static slice, numerator",
   "status": "computed",
   "values": {
    "linearized_i0": "value at sigma = +1 for the uncut linearized propagator 1/(D5 + i sigma 0); sigma = -1 reverses the sign; the principal-value part is zero",
    "graviton_i0": "independent of the graviton i0 assignment (static slice, radiation cone not crossed)",
    "exact": {
     "-1": "0",
     "0": "(128/81)*i*pi^5",
     "1": "((1024/27) + (-1280/81)*ln2 + (-512/81)*gammaE)*i*pi^5"
    },
    "exact_identification": {
     "0": "integer relation, re-verified to 1.64e-151",
     "1": "integer relation over i pi^5 (1, ln2, gammaE), re-verified to 1.25e-150"
    },
    "numerical_sigma_plus": {
     "0": {
      "re": "-2.129925553167125050049916848307493516164e-120",
      "im": "483.5866623767410619460603417970340448084"
     },
     "1": {
      "re": "-1.827863383808878224770110458911158072053e-118",
      "im": "7137.577393768248297734692341840493916999"
     },
     "2": {
      "re": "1.998257428062248228774103806775757553346e-117",
      "im": "92336.3756920275191718609985076607658104"
     }
    },
    "note": "purely imaginary; the listed real parts are numerical zeros of the evaluation; order eps^2 numerical only"
   }
  },
  {
   "name": "I_r7",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 7,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,0,1,0,1,0,-1,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    -1,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090847,
   "uncut_denominators": [
    "D5",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5"
   ],
   "dotted": [],
   "numerators": [
    "D13"
   ],
   "class": "static slice, numerator",
   "status": "computed",
   "values": {
    "linearized_i0": "value at sigma = +1 for the uncut linearized propagator 1/(D5 + i sigma 0); sigma = -1 reverses the sign; the principal-value part is zero",
    "graviton_i0": "independent of the graviton i0 assignment (static slice, radiation cone not crossed)",
    "exact": {
     "-1": "0",
     "0": "(32/81)*i*pi^5",
     "1": "((736/81) + (-320/81)*ln2 + (-128/81)*gammaE)*i*pi^5"
    },
    "exact_identification": {
     "0": "integer relation, re-verified to 3.31e-152",
     "1": "integer relation over i pi^5 (1, ln2, gammaE), re-verified to 2.48e-151"
    },
    "numerical_sigma_plus": {
     "0": {
      "re": "-8.434989264531171362981772973126835117989e-120",
      "im": "120.8966655941852654865150854492585112021"
     },
     "1": {
      "re": "8.214735599374116386215247480858673856658e-119",
      "im": "1663.497682847876808947158000010864968048"
     },
     "2": {
      "re": "2.865718016988495521885342668631900367202e-117",
      "im": "20937.00957778226192207203128510729243974"
     }
    },
    "note": "purely imaginary; the listed real parts are numerical zeros of the evaluation; order eps^2 numerical only"
   }
  },
  {
   "name": "I_r9",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 9,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,-1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    -1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090895,
   "uncut_denominators": [
    "D7",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D7"
   ],
   "dotted": [],
   "numerators": [
    "D5"
   ],
   "class": "one uncut linearized propagator D7, odd numerator",
   "status": "not computed"
  },
  {
   "name": "I_r10",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 10,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,1,-1,1,0,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    1,
    -1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090895,
   "uncut_denominators": [
    "D7",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D7"
   ],
   "dotted": [],
   "numerators": [
    "D8"
   ],
   "class": "one uncut linearized propagator D7, numerator",
   "status": "not computed"
  },
  {
   "name": "I_r18",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 18,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090911,
   "uncut_denominators": [
    "D5",
    "D7",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5",
    "D7"
   ],
   "dotted": [],
   "numerators": [],
   "class": "two uncut linearized propagators D5, D7",
   "status": "not computed"
  },
  {
   "name": "I_r19",
   "sector": "S2",
   "top_sector_label": 1091071,
   "response_matrix_row": 19,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,1,0,1,0,1,0,-1,1,0,1,0,0,0,0,1,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    -1,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0
   ],
   "kira_sector": 1090911,
   "uncut_denominators": [
    "D5",
    "D7",
    "D9",
    "D11",
    "D14",
    "D16",
    "D21"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5",
    "D7"
   ],
   "dotted": [],
   "numerators": [
    "D13"
   ],
   "class": "two uncut linearized propagators D5, D7, numerator",
   "status": "not computed"
  },
  {
   "name": "Itilde_0",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 0,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599311,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [],
   "class": "radiative corner (image of I_0)",
   "status": "computed (identical to an S_1 integral by a relabeling of loop momenta)",
   "equal_to": "I_0"
  },
  {
   "name": "Itilde_1",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 1,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,-1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    -1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599311,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D5"
   ],
   "class": "odd numerator, no linearized denominator: vanishes",
   "status": "computed",
   "values": {
    "exact": "0",
    "note": "vanishes identically, all orders in eps, any i0 assignment (reflection of the two uncut worldline frequency components)"
   }
  },
  {
   "name": "Itilde_2",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 2,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,-1,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    -1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599311,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D10"
   ],
   "class": "radiative corner, numerator (image of I_3)",
   "status": "computed (identical to an S_1 integral by a relabeling of loop momenta)",
   "equal_to": "I_3"
  },
  {
   "name": "Itilde_3",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 3,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,1,-1,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    -1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599311,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [],
   "numerators": [
    "D12"
   ],
   "class": "radiative corner, numerator (image of I_2)",
   "status": "computed (identical to an S_1 integral by a relabeling of loop momenta)",
   "equal_to": "I_2"
  },
  {
   "name": "Itilde_4",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 4,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,0,0,1,0,1,0,0,2,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    2,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599311,
   "uncut_denominators": [
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [],
   "dotted": [
    "D14"
   ],
   "numerators": [],
   "class": "radiative corner, dotted graviton propagator (image of I_r4)",
   "status": "not computed directly; the reduction identities in boundary_ibp_identities_PX2.m equate it to I_r4"
  },
  {
   "name": "Itilde_5",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 5,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599327,
   "uncut_denominators": [
    "D5",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5"
   ],
   "dotted": [],
   "numerators": [],
   "class": "static slice (image of I_r5)",
   "status": "computed",
   "values": {
    "linearized_i0": "value at sigma = +1 for the uncut linearized propagator 1/(D5 + i sigma 0); sigma = -1 reverses the sign; the principal-value part is zero",
    "graviton_i0": "independent of the graviton i0 assignment",
    "exact": {
     "-1": "0",
     "0": "-16*i*pi^5/3",
     "1": "32*i*pi^5*(-12 + 2*gammaE + 5*ln2)/3"
    },
    "exact_identification": {
     "0": "integer relation, re-verified (relative residual 0.0)",
     "1": "integer relation over i pi^5 (1, ln2, gammaE), re-verified (relative residual 6.465e-212)"
    },
    "equal_to": "I_r5 (same values through order eps; independent evaluation in the S_3 variables)"
   }
  },
  {
   "name": "Itilde_6",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 6,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,0,1,0,1,-1,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    -1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599327,
   "uncut_denominators": [
    "D5",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5"
   ],
   "dotted": [],
   "numerators": [
    "D12"
   ],
   "class": "static slice, numerator (image of I_r6)",
   "status": "computed",
   "values": {
    "linearized_i0": "value at sigma = +1 for the uncut linearized propagator 1/(D5 + i sigma 0); sigma = -1 reverses the sign; the principal-value part is zero",
    "graviton_i0": "independent of the graviton i0 assignment",
    "exact": {
     "-1": "0",
     "0": "128*i*pi^5/81",
     "1": "i*pi^5*(3072 - 1280*ln2 - 512*gammaE)/81"
    },
    "exact_identification": {
     "0": "integer relation, re-verified (relative residual 0.0)",
     "1": "integer relation over i pi^5 (1, ln2, gammaE), re-verified (relative residual 1.746e-210)"
    },
    "equal_to": "I_r6 (same values through order eps; independent evaluation in the S_3 variables)"
   }
  },
  {
   "name": "Itilde_7",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 7,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,0,1,0,1,0,-1,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    -1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599327,
   "uncut_denominators": [
    "D5",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5"
   ],
   "dotted": [],
   "numerators": [
    "D13"
   ],
   "class": "static slice, numerator (image of I_r7)",
   "status": "computed",
   "values": {
    "linearized_i0": "value at sigma = +1 for the uncut linearized propagator 1/(D5 + i sigma 0); sigma = -1 reverses the sign; the principal-value part is zero",
    "graviton_i0": "independent of the graviton i0 assignment",
    "exact": {
     "-1": "0",
     "0": "32*i*pi^5/81",
     "1": "i*pi^5*(736 - 320*ln2 - 128*gammaE)/81"
    },
    "exact_identification": {
     "0": "integer relation, re-verified (relative residual 0.0)",
     "1": "integer relation over i pi^5 (1, ln2, gammaE), re-verified (relative residual 1.872e-210)"
    },
    "equal_to": "I_r7 (same values through order eps; independent evaluation in the S_3 variables)"
   }
  },
  {
   "name": "Itilde_9",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 9,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,-1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    -1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599375,
   "uncut_denominators": [
    "D7",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D7"
   ],
   "dotted": [],
   "numerators": [
    "D5"
   ],
   "class": "one uncut linearized propagator D7, odd numerator",
   "status": "not computed"
  },
  {
   "name": "Itilde_10",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 10,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,1,-1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    1,
    -1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599375,
   "uncut_denominators": [
    "D7",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D7"
   ],
   "dotted": [],
   "numerators": [
    "D8"
   ],
   "class": "one uncut linearized propagator D7, numerator",
   "status": "not computed"
  },
  {
   "name": "Itilde_19",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 19,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,-1,0,0,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    -1,
    0,
    0,
    1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599439,
   "uncut_denominators": [
    "D8",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D8"
   ],
   "dotted": [],
   "numerators": [
    "D5"
   ],
   "class": "one uncut linearized propagator D8, odd numerator",
   "status": "not computed"
  },
  {
   "name": "Itilde_20",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 20,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,0,0,-1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    0,
    0,
    -1,
    1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599439,
   "uncut_denominators": [
    "D8",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D8"
   ],
   "dotted": [],
   "numerators": [
    "D7"
   ],
   "class": "one uncut linearized propagator D8, numerator",
   "status": "not computed"
  },
  {
   "name": "Itilde_23",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 23,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599391,
   "uncut_denominators": [
    "D5",
    "D7",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5",
    "D7"
   ],
   "dotted": [],
   "numerators": [],
   "class": "two uncut linearized propagators D5, D7",
   "status": "not computed"
  },
  {
   "name": "Itilde_24",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 24,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,1,0,1,0,1,0,-1,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    -1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599391,
   "uncut_denominators": [
    "D5",
    "D7",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5",
    "D7"
   ],
   "dotted": [],
   "numerators": [
    "D13"
   ],
   "class": "two uncut linearized propagators D5, D7, numerator",
   "status": "not computed"
  },
  {
   "name": "Itilde_31",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 31,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599455,
   "uncut_denominators": [
    "D5",
    "D8",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5",
    "D8"
   ],
   "dotted": [],
   "numerators": [],
   "class": "two uncut linearized propagators D5, D8",
   "status": "not computed"
  },
  {
   "name": "Itilde_32",
   "sector": "S3",
   "top_sector_label": 599551,
   "response_matrix_row": 32,
   "kira_integral": "pm5_2SF_PX2_diss[1,1,1,1,1,0,0,1,1,0,1,-1,0,1,0,0,1,0,0,1,0,0]",
   "index_vector": [
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    1,
    1,
    0,
    1,
    -1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0
   ],
   "kira_sector": 599455,
   "uncut_denominators": [
    "D5",
    "D8",
    "D9",
    "D11",
    "D14",
    "D17",
    "D20"
   ],
   "uncut_linearized_worldline_propagators": [
    "D5",
    "D8"
   ],
   "dotted": [],
   "numerators": [
    "D12"
   ],
   "class": "two uncut linearized propagators D5, D8, numerator",
   "status": "not computed"
  }
 ],
 "flow_free_relations": {
  "note": "Left null vectors v of the response matrices A(eps) of Eq. (27) (v^T A = 0), i.e. the flow-free directions of Table 3, normalized to 1 on one support row.  The relation among master integrals is sum_row weight[row] * M[row] = 0 at each eps.  Rows are response-matrix rows (field response_matrix_row of the masters above).  Weights that are rational and independent of eps are given exactly; the others are given at the twelve eps values of the computation.",
  "S1": [
   {
    "support": [
     "I_0",
     "I_2",
     "I_3"
    ],
    "rows": [
     0,
     2,
     3
    ],
    "weights_exact": [
     "1",
     "16/3",
     "-6"
    ],
    "eps_dependence": "none (checked to 4e-84 over the twelve eps values)",
    "relation": "I_0 + (16/3) I_2 - 6 I_3 = 0, Eq. (36) of the paper"
   }
  ],
  "S2": [
   {
    "support": [
     "I_r0",
     "I_r2",
     "I_r3"
    ],
    "rows": [
     0,
     2,
     3
    ],
    "weights_exact": [
     "-1/6",
     "1",
     "-8/9"
    ],
    "eps_dependence": "none (spread 2.4e-83 over the twelve eps values)",
    "relation": "-(1/6) I_r0 + I_r2 - (8/9) I_r3 = 0 (the same relation as in S_1 after relabeling)"
   },
   {
    "support": [
     "I_r1",
     "I_r5",
     "I_r6"
    ],
    "rows": [
     1,
     5,
     6
    ],
    "normalized_row": 6,
    "per_eps": [
     {
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      "weights": {
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        "im": "3.6776704130771185410963479453287253095504492099046e-80"
       },
       "I_r5": {
        "re": "0.29629629949674378391667389185574243589193619697742",
        "im": "4.5765223674786107762903475453440305159321914590415e-84"
       },
       "I_r6": {
        "re": "1.0",
        "im": "0"
       }
      },
      "max_off_support_weight": "8.59e-78",
      "residual_vT_A": "1.21e-77"
     },
     {
      "eps": "0.0003104656021947690595436839176405119643851",
      "weights": {
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        "im": "3.7338568232810923535796414180851822050027304655869e-80"
       },
       "I_r5": {
        "re": "0.29629629947551259111934507895308643545470306089137",
        "im": "4.6027992014555288792451064589892025808295550497523e-84"
       },
       "I_r6": {
        "re": "1.0",
        "im": "0"
       }
      },
      "max_off_support_weight": "8.68e-78",
      "residual_vT_A": "1.22e-77"
     },
     {
      "eps": "0.0003084681229037284362826933778519755147468",
      "weights": {
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        "im": "3.8453865795105779002822851870698586264357892761146e-80"
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       },
       "I_r6": {
        "re": "1.0",
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       }
      },
      "max_off_support_weight": "8.86e-78",
      "residual_vT_A": "1.25e-77"
     },
     {
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      "weights": {
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      "max_off_support_weight": "9.12e-78",
      "residual_vT_A": "1.29e-77"
     },
     {
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       "I_r6": {
        "re": "1.0",
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      },
      "max_off_support_weight": "9.46e-78",
      "residual_vT_A": "1.33e-77"
     },
     {
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      "weights": {
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        "re": "1.0",
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      },
      "max_off_support_weight": "9.85e-78",
      "residual_vT_A": "1.39e-77"
     },
     {
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      "weights": {
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      },
      "max_off_support_weight": "1.03e-77",
      "residual_vT_A": "1.45e-77"
     },
     {
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      "weights": {
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      "max_off_support_weight": "3.91e-78",
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     {
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      "residual_vT_A": "1.57e-77"
     },
     {
      "eps": "0.0002841863011363383416805787423483583750696",
      "weights": {
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      },
      "max_off_support_weight": "1.15e-77",
      "residual_vT_A": "1.62e-77"
     },
     {
      "eps": "0.0002821888218452977184195882025598219254313",
      "weights": {
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       "I_r6": {
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      },
      "max_off_support_weight": "4.46e-78",
      "residual_vT_A": "1.66e-77"
     },
     {
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      "weights": {
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      },
      "max_off_support_weight": "4.53e-78",
      "residual_vT_A": "1.67e-77"
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    ],
    "weight_digits": "extracted at 120-digit working precision from response-matrix entries with radii below 1e-107; at least 70 digits",
    "weights_at_eps_0": "(-7/54, 8/27, 1) (rational values reached in the limit eps -> 0; Table 5 of the paper)"
   },
   {
    "support": [
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    "rows": [
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    "normalized_row": 7,
    "per_eps": [
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     {
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      "max_off_support_weight": "8.68e-78",
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     {
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      },
      "two_extraction_agreement_digits": 46,
      "max_off_support_weight": "4.33e-79",
      "residual_vT_A": "3.76e-80"
     }
    ],
    "weight_digits": "two extractions at 60 and 120 digits agree to the number of digits listed per eps (at least 45)"
   }
  ],
  "S3_check": "the combination (direction normalized on row 0) - 6 (direction normalized on row 2) has weight 5.3333333333333333333 on Itilde_3 (16/3 to 3.3e-45) and weights below 6.0e-46 on all other rows: the relation Itilde_0 - 6 Itilde_2 + (16/3) Itilde_3 = 0, the S_3 image of Eq. (36), lies in the span"
 },
 "source_sha256": {
  "families": {
   "description": "families_dissipative.json (this package)",
   "sha256": "9c1b07e246b5b15fbee7d5e0180fa353e9f8c88ad1dcb5c1bfcbb15c335a3250"
  },
  "targets": {
   "description": "table of the 42 target integrals of the three top sectors with their Kira index vectors",
   "sha256": "d6e098f424000115e3661c3c89039c6a6757a068408c71e9c64b148b68b9c3c0"
  },
  "S1_values": {
   "description": "direct evaluation of the S_1 corner integrals I_0, I_2, I_3 (two-frequency Bessel-K cores, closed order-0 forms, numerical order-1 moments)",
   "sha256": "25e4dc58663b22973a9a4eaece5bf41b469925b0c00b81ba92e2a0bb8fb081ee"
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  "S2_values": {
   "description": "assembled S_2 boundary values I_r0..I_r7 with exact forms and routing structure",
   "sha256": "a79c2960dc2f5b72a016b851c139f015ce8527f8b84a4994ae1ee622b2f0e0f8"
  },
  "I_r5": {
   "description": "static-slice evaluation of I_r5 (Weber-Schafheitlin and Bessel-K Mellin closed forms)",
   "sha256": "83a0e798d2fabee3c71248820cfb84545428754f4cda27d5864d8417d6857f35"
  },
  "I_r4": {
   "description": "evaluation of the dotted corner integral I_r4",
   "sha256": "32a84cdeddd9af702f50ae44a0fe06e0712717e49f1ea07505689921e7bb74ef"
  },
  "I_r6": {
   "description": "static-slice evaluation of I_r6",
   "sha256": "aa202fcc372b0ad811dc166c623ded33906b5ce4bfee7ef5b2fb66bd61d7a392"
  },
  "I_r7": {
   "description": "static-slice evaluation of I_r7",
   "sha256": "56dcb9857cfd7b7df7ce7aa353324d6c2c6eebc9a670fd41fc158a24070c980f"
  },
  "I_r5_closed": {
   "description": "integer-relation identification of the I_r5 coefficients (two precisions, re-verified below 1e-150)",
   "sha256": "6fa758ff689a38e026006edd768e57a1536d92c7dc1744c0244cf213ed4606a8"
  },
  "I_r67_closed": {
   "description": "integer-relation identification of the I_r6, I_r7 coefficients",
   "sha256": "18feda6faebe985c7c210639aaf0353645ff450a9e6769524b3c89ab3d061e1d"
  },
  "I_r4_closed": {
   "description": "integer-relation identification of the I_r4 coefficients",
   "sha256": "10126cf3898e1ff2d1e1fe21a078b612d87a9f44b13b6d80242c158db408aa02"
  },
  "S3_values": {
   "description": "S_3 boundary values (sigma images of the S_1 corner integrals; static-slice closed forms)",
   "sha256": "0b0814e0b5acb377a85c1f25238c23a3200cb1a145f17fdff28f2c2c5539f30f"
  },
  "S3_static_corrected": {
   "description": "independent closed-form evaluation of the S_3 static-slice integrals Itilde_5,6,7",
   "sha256": "34a4f0e48268ea6f5976021e5f99a47d7a606b8cf329be87dc12e3845b247b26"
  },
  "S3_static_pslq": {
   "description": "integer-relation identification of the Itilde_5,6,7 coefficients (re-verified below 1e-200)",
   "sha256": "474f9f32e42458911e69f6ca3e8c09e482a8921605dc40ffc014cb98b071a48c"
  },
  "S2_nullvectors": {
   "description": "left null vectors of the S_2 response matrix at twelve values of epsilon (120-digit extraction)",
   "sha256": "4876a592e46a1798c008cfd925dce52cec36082b6d8647f94f37db29178a999a"
  },
  "S3_nullvectors": {
   "description": "left null vectors of the S_3 response matrix at twelve values of epsilon (two extractions at 60 and 120 digits)",
   "sha256": "53de1b3fdf6260c5d3ac0e221f5506fdeefe865d335eeed8ffbcb1ae6b1f9653"
  },
  "S2_response_matrix": {
   "description": "response matrix A(epsilon) of S_2 (source of the epsilon grid, common to S_1, S_2, S_3)",
   "sha256": "c6255a2eca5bf90cd765e1657a128287c48aa2bf412d3446ceec23e99b8cccb5"
  }
 }
}