{
 "row": 1,
 "object": "outer-mass double box g10 = LS*G52 (outer-dbox.tex eq:outer-dbox-final)",
 "provenance": {
  "symbol": "the results paper (Thirty frontier Feynman integrals from a hybrid bootstrap), Sec. 2.2, eq. (5) \u2014 the 18-word symbol; verified against the paper's word list",
  "letters": "12 multiplicative (w,z) factors printed in the paper's Sec. 2.2; exponent vectors verified symbolically against u,v,1+u,u+v and the odd letters",
  "constant": "beyond-symbol constant == 0 ANALYTICALLY: iterated integral from the u,v->infinity base line w=z (g10 -> 0 there, the paper's boundary condition); all first-entry letters vanish on that line => integrals convergent, no reg.",
  "builder": "built once by a sympy fibration script (integrability + parity + letter checks hard-asserted at build time)"
 },
 "symbol_words": [
  [
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   [
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    1,
    6,
    9
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  ],
  [
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   ]
  ],
  [
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   [
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   ]
  ]
 ],
 "letter_exps": {
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   1,
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   0,
   0,
   0,
   0,
   0
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   0,
   0,
   0
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   0,
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   0,
   0,
   0,
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   2,
   0,
   0,
   0,
   0
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   0,
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   1
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   0,
   0,
   0,
   0,
   0
  ],
  "7": [
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   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  "8": [
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   1,
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  ],
  "9": [
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   1,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  "10": [
   0,
   0,
   1,
   -1,
   1,
   -1,
   0,
   0,
   0,
   0,
   0,
   0
  ],
  "11": [
   0,
   0,
   0,
   0,
   0,
   0,
   -2,
   0,
   0,
   2,
   0,
   0
  ],
  "12": [
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   1,
   1,
   1,
   -1,
   -1,
   0,
   0,
   0,
   0,
   0,
   0
  ]
 },
 "factor_names": [
  "w",
  "z",
  "1-w",
  "1+w",
  "1-z",
  "1+z",
  "w-z",
  "w+z",
  "1-w*z",
  "1+w*z",
  "1-w+z+w*z",
  "1+w-z+w*z"
 ],
 "fiber": {
  "description": "path: fixed w=W, y = W - z from y=0 (the base line w=z) to Y=W-Z; G(a1..a4;Y) standard (dG/dx = G(a2..;x)/(x-a1)); innermost a4 <-> first symbol entry",
  "gpl_letters": [
   "0",
   "W",
   "W - 1",
   "W + 1",
   "2*W",
   "(W**2 - 1)/W",
   "(W**2 + 1)/W",
   "(W**2 + 1)/(W + 1)",
   "(W**2 + 1)/(W - 1)"
  ]
 },
 "gwords": [
  [
   1,
   [
    1,
    1,
    2,
    2
   ]
  ],
  [
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   -1,
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   1,
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  [
   1,
   [
    3,
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   1,
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 ],
 "references": [
  {
   "uv": [
    "16/3",
    "10/3"
   ],
   "g10": "0.043932114436094196830356359044508790434",
   "abs_err": "2.34e-40",
   "source": "AMFlow goal 40 (dedicated reference run, held out of the construction)"
  },
  {
   "uv": [
    "10/3",
    "16/3"
   ],
   "g10": "0.0533210884409164222838928772256972885579",
   "abs_err": "8.88e-41",
   "source": "AMFlow goal 40 (dedicated reference run, held out of the construction)"
  },
  {
   "uv": [
    "23/4",
    "9/4"
   ],
   "g10": "0.055529723485597815858370168109826582502",
   "abs_err": "2.98e-40",
   "source": "AMFlow goal 40 (dedicated reference run, held out of the construction)"
  },
  {
   "uv": [
    "5/2",
    "4"
   ],
   "g10": "0.091292630176534924944595318465798723032",
   "abs_err": "6.56e-40",
   "source": "AMFlow goal 40 (dedicated reference run, held out of the construction)"
  },
  {
   "uv": [
    "10/3",
    "5/2"
   ],
   "J": "-0.059430533153932780098939885130423839071",
   "abs_err": "2.22e-40",
   "source": "AMFlow goal 40 (independent sample run)"
  },
  {
   "uv": [
    "11/2",
    "7/3"
   ],
   "J": "-0.065880024544258671140313010194595017093",
   "abs_err": "2.16e-40",
   "source": "AMFlow goal 40 (independent sample run)"
  },
  {
   "uv": [
    "4",
    "9/2"
   ],
   "J": "-0.063474824868670433544867800610169267374",
   "abs_err": "3.96e-40",
   "source": "AMFlow goal 40 (independent sample run)"
  },
  {
   "uv": [
    "4",
    "4"
   ],
   "g10": "0.0530386297835364296406023741052",
   "abs_err": "1e-30",
   "source": "published value, Caron-Huot & Henn 1404.2922",
   "note": "abs_err was 1e-31 until 2026-09-11: the 30-significant-digit published value differs from the served evaluator's transported value (dps 60: 0.05303862978353642964060237410606277414...) in its last two digits, by 8.63e-31, so the honest width of this reference is 1e-30; the gate (>= 30 digits at two or more of the eight points) never read abs_err, which enters only the printed 'ref limit' of this row"
  }
 ]
}