{
 "_provenance": "Gate oracles: independent reference values for the unequal-mass two-loop sunrise (d = 2 - 2 eps, master (1,1,1,0,0), eps^0 coefficient), computed independently with the auxiliary-mass-flow method (AMFlow, Liu & Ma, arXiv:2201.11669) in arbitrary-precision ball arithmetic. Used only for the gate comparison, never in the evaluation. The three rational coefficients [-1, -1/3, +8/3] of the closed form were PSLQ-identified and verified exact (139-160 digit closures); the runtime formula has ZERO free parameters. Two kinds of reference point. in_fit marks the 4 points that were the PSLQ fit points (t = -1/2, t = -1, t = -2, t = -5; an overdetermined fit, 4 points for three coefficients). held_out_in_pslq_fit marks the 2 points that were held out of the PSLQ identification (t = -3, t = -7; neither among the fit points): AMFlow values at goal 150 digits computed after the closed form and its coefficients were fixed; each carries the sha256 of its AMFlow input configuration and of its AMFlow output file, its ball radius and the digits that radius certifies (see each point's provenance). paper_literals carries the digits printed in the paper's sunrise-family section ('Reference values for an independent re-check'); paper_claims carries the digit count the paper's own sentence states there (its `text` is the paper's wording, quoted), which the evaluator measures as the worst agreement over the 2 held-out points (measured_over = held_out_points); the 4 fit points are gated separately and reported as in-sample agreement.",
 "row": 9,
 "family": "sun112",
 "masses_sq": [
  1,
  1,
  2
 ],
 "gate_points": [
  {
   "t_num": -1,
   "t_den": 2,
   "oracle_mid": "-1.7981575707676599266815028881046788623741365485767451379072015773907278208908840199663223686163983346110296798500704963803509494218922953639799086123674632873433075657915888113854559815103434763528915633009223662124456075849549881320333846596907255627301880093082108197225940784944155447098",
   "oracle_digits": 289,
   "held_out_in_pslq_fit": false,
   "in_fit": true,
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), 289 digits"
  },
  {
   "t_num": -1,
   "t_den": 1,
   "oracle_mid": "-1.7661200788746117700988174424591915867221279861065432505340284490003149148764872299074201030552485993757381383259024880926916455502484862281713525154726663610586972588399815987549069308836866719716491682835166709378857742331575937292018287586262375466180178731645750923973284686261556714128",
   "oracle_digits": 290,
   "held_out_in_pslq_fit": false,
   "in_fit": true,
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), 290 digits"
  },
  {
   "t_num": -2,
   "t_den": 1,
   "oracle_mid": "-1.706678728845436215329563616943060744682801099453692340831078663231230047014818284210003515147697640315687662800650309428349544543059021217061110762172334757709",
   "oracle_digits": 159,
   "held_out_in_pslq_fit": false,
   "in_fit": true,
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), 159 digits"
  },
  {
   "t_num": -5,
   "t_den": 1,
   "oracle_mid": "-1.557651229351457426731311771769945612570969979453271307605753135011402526934883701535677811395316606791917408825760958701342134148042496231560808600112889638867",
   "oracle_digits": 160,
   "held_out_in_pslq_fit": false,
   "in_fit": true,
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), 160 digits"
  },
  {
   "t_num": -3,
   "t_den": 1,
   "oracle_mid": "-1.652616990806520655424150564273537185703684173526137329102260143099054996791746772496125926799937245471844568556423887631986717505841700803305334483291743588629",
   "oracle_digits": 160,
   "held_out_in_pslq_fit": true,
   "in_fit": false,
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), 160 digits; held out of the PSLQ fit",
   "amflow_goal_digits": 150,
   "amflow_eps_order": 11,
   "amflow_ball_radius": "3.29e-161",
   "amflow_ball_digits": 160,
   "amflow_config_sha256": "b4789d3265a445235411dd9e4ef333863a2cd92409b602311f6105a37fb0f9db",
   "amflow_output_sha256": "ede754ac46ced0c5ba3cfb4c66e6a21c4208e4ad669b47829fb50bd5b8da8c66",
   "provenance": "Held out of the PSLQ fit: computed with AMFlow at t = -3 (numeric s = -3, squared masses 1, 1, 2; d = 2 - 2 eps; requested goal 150 digits; eps order 11) after the closed form and its three rational coefficients were fixed, so this value never entered the identification. The AMFlow input configuration has sha256 b4789d3265a445235411dd9e4ef333863a2cd92409b602311f6105a37fb0f9db; the AMFlow output file has sha256 ede754ac46ced0c5ba3cfb4c66e6a21c4208e4ad669b47829fb50bd5b8da8c66. The printed ball radius 3.29e-161 puts 160 digits in the ball; the gate's agreement is capped at min(160, working precision)."
  },
  {
   "t_num": -7,
   "t_den": 1,
   "oracle_mid": "-1.476584679023782856973196584499586861445370283901096372210993861197645897765459122205628365358469878608047289993329224824116336642935997053018168192378564388493",
   "oracle_digits": 159,
   "held_out_in_pslq_fit": true,
   "in_fit": false,
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), 159 digits; held out of the PSLQ fit",
   "amflow_goal_digits": 150,
   "amflow_eps_order": 11,
   "amflow_ball_radius": "3.05e-160",
   "amflow_ball_digits": 159,
   "amflow_config_sha256": "982caed31694b39f5d431f8702b62874aa9fe534642e636e24cee9db821131d9",
   "amflow_output_sha256": "184358df6c6a414af928bea0463c979286bb6e66f9af46831bc6fe2be9532365",
   "provenance": "Held out of the PSLQ fit: computed with AMFlow at t = -7 (numeric s = -7, squared masses 1, 1, 2; d = 2 - 2 eps; requested goal 150 digits; eps order 11) after the closed form and its three rational coefficients were fixed, so this value never entered the identification. The AMFlow input configuration has sha256 982caed31694b39f5d431f8702b62874aa9fe534642e636e24cee9db821131d9; the AMFlow output file has sha256 184358df6c6a414af928bea0463c979286bb6e66f9af46831bc6fe2be9532365. The printed ball radius 3.05e-160 puts 159 digits in the ball; the gate's agreement is capped at min(159, working precision)."
  }
 ],
 "physical_gate_points": [
  {
   "t": "16",
   "physical_region": true,
   "in_fit": false,
   "held_out_in_pslq_fit": false,
   "J111_eps0": {
    "re": "-1.6872310858621605878750003373139396924172856633489436596812705951805336240582352748224228785599007869116057398",
    "re_radius": "1.73e-110",
    "im": "-3.5269450303272708825604643255424837307046521692443127913413369130931398390333015797566401123473673280877197335",
    "im_radius": "2.40e-110"
   },
   "twin_J111_eps0": {
    "re": "-1.6872310858621605878750003373139396924172856633489436596812705951805336128506063149237258580428450151977708735",
    "re_radius": "1.02e-110",
    "im": "-3.5269450303272708825604643255424837307046521692443127913413369130931398390333015814452469919504182260896498664",
    "im_radius": "4.91e-110"
   },
   "goal_digits": 60,
   "twin_goal_digits": 40,
   "eps_order": 11,
   "n_thread": 4,
   "config_sha256": "ee02ff95ca23aff55a2a8facbcc78e4a6579eb7f7558eb5028e69daeaa57c19d",
   "out_sha256": "4feb1a061c03bdb26785a1596841b4f01e2325577b34a5f1e38d0d9081a7c00d",
   "twin_config_sha256": "7f4e07673aa3e51d29850336ec009485ae00a3b0b641aeea0ba5622bd6b3acc5",
   "twin_out_sha256": "df3567028721d605eea98990d3156bb9d8e59ddbf1b1b56424e00aefca8c38ea",
   "wall": {
    "elapsed": "3:26.95",
    "maxrss_kb": 245580
   },
   "twin_wall": {
    "elapsed": "1:01.25",
    "maxrss_kb": 167412
   },
   "i0_prescription": "the point entered as the exact rational s on the real axis; the port's per-system prescription analysis pins the eta contour (NegIm = Feynman +i0); no imaginary offset",
   "run_direction_knob": "NegRe",
   "prediction_filed_before_the_run_sha256": "1e7b5435396af38ff2e24909957cda0e1a315159409dcf125c4987eb923263fc",
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), goal 60 digits, physical region t > 0 (above the threshold); computed 2026-09-06 after the closed form and its coefficients were fixed and after this evaluator's continued value at t = 16 had been filed (that filing has sha256 1e7b5435396af38f...), so the comparison was a prediction; goal-40 twin beside it"
  },
  {
   "t": "20",
   "physical_region": true,
   "in_fit": false,
   "held_out_in_pslq_fit": false,
   "J111_eps0": {
    "re": "-0.85473684406424220596414675644381611787593550975915062959192893451456046419841878813906167414532352446728147468",
    "re_radius": "3.52e-111",
    "im": "-2.9747556315410546063287129166071898161743243553607014112103980604204778924396119530945436646571646068770979707",
    "im_radius": "3.85e-110"
   },
   "twin_J111_eps0": {
    "re": "-0.85473684406424220596414675644381611787593550975915062959192893451456045299078642306671508039190597380868194196",
    "re_radius": "3.27e-111",
    "im": "-2.9747556315410546063287129166071898161743243553607014112103980604204778924396119542985206217433366916236878506",
    "im_radius": "3.38e-110"
   },
   "goal_digits": 60,
   "twin_goal_digits": 40,
   "eps_order": 11,
   "n_thread": 4,
   "config_sha256": "4580e329414b74e58bf1806d7af042c9cf9f68ceb33446bb44f6bc2b4e25e0b2",
   "out_sha256": "6866bae64e906b5202b4695d24ba0d48de96e59d0a14537b92df2a84be7730db",
   "twin_config_sha256": "1f4364ee005653f501d557867afa9181ae01fcf659d023e96dd53fdd71171c32",
   "twin_out_sha256": "e138083171878083ab6ac9c55914dc8e22b2def4a9098f5b52e860798ee18fc5",
   "wall": {
    "elapsed": "3:28.40",
    "maxrss_kb": 228044
   },
   "twin_wall": {
    "elapsed": "0:56.39",
    "maxrss_kb": 173852
   },
   "i0_prescription": "the point entered as the exact rational s on the real axis; the port's per-system prescription analysis pins the eta contour (NegIm = Feynman +i0); no imaginary offset",
   "run_direction_knob": "NegRe",
   "prediction_filed_before_the_run_sha256": "3a0e915cf607564290c2f7083a876e42d15c7ed768031aef299a1773d0671600",
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), goal 60 digits, physical region t > 0 (above the threshold); computed 2026-09-06 after the closed form and its coefficients were fixed and after this evaluator's continued value at t = 20 had been filed (that filing has sha256 3a0e915cf6075642...), so the comparison was a prediction; goal-40 twin beside it"
  },
  {
   "t": "12",
   "physical_region": true,
   "in_fit": false,
   "held_out_in_pslq_fit": false,
   "J111_eps0": {
    "re": "-5.560516781595728587212915028525906510270468224469309491441666772572633305641434363311892299251301577109266018516696091407997343566069619271619565242135199122757",
    "re_radius": "3.24e-160",
    "im": "-4.392978811439266665253392303304718649707329552937354222566238443194134788759744186000310628506230918391649605508772524013786908173516845292819321043635263642485",
    "im_radius": "2.72e-160"
   },
   "twin_J111_eps0": {
    "re": "-5.560516781595728587212915028525906510270468224469309491441666772572633305641434363311892299251301577109266018516696091407997343566",
    "re_radius": "6.97e-131",
    "im": "-4.392978811439266665253392303304718649707329552937354222566238443194134788759744186000310628506230918391649605508772524013786908174",
    "im_radius": "4.84e-130"
   },
   "goal_digits": 150,
   "twin_goal_digits": 120,
   "eps_order": 11,
   "n_thread": 16,
   "config_sha256": "29298cc64edb66fa256f180f1f6cb8630519afb3b55de727f1e39bd6f5d472b1",
   "out_sha256": "6a5466c9b046b6c2825160516bcccaa77b1d3922558e9c7a3a42fb00dcaf14bd",
   "twin_config_sha256": "26c760ea1502783bddd694f67764db68b7635b8e704722bc3c0e06ac6395d2d3",
   "twin_out_sha256": "ee36361c4529b10a64381b9ba954ca22889cbd5012090d2e4af1cb594f8c8e53",
   "wall": {
    "elapsed": "1:45:48",
    "maxrss_kb": 586164
   },
   "twin_wall": {
    "elapsed": "1:11:06",
    "maxrss_kb": 441464
   },
   "i0_prescription": "the point entered as the exact rational s on the real axis; the port's per-system prescription analysis pins the eta contour (NegIm = Feynman +i0); no imaginary offset",
   "run_direction_knob": "NegRe",
   "source": "AMFlow independent reference (d=2-2eps, master (1,1,1,0,0), eps^0 coeff, arb ball), goal 150 digits, physical region t > 0 (above the threshold); computed 2026-06 as part of a physical-region reference scan of this family, never among the fit points; goal-120 twin beside it"
  }
 ],
 "physical_provenance": {
  "_provenance": "Physical-region reference values (t > 0) for the --point t > 0 arm: the (1,1,1,0,0) eps^0 master J^(0)(t + i0) computed with the auxiliary-mass-flow method at three points above the normal threshold t = (m1+m2+m3)^2 = 6 + 4 sqrt2, each as a ball midpoint with its radius, with a lower-goal twin run beside it (the two-precision pair of the reference). The point is entered as the exact rational s = t on the real axis; the engine's per-system prescription analysis pins its auxiliary-mass contour to the Feynman +i0 propagators (no imaginary offset is entered), so the values are J^(0)(t + i0); with J[1,1,1] = -S_111 the imaginary part is negative above the threshold. t = 16 and t = 20 (goal 60 digits, eps order 11, 4 threads, goal-40 twins) were computed on 2026-09-06 after this evaluator's continued values at both points had been filed, so each comparison was a prediction; t = 12 (goal 150, eps order 11, 16 threads, goal-120 twin) is the reference of 2026-06. Each entry carries the sha256 of its AMFlow input configuration and output file and of its twin's, the ball radii, the wall (h:mm:ss or m:ss.ss, on a shared host under load: a contended wall, not a price) and the max RSS. Used only for the --point t > 0 gate (the members, the floor and the bar are printed by the evaluator), never in the evaluation; the default run does not evaluate these points.",
  "threshold": "(m1+m2+m3)^2 = (2+sqrt2)^2 = 6+4sqrt2",
  "convention": "J[1,1,1] = -S_111, d = 2 - 2 eps, AMFlow normalization; Im J < 0 above threshold",
  "gate_receipts_sha256": {
   "t16": {
    "sha256": "5e5f9b7ee65ed217f93bb836dc6a0de7ec75d881fc48bc2b70049fb2982e1f46",
    "v2_sha256": "6ee1b8ffc3d6320eba14af3da1ecb7a1d2bec7011ffad746566abdccbca3da3e"
   },
   "t20": {
    "sha256": "7b3fc73862a8152f277a5c5b5a7a0d99a4cfc949228006efa455300f1b75d21c",
    "v2_sha256": "ef7ff43d8ce2244030b9d120aac34c66d62c27089357179211212504d28f6685"
   }
  },
  "reference_block_sha256": "9b775148ef647b32b22794dd64234eacef0986e35fc6663f26a43aabec34b6d8",
  "receipt_of_record_sha256": "594277b0a46ec5d7990a0986043085d8f9abf4fe984dc60b5506e8a18f308920"
 },
 "paper_literals": [
  {
   "t_num": -1,
   "t_den": 1,
   "E0": "-2.3471191",
   "where": "paper, sunrise-family section, 'Reference values for an independent re-check', (1,1,2) eps^0 item, t = -1 (8 printed digits, trailing digits truncated)"
  },
  {
   "t_num": -5,
   "t_den": 1,
   "E0": "-3.2711938",
   "where": "paper, sunrise-family section, 'Reference values for an independent re-check', (1,1,2) eps^0 item, t = -5 (8 printed digits, trailing digits truncated)"
  }
 ],
 "paper_claims": [
  {
   "held_out_digits": 159,
   "text": "held out to 159 digits at two fresh points, t=-3 and t=-7, neither among the four fit points t=-1/2,-1,-2,-5",
   "where": "paper, sunrise-family section, 'Reference values for an independent re-check', (1,1,2) eps^0 item",
   "measured_over": "held_out_points"
  }
 ]
}