{
 "what": "M87*: the lensing maps of Phase 1 (COMPUTED, double precision, stored as half floats) graded against Phase 0's decided Kerr curve and against Gralla & Lupsasca's closed form",
 "standing": "COMPUTED: the maps draw dashed; only the Phase 0 curve draws solid. AGREES means the computed layer reached the premise ladder's \"verified\" rung against the decided one, at the stated resolution; it is never CERTIFIED",
 "verdict": "AGREES",
 "preregistration": {
  "path": "notes/black-hole-phase0-preregistration-2026-10-31.md",
  "sha256": "01e09d68931177396a929aa3a3d776258630d375b2c6333948f119601e98488b",
  "section": "Phase 1",
  "committedBeforeAnyRay": "455fa5fb"
 },
 "code": {
  "instruments/kerr/rays.js": "1aa399df725d7fa309540f1d6e3fe0414ee74c081fcfd845bea39c7a7c3f40fa",
  "instruments/kerr/kerr.js": "f25ee51474069f12db6dbce4a1fc516acdc87c4231e9c1a55f37b6d3d9873de6",
  "tools/run-bh-maps.js": "37a74ab313fb626b956fa46fbd6fd3616994f1930b90583a261584988f9ca533",
  "instruments/interval/interval.js": "9891280d08e59f7f3cf1549257d86af988f93971a4c307abc309cb0550a315cd",
  "instruments/interval/transcendental.js": "7d62c491ab6e79a7873f78111f666eb71924b26cc406a8758b91ebd77ad69b79",
  "instruments/interval/algebraic.js": "bf6bbbccc41237c3519e173cf5a9439c3da59f8487b74c090f56a3c3fa57cfb0",
  "instruments/interval/rational.js": "59e97fc40328adc7866f148d8ee61156810dbbcd890b4361dca697aa58d71920"
 },
 "phase0": {
  "record": "certs/bh-shadow.json",
  "sha256": "8019e1ed10dbda04923a6f699f360be0c6704abaf538ddab2ed5026fb49fc92b"
 },
 "maps": {
  "manifest": "corpus/bh-maps/manifest.json",
  "manifestSha256": "bd7f6cf3367f9f80b981a9de279219936d8649d900637c548644017a27d27040",
  "files": 24,
  "totalBytes": 7273435,
  "grid": {
   "n": 512,
   "alpha": [
    -20,
    20
   ],
   "beta": [
    -20,
    20
   ],
   "pitchM": "5/64",
   "pixelCentre": "α_i = −20 + (i + ½)·5/64, β_j = 20 − (j + ½)·5/64 (row 0 the top)",
   "axes": "Bardeen's image plane in units of M, observer at infinity: α to the right, β up along the projected spin axis; λ = −α sin θo, η = (α² − a²) cos²θo + β²"
  },
  "spins": [
   "0",
   "1/2",
   "47/50",
   "499/500"
  ],
  "defaultSpin": "47/50",
  "camera": {
   "inclinationDeg": 17,
   "cos": 0.9563047559630355,
   "sin": 0.2923717047227367,
   "note": "the operator's ruling: fixed at 17° (the jet's 17.2° ± 3.3°, Mertens et al. 2016); the EHT's 163° is the mirror image"
  },
  "views": [
   {
    "key": "47/50 @ 45",
    "spin": "47/50",
    "inclinationDeg": "45",
    "cos": 0.7071067811865476,
    "sin": 0.7071067811865475,
    "files": "a47_50-i45-*",
    "note": "Phase 2 (pre-registered 2026-10-31): leaving M87*'s 17° view, a picture of the model, not of M87*; the default spin only; cos and sin fixed doubles inside kerr.js's enclosures"
   },
   {
    "key": "47/50 @ 80",
    "spin": "47/50",
    "inclinationDeg": "80",
    "cos": 0.17364817766693041,
    "sin": 0.984807753012208,
    "files": "a47_50-i80-*",
    "note": "Phase 2 (pre-registered 2026-10-31): leaving M87*'s 17° view, a picture of the model, not of M87*; the default spin only; cos and sin fixed doubles inside kerr.js's enclosures"
   }
  ],
  "disk": {
   "standing": "ASSUMED (the operator's simple thin-disk model)",
   "velocity": "prograde Keplerian circular orbits, Ω = 1/(r^{3/2} + a); g = 1/[u^t (1 − Ω λ)], u^t = (r^{3/2} + a)/(r^{3/4} √(r^{3/2} − 3 r^{1/2} + 2a))",
   "innerEdge": "cut at the ISCO: g only where r_s ≥ the upper end of Phase 0's ISCO enclosure; inside it r_s and φ_s are kept, g is NaN (no plunging matter)",
   "riscoUsed": {
    "0": 6.000001,
    "1/2": 4.233003,
    "47/50": 2.023594,
    "499/500": 1.236971
   },
   "emissionForPhase2": "declared, not used by the maps: optically thin, every image adds; J(r) ∝ r⁻² on [r_isco, 20 M]; I_obs = Σ_n g_n³ J(r_n)"
  }
 },
 "words": {
  "AGREES": "the check holds at its stated resolution",
  "DISAGREES": "it fails: the map (or the control) is not the decided geometry"
 },
 "checks": {
  "pins": {
   "files": 24,
   "verdict": "AGREES",
   "rule": "every stored file and its decompressed bytes match the manifest's sha256"
  },
  "schwarzschild": {
   "sqrt27": "[5.196152422706631, 5.196152422706633] (Phase 0)",
   "maxTracedEdgeMinusSqrt27M": "8.88e-16",
   "threshold": "1e-8 M",
   "verdict": "AGREES"
  },
  "perSpin": {
   "0": {
    "spin": "0",
    "coverage": {
     "n0": {
      "pixels": 257988,
      "beyond200M": 0,
      "withG": 237946
     },
     "n1": {
      "pixels": 6982,
      "beyond200M": 266,
      "withG": 4158
     },
     "n2": {
      "pixels": 260,
      "beyond200M": 8,
      "withG": 104
     }
    },
    "retrace": {
     "sampled": 2703,
     "bitIdentical": 2703,
     "differ": 0,
     "verdict": "AGREES"
    },
    "closedForm": {
     "crossings": 2732,
     "maxMinoTimeVsAngular": "1.51e-14",
     "maxRadiusErrorM": "3.07e-10",
     "worstAt": {
      "alpha": 5.1953125,
      "beta": 2.9296875,
      "n": 1,
      "r": 166.449275
     },
     "threshold": "1e-6 M",
     "verdict": "AGREES"
    },
    "curve": {
     "decidedPoints": 4534,
     "maxBoxHalfWidthM": "3.50e-9",
     "smallestEndBeta": "6.21e-5"
    },
    "pointwise": {
     "epsilon": 0.000001,
     "points": 756,
     "rule": "the ray at (1 − ε)·P captured and at (1 + ε)·P escaped, P proven on the decided curve",
     "fail": 0,
     "firstFailures": [],
     "verdict": "AGREES"
    },
    "bisected": {
     "points": 24,
     "resolution": "2e-3 / 2^44 relative",
     "maxDistanceToDecidedM": "2.31e-15"
    },
    "texture": {
     "capturedPixels": 13900,
     "insideDecidedCurve": 13900,
     "mismatched": 0,
     "unjudgedWithin1e4M": 0,
     "extents": {
      "W": {
       "fromMap": 10.390625,
       "trueExtentIn": "[10.3902, 10.5469]",
       "phase0": "[10.392304, 10.392306]",
       "meets": true
      },
      "H": {
       "fromMap": 10.390625,
       "trueExtentIn": "[10.3902, 10.5469]",
       "phase0": "[10.392304, 10.392305]",
       "meets": true
      },
      "d": {
       "fromMap": 10.390625,
       "trueExtentIn": "[10.3902, 10.5469]",
       "phase0": "[10.392304, 10.392305]",
       "meets": true
      }
     },
     "verdict": "AGREES"
    },
    "convergence": {
     "spokes": [
      {
       "at": {
        "alpha": -5.1962,
        "beta": 0.0001,
        "rOrbit": 3
       },
       "distanceM": [
        "9.714e-1",
        "3.179e-2",
        "1.353e-3",
        "5.842e-5"
       ],
       "ratios": [
        0.0327,
        0.0426,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": -3.8441,
        "beta": 3.4961,
        "rOrbit": 3
       },
       "distanceM": [
        "7.513e-1",
        "2.588e-2",
        "1.104e-3",
        "4.769e-5"
       ],
       "ratios": [
        0.0344,
        0.0427,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": -0.0075,
        "beta": 5.1961,
        "rOrbit": 3
       },
       "distanceM": [
        "6.697e-1",
        "2.354e-2",
        "1.005e-3",
        "4.342e-5"
       ],
       "ratios": [
        0.0351,
        0.0427,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": 3.8366,
        "beta": 3.5044,
        "rOrbit": 3
       },
       "distanceM": [
        "7.509e-1",
        "2.587e-2",
        "1.104e-3",
        "4.767e-5"
       ],
       "ratios": [
        0.0344,
        0.0427,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": 5.1962,
        "beta": 0.0003,
        "rOrbit": 3
       },
       "distanceM": [
        "9.714e-1",
        "3.179e-2",
        "1.353e-3",
        "5.842e-5"
       ],
       "ratios": [
        0.0327,
        0.0426,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": 3.8554,
        "beta": -3.4837,
        "rOrbit": 3
       },
       "distanceM": [
        "1.273e+0",
        "3.903e-2",
        "1.657e-3",
        "7.151e-5"
       ],
       "ratios": [
        0.0307,
        0.0424,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": 0.0301,
        "beta": -5.1961,
        "rOrbit": 3
       },
       "distanceM": [
        "1.454e+0",
        "4.298e-2",
        "1.821e-3",
        "7.860e-5"
       ],
       "ratios": [
        0.0296,
        0.0424,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      },
      {
       "at": {
        "alpha": -3.8253,
        "beta": -3.5167,
        "rOrbit": 3
       },
       "distanceM": [
        "1.276e+0",
        "3.911e-2",
        "1.660e-3",
        "7.164e-5"
       ],
       "ratios": [
        0.0306,
        0.0424,
        0.0432
       ],
       "expMinusGamma": 0.0432,
       "decreasingAndBelowPixel": true,
       "withinFivePercentOfExpMinusPi": true
      }
     ],
     "rule": "the outer edge of the n-th lensing band (crossings drop below n + 1) along a spoke through a decided point, n = 1…4: strictly decreasing, the last below one pixel; at a = 0 successive ratios within 5% of e^(−π) for n ≥ 2",
     "verdict": "AGREES"
    }
   },
   "1/2": {
    "spin": "1/2",
    "coverage": {
     "n0": {
      "pixels": 258228,
      "beyond200M": 0,
      "withG": 248610
     },
     "n1": {
      "pixels": 7254,
      "beyond200M": 261,
      "withG": 5033
     },
     "n2": {
      "pixels": 263,
      "beyond200M": 2,
      "withG": 157
     }
    },
    "retrace": {
     "sampled": 2703,
     "bitIdentical": 2703,
     "differ": 0,
     "verdict": "AGREES"
    },
    "closedForm": {
     "crossings": 2739,
     "maxMinoTimeVsAngular": "1.83e-12",
     "maxRadiusErrorM": "3.49e-10",
     "worstAt": {
      "alpha": 4.3359375,
      "beta": -4.9609375,
      "n": 1,
      "r": 139.363306
     },
     "threshold": "1e-6 M",
     "verdict": "AGREES"
    },
    "curve": {
     "decidedPoints": 4526,
     "maxBoxHalfWidthM": "1.04e-8",
     "smallestEndBeta": "1.99e-5"
    },
    "pointwise": {
     "epsilon": 0.000001,
     "points": 755,
     "rule": "the ray at (1 − ε)·P captured and at (1 + ε)·P escaped, P proven on the decided curve",
     "fail": 0,
     "firstFailures": [],
     "verdict": "AGREES"
    },
    "bisected": {
     "points": 24,
     "resolution": "2e-3 / 2^44 relative",
     "maxDistanceToDecidedM": "2.25e-15"
    },
    "texture": {
     "capturedPixels": 13510,
     "insideDecidedCurve": 13510,
     "mismatched": 0,
     "unjudgedWithin1e4M": 0,
     "extents": {
      "W": {
       "fromMap": 10.15625,
       "trueExtentIn": "[10.1558, 10.3125]",
       "phase0": "[10.239951, 10.239962]",
       "meets": true
      },
      "H": {
       "fromMap": 10.234375,
       "trueExtentIn": "[10.2340, 10.3906]",
       "phase0": "[10.254574, 10.254579]",
       "meets": true
      },
      "d": {
       "fromMap": 10.195313,
       "trueExtentIn": "[10.1949, 10.3516]",
       "phase0": "[10.247263, 10.247270]",
       "meets": true
      }
     },
     "verdict": "AGREES"
    },
    "convergence": {
     "spokes": [
      {
       "at": {
        "alpha": -4.8188,
        "beta": 0,
        "rOrbit": 2.7097
       },
       "distanceM": [
        "1.014e+0",
        "3.705e-2",
        "1.780e-3",
        "8.690e-5"
       ],
       "ratios": [
        0.0365,
        0.048,
        0.0488
       ],
       "expMinusGamma": 0.0489,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": -3.5422,
        "beta": 3.3878,
        "rOrbit": 2.7567
       },
       "distanceM": [
        "7.844e-1",
        "3.027e-2",
        "1.460e-3",
        "7.136e-5"
       ],
       "ratios": [
        0.0386,
        0.0482,
        0.0489
       ],
       "expMinusGamma": 0.0489,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 0.2898,
        "beta": 5.1273,
        "rOrbit": 2.8933
       },
       "distanceM": [
        "7.038e-1",
        "2.751e-2",
        "1.320e-3",
        "6.412e-5"
       ],
       "ratios": [
        0.0391,
        0.048,
        0.0486
       ],
       "expMinusGamma": 0.0486,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 4.0695,
        "beta": 3.4708,
        "rOrbit": 3.0216
       },
       "distanceM": [
        "7.888e-1",
        "2.974e-2",
        "1.404e-3",
        "6.717e-5"
       ],
       "ratios": [
        0.0377,
        0.0472,
        0.0478
       ],
       "expMinusGamma": 0.0479,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 5.4212,
        "beta": 0.0002,
        "rOrbit": 3.066
       },
       "distanceM": [
        "1.004e+0",
        "3.574e-2",
        "1.672e-3",
        "7.943e-5"
       ],
       "ratios": [
        0.0356,
        0.0468,
        0.0475
       ],
       "expMinusGamma": 0.0476,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 4.088,
        "beta": -3.4506,
        "rOrbit": 3.0222
       },
       "distanceM": [
        "1.298e+0",
        "4.363e-2",
        "2.047e-3",
        "9.791e-5"
       ],
       "ratios": [
        0.0336,
        0.0469,
        0.0478
       ],
       "expMinusGamma": 0.0479,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 0.3249,
        "beta": -5.1272,
        "rOrbit": 2.8945
       },
       "distanceM": [
        "1.498e+0",
        "4.905e-2",
        "2.332e-3",
        "1.132e-4"
       ],
       "ratios": [
        0.0328,
        0.0475,
        0.0486
       ],
       "expMinusGamma": 0.0486,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": -3.5255,
        "beta": -3.4067,
        "rOrbit": 2.7573
       },
       "distanceM": [
        "1.333e+0",
        "4.546e-2",
        "2.179e-3",
        "1.065e-4"
       ],
       "ratios": [
        0.0341,
        0.0479,
        0.0489
       ],
       "expMinusGamma": 0.0489,
       "decreasingAndBelowPixel": true
      }
     ],
     "rule": "the outer edge of the n-th lensing band (crossings drop below n + 1) along a spoke through a decided point, n = 1…4: strictly decreasing, the last below one pixel; at a = 0 successive ratios within 5% of e^(−π) for n ≥ 2",
     "verdict": "AGREES"
    }
   },
   "47/50": {
    "spin": "47/50",
    "coverage": {
     "n0": {
      "pixels": 259308,
      "beyond200M": 0,
      "withG": 257451
     },
     "n1": {
      "pixels": 8556,
      "beyond200M": 274,
      "withG": 7159
     },
     "n2": {
      "pixels": 475,
      "beyond200M": 7,
      "withG": 340
     }
    },
    "retrace": {
     "sampled": 2703,
     "bitIdentical": 2703,
     "differ": 0,
     "verdict": "AGREES"
    },
    "closedForm": {
     "crossings": 2760,
     "maxMinoTimeVsAngular": "3.97e-13",
     "maxRadiusErrorM": "1.74e-10",
     "worstAt": {
      "alpha": 4.0234375,
      "beta": 4.5703125,
      "n": 1,
      "r": 90.585377
     },
     "threshold": "1e-6 M",
     "verdict": "AGREES"
    },
    "curve": {
     "decidedPoints": 4840,
     "maxBoxHalfWidthM": "3.25e-9",
     "smallestEndBeta": "7.38e-5"
    },
    "pointwise": {
     "epsilon": 0.000001,
     "points": 807,
     "rule": "the ray at (1 − ε)·P captured and at (1 + ε)·P escaped, P proven on the decided curve",
     "fail": 0,
     "firstFailures": [],
     "verdict": "AGREES"
    },
    "bisected": {
     "points": 24,
     "resolution": "2e-3 / 2^44 relative",
     "maxDistanceToDecidedM": "2.19e-15"
    },
    "texture": {
     "capturedPixels": 12312,
     "insideDecidedCurve": 12312,
     "mismatched": 0,
     "unjudgedWithin1e4M": 0,
     "extents": {
      "W": {
       "fromMap": 9.609375,
       "trueExtentIn": "[9.6090, 9.7656]",
       "phase0": "[9.732062, 9.732134]",
       "meets": true
      },
      "H": {
       "fromMap": 9.765625,
       "trueExtentIn": "[9.7652, 9.9219]",
       "phase0": "[9.833778, 9.833817]",
       "meets": true
      },
      "d": {
       "fromMap": 9.6875,
       "trueExtentIn": "[9.6871, 9.8438]",
       "phase0": "[9.782920, 9.782976]",
       "meets": true
      }
     },
     "verdict": "AGREES"
    },
    "convergence": {
     "spokes": [
      {
       "at": {
        "alpha": -4.2259,
        "beta": 0.0001,
        "rOrbit": 2.0818
       },
       "distanceM": [
        "1.219e+0",
        "7.682e-2",
        "6.945e-3",
        "6.503e-4"
       ],
       "ratios": [
        0.063,
        0.0904,
        0.0936
       ],
       "expMinusGamma": 0.0941,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": -2.5819,
        "beta": 3.693,
        "rOrbit": 2.2615
       },
       "distanceM": [
        "9.093e-1",
        "5.734e-2",
        "4.810e-3",
        "4.149e-4"
       ],
       "ratios": [
        0.0631,
        0.0839,
        0.0863
       ],
       "expMinusGamma": 0.0865,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 0.369,
        "beta": 4.91,
        "rOrbit": 2.5392
       },
       "distanceM": [
        "8.238e-1",
        "4.692e-2",
        "3.458e-3",
        "2.608e-4"
       ],
       "ratios": [
        0.057,
        0.0737,
        0.0754
       ],
       "expMinusGamma": 0.0756,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 3.8441,
        "beta": 3.6952,
        "rOrbit": 2.8169
       },
       "distanceM": [
        "8.694e-1",
        "4.346e-2",
        "2.821e-3",
        "1.870e-4"
       ],
       "ratios": [
        0.05,
        0.0649,
        0.0663
       ],
       "expMinusGamma": 0.0664,
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      },
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       "distanceM": [
        "1.092e+0",
        "4.926e-2",
        "3.026e-3",
        "1.902e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.063,
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      },
      {
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        "rOrbit": 2.8164
       },
       "distanceM": [
        "1.435e+0",
        "6.280e-2",
        "4.042e-3",
        "2.677e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.0664,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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        "rOrbit": 2.5387
       },
       "distanceM": [
        "1.650e+0",
        "7.721e-2",
        "5.612e-3",
        "4.227e-4"
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       "ratios": [
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       "expMinusGamma": 0.0756,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "1.592e+0",
        "8.497e-2",
        "7.038e-3",
        "6.063e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.0866,
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      }
     ],
     "rule": "the outer edge of the n-th lensing band (crossings drop below n + 1) along a spoke through a decided point, n = 1…4: strictly decreasing, the last below one pixel; at a = 0 successive ratios within 5% of e^(−π) for n ≥ 2",
     "verdict": "AGREES"
    }
   },
   "499/500": {
    "spin": "499/500",
    "coverage": {
     "n0": {
      "pixels": 259863,
      "beyond200M": 0,
      "withG": 259490
     },
     "n1": {
      "pixels": 9420,
      "beyond200M": 270,
      "withG": 8678
     },
     "n2": {
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      "beyond200M": 6,
      "withG": 559
     }
    },
    "retrace": {
     "sampled": 2703,
     "bitIdentical": 2703,
     "differ": 0,
     "verdict": "AGREES"
    },
    "closedForm": {
     "crossings": 2778,
     "maxMinoTimeVsAngular": "7.50e-13",
     "maxRadiusErrorM": "1.68e-10",
     "worstAt": {
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      "beta": 4.5703125,
      "n": 1,
      "r": 84.689502
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     "threshold": "1e-6 M",
     "verdict": "AGREES"
    },
    "curve": {
     "decidedPoints": 4370,
     "maxBoxHalfWidthM": "4.52e-9",
     "smallestEndBeta": "4.49e-5"
    },
    "pointwise": {
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     "points": 729,
     "rule": "the ray at (1 − ε)·P captured and at (1 + ε)·P escaped, P proven on the decided curve",
     "fail": 0,
     "firstFailures": [],
     "verdict": "AGREES"
    },
    "bisected": {
     "points": 24,
     "resolution": "2e-3 / 2^44 relative",
     "maxDistanceToDecidedM": "2.44e-15"
    },
    "texture": {
     "capturedPixels": 12038,
     "insideDecidedCurve": 12036,
     "mismatched": 0,
     "unjudgedWithin1e4M": 2,
     "extents": {
      "W": {
       "fromMap": 9.453125,
       "trueExtentIn": "[9.4527, 9.6094]",
       "phase0": "[9.599985, 9.600050]",
       "meets": true
      },
      "H": {
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       "phase0": "[9.742479, 9.742522]",
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       "meets": true
      }
     },
     "verdict": "AGREES"
    },
    "convergence": {
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        "rOrbit": 1.9049
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       "distanceM": [
        "1.293e+0",
        "1.002e-1",
        "1.195e-2",
        "1.513e-3"
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        0.1266
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       "decreasingAndBelowPixel": true
      },
      {
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       },
       "distanceM": [
        "9.821e-1",
        "7.347e-2",
        "7.687e-3",
        "8.386e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.1099,
       "decreasingAndBelowPixel": true
      },
      {
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        "3.330e-4"
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       "ratios": [
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       "expMinusGamma": 0.0819,
       "decreasingAndBelowPixel": true
      },
      {
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        "rOrbit": 2.7924
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       "distanceM": [
        "9.024e-1",
        "4.723e-2",
        "3.254e-3",
        "2.295e-4"
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      },
      {
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       },
       "distanceM": [
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        "5.254e-2",
        "3.420e-3",
        "2.283e-4"
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       "ratios": [
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       "expMinusGamma": 0.0669,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "1.423e+0",
        "6.575e-2",
        "4.490e-3",
        "3.163e-4"
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       "ratios": [
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       "expMinusGamma": 0.0707,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "1.660e+0",
        "8.243e-2",
        "6.452e-3",
        "5.257e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.0819,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "1.626e+0",
        "1.029e-1",
        "1.059e-2",
        "1.153e-3"
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       "ratios": [
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       "expMinusGamma": 0.1098,
       "decreasingAndBelowPixel": true
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     ],
     "rule": "the outer edge of the n-th lensing band (crossings drop below n + 1) along a spoke through a decided point, n = 1…4: strictly decreasing, the last below one pixel; at a = 0 successive ratios within 5% of e^(−π) for n ≥ 2",
     "verdict": "AGREES"
    }
   }
  },
  "perView": {
   "47/50 @ 45": {
    "spin": "47/50",
    "inclinationDeg": "45",
    "coverage": {
     "n0": {
      "pixels": 259185,
      "beyond200M": 0,
      "withG": 257485
     },
     "n1": {
      "pixels": 11558,
      "beyond200M": 621,
      "withG": 9832
     },
     "n2": {
      "pixels": 498,
      "beyond200M": 14,
      "withG": 373
     }
    },
    "retrace": {
     "sampled": 2703,
     "bitIdentical": 2703,
     "differ": 0,
     "verdict": "AGREES"
    },
    "closedForm": {
     "crossings": 2795,
     "maxMinoTimeVsAngular": "3.83e-13",
     "maxRadiusErrorM": "3.83e-10",
     "worstAt": {
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      "n": 2,
      "r": 57.648833
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     "threshold": "1e-6 M",
     "verdict": "AGREES"
    },
    "curve": {
     "decidedPoints": 4382,
     "maxBoxHalfWidthM": "4.31e-9",
     "smallestEndBeta": "4.98e-5"
    },
    "pointwise": {
     "epsilon": 0.000001,
     "points": 731,
     "rule": "the ray at (1 − ε)·P captured and at (1 + ε)·P escaped, P proven on the decided curve",
     "fail": 0,
     "firstFailures": [],
     "verdict": "AGREES"
    },
    "bisected": {
     "points": 24,
     "resolution": "2e-3 / 2^44 relative",
     "maxDistanceToDecidedM": "4.07e-15"
    },
    "texture": {
     "capturedPixels": 12556,
     "insideDecidedCurve": 12556,
     "mismatched": 0,
     "unjudgedWithin1e4M": 0,
     "extents": {
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       "fromMap": 9.53125,
       "trueExtentIn": "[9.5308, 9.6875]",
       "phase0": "[9.595175, 9.595945]",
       "meets": true
      },
      "H": {
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     },
     "verdict": "AGREES"
    },
    "convergence": {
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        "rOrbit": 1.5892
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       "distanceM": [
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        "8.715e-2",
        "7.713e-3",
        "6.890e-4"
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      {
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       "distanceM": [
        "6.160e-1",
        "4.820e-2",
        "4.628e-3",
        "4.541e-4"
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       "ratios": [
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       "expMinusGamma": 0.0984,
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        "1.682e-3",
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      {
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       "distanceM": [
        "5.804e-1",
        "2.534e-2",
        "1.322e-3",
        "6.978e-5"
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       "ratios": [
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       "expMinusGamma": 0.0528,
       "decreasingAndBelowPixel": true
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      {
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       "distanceM": [
        "1.028e+0",
        "3.801e-2",
        "1.855e-3",
        "9.211e-5"
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       "ratios": [
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       "expMinusGamma": 0.0497,
       "decreasingAndBelowPixel": true
      },
      {
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       "distanceM": [
        "2.061e+0",
        "6.557e-2",
        "3.360e-3",
        "1.770e-4"
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       "ratios": [
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       "expMinusGamma": 0.0528,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       "distanceM": [
        "3.201e+0",
        "1.003e-1",
        "6.194e-3",
        "3.990e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.0647,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "3.126e+0",
        "1.410e-1",
        "1.296e-2",
        "1.262e-3"
       ],
       "ratios": [
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       "expMinusGamma": 0.0981,
       "decreasingAndBelowPixel": true
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     ],
     "rule": "the outer edge of the n-th lensing band (crossings drop below n + 1) along a spoke through a decided point, n = 1…4: strictly decreasing, the last below one pixel; at a = 0 successive ratios within 5% of e^(−π) for n ≥ 2",
     "searchedOutTo": "8 × P (Phase 2 deviation 1)",
     "verdict": "AGREES"
    }
   },
   "47/50 @ 80": {
    "spin": "47/50",
    "inclinationDeg": "80",
    "coverage": {
     "n0": {
      "pixels": 258680,
      "beyond200M": 0,
      "withG": 257353
     },
     "n1": {
      "pixels": 76185,
      "beyond200M": 23873,
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     },
     "n2": {
      "pixels": 636,
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      "withG": 493
     }
    },
    "retrace": {
     "sampled": 2703,
     "bitIdentical": 2703,
     "differ": 0,
     "verdict": "AGREES"
    },
    "closedForm": {
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     "maxMinoTimeVsAngular": "7.60e-13",
     "maxRadiusErrorM": "4.73e-10",
     "worstAt": {
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      "beta": 3.2421875,
      "n": 1,
      "r": 129.895672
     },
     "threshold": "1e-6 M",
     "verdict": "AGREES"
    },
    "curve": {
     "decidedPoints": 4516,
     "maxBoxHalfWidthM": "4.40e-10",
     "smallestEndBeta": "5.87e-5"
    },
    "pointwise": {
     "epsilon": 0.000001,
     "points": 753,
     "rule": "the ray at (1 − ε)·P captured and at (1 + ε)·P escaped, P proven on the decided curve",
     "fail": 0,
     "firstFailures": [],
     "verdict": "AGREES"
    },
    "bisected": {
     "points": 24,
     "resolution": "2e-3 / 2^44 relative",
     "maxDistanceToDecidedM": "2.99e-15"
    },
    "texture": {
     "capturedPixels": 12878,
     "insideDecidedCurve": 12878,
     "mismatched": 0,
     "unjudgedWithin1e4M": 0,
     "extents": {
      "W": {
       "fromMap": 9.453125,
       "trueExtentIn": "[9.4527, 9.6094]",
       "phase0": "[9.540638, 9.546274]",
       "meets": true
      },
      "H": {
       "fromMap": 10.234375,
       "trueExtentIn": "[10.2340, 10.3906]",
       "phase0": "[10.376849, 10.378078]",
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      },
      "d": {
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       "trueExtentIn": "[9.8433, 10.0000]",
       "phase0": "[9.958743, 9.962176]",
       "meets": true
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     },
     "verdict": "AGREES"
    },
    "convergence": {
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      {
       "at": {
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        "rOrbit": 1.4305
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       "distanceM": [
        "1.242e+0",
        "5.097e-2",
        "2.316e-3",
        "1.053e-4"
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       "ratios": [
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        0.0455
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       "expMinusGamma": 0.0455,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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        "rOrbit": 1.9811
       },
       "distanceM": [
        "3.370e-1",
        "2.874e-2",
        "2.771e-3",
        "2.708e-4"
       ],
       "ratios": [
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       "expMinusGamma": 0.0979,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "2.502e-1",
        "1.380e-2",
        "8.336e-4",
        "5.070e-5"
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       "ratios": [
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       "expMinusGamma": 0.0609,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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        "rOrbit": 3.6967
       },
       "distanceM": [
        "2.415e-1",
        "1.038e-2",
        "4.846e-4",
        "2.274e-5"
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       "ratios": [
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       "expMinusGamma": 0.0469,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 6.8711,
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        "rOrbit": 3.9252
       },
       "distanceM": [
        "9.936e-1",
        "3.279e-2",
        "1.405e-3",
        "6.109e-5"
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       "ratios": [
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       "expMinusGamma": 0.0435,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
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       },
       "distanceM": [
        "1.081e+1",
        "1.265e-1",
        "5.640e-3",
        "2.637e-4"
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       "ratios": [
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       "expMinusGamma": 0.0469,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": 2.0061,
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        "rOrbit": 3.022
       },
       "distanceM": [
        "1.951e+1",
        "1.738e-1",
        "9.823e-3",
        "5.930e-4"
       ],
       "ratios": [
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        0.0604
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       "expMinusGamma": 0.0607,
       "decreasingAndBelowPixel": true
      },
      {
       "at": {
        "alpha": -1.4897,
        "beta": -3.6851,
        "rOrbit": 1.9866
       },
       "distanceM": [
        "1.961e+1",
        "2.450e-1",
        "2.154e-2",
        "2.080e-3"
       ],
       "ratios": [
        0.0125,
        0.0879,
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       ],
       "expMinusGamma": 0.0977,
       "decreasingAndBelowPixel": true
      }
     ],
     "rule": "the outer edge of the n-th lensing band (crossings drop below n + 1) along a spoke through a decided point, n = 1…4: strictly decreasing, the last below one pixel; at a = 0 successive ratios within 5% of e^(−π) for n ≥ 2",
     "searchedOutTo": "8 × P (Phase 2 deviation 1)",
     "verdict": "AGREES"
    }
   }
  }
 },
 "redControls": [
  {
   "control": "the a = 0 map against the a = 47/50 decided curve (wrong spin): 2312 pixels mismatched",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  },
  {
   "control": "a 128² map at a = 47/50, θo = 25° (wrong inclination) against the 17° decided curve: 56 pixels mismatched",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  },
  {
   "control": "rays at θo = 25° at the a = 47/50, 17° decided points (73 of 73 fail)",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  },
  {
   "control": "rays at a = 1/2 at the a = 47/50 decided points (wrong spin; 73 of 73 fail)",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  },
  {
   "control": "one byte of a47_50-n0.rpg.f16.gz flipped: the manifest pin",
   "expected": "fails",
   "got": "fails",
   "ok": true
  },
  {
   "control": "a planted √26 for the Schwarzschild edge",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  },
  {
   "control": "the 45° map against the 80° decided curve (wrong view): 1762 pixels mismatched",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  },
  {
   "control": "rays at 45° at the 80° decided points (wrong view; 73 of 73 fail)",
   "expected": "DISAGREES",
   "got": "DISAGREES",
   "ok": true
  }
 ],
 "timing": {
  "ms": 13500
 }
}