{
  "method": "All reconstructions start from random XYZ and fit only edge distances. Independent reference coordinates are used solely to fabricate control measurements and evaluate models, never to initialize or constrain a reconstruction. No sphere prior or projection is added.",
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        {
          "from": "ICN",
          "to": "CTS",
          "hours": 3.125,
          "expectedHours": 1.8303188109767106,
          "relativeError": 0.7073528290584581,
          "observations": 2
        },
        {
          "from": "SZX",
          "to": "XIY",
          "hours": 3,
          "expectedHours": 1.8060537600583675,
          "relativeError": 0.6610801219466728,
          "observations": 3
        },
        {
          "from": "PEK",
          "to": "CKG",
          "hours": 3.0833333333333335,
          "expectedHours": 1.8855480263421731,
          "relativeError": 0.6352451861514116,
          "observations": 1
        },
        {
          "from": "DEL",
          "to": "ALA",
          "hours": 3.4166666666666665,
          "expectedHours": 2.117483782260583,
          "relativeError": 0.6135503352092275,
          "observations": 1
        },
        {
          "from": "HKG",
          "to": "TAO",
          "hours": 3.375,
          "expectedHours": 2.154013213023197,
          "relativeError": 0.5668427563929035,
          "observations": 2
        },
        {
          "from": "HND",
          "to": "DLC",
          "hours": 3.3333333333333335,
          "expectedHours": 2.1318881628578032,
          "relativeError": 0.5635591919910982,
          "observations": 1
        },
        {
          "from": "PEK",
          "to": "CTU",
          "hours": 3.0833333333333335,
          "expectedHours": 2.0041074364716662,
          "relativeError": 0.5385070067709044,
          "observations": 4
        },
        {
          "from": "PVG",
          "to": "MNL",
          "hours": 3.6666666666666665,
          "expectedHours": 2.3845266878456095,
          "relativeError": 0.537691603686539,
          "observations": 4
        }
      ],
      "affineComparison": {
        "slope": 7.2996006551036,
        "interceptHours": 1.1354119978914685,
        "normalizedError": 0.0566427926049891,
        "description": "Validation-only regression allowing a common additive duration; no parameters are used by the reconstruction."
      }
    }
  ],
  "hubReferenceCoverage": {
    "zMin": 0.023563080038603145,
    "zMax": 0.7913153239040152,
    "southernHubs": [],
    "latitudeMin": 1.3501900000000002,
    "latitudeMax": 52.308600999999996
  },
  "exactAmbiguityProof": {
    "description": "Evaluation only: start with independently known sphere points, then rotate each degree-one point around its sole fixed neighbor onto the outward radial ray. Every observed chord length is unchanged. No reconstruction is initialized from these positions.",
    "airports": 200,
    "pairs": 1913,
    "movedAirports": [
      {
        "airport": "DAD",
        "anchor": "ICN",
        "radiusBefore": 1,
        "radiusAfter": 1.4636399153739827
      },
      {
        "airport": "SUB",
        "anchor": "HKG",
        "radiusBefore": 1,
        "radiusAfter": 1.5127355114012633
      },
      {
        "airport": "BSB",
        "anchor": "LIS",
        "radiusBefore": 1,
        "radiusAfter": 2.0833032909603997
      },
      {
        "airport": "ASU",
        "anchor": "MAD",
        "radiusBefore": 1,
        "radiusAfter": 2.320534056929506
      },
      {
        "airport": "MVD",
        "anchor": "MAD",
        "radiusBefore": 1,
        "radiusAfter": 2.407424251770906
      },
      {
        "airport": "YEG",
        "anchor": "AMS",
        "radiusBefore": 1,
        "radiusAfter": 2.0381696238084546
      },
      {
        "airport": "LAD",
        "anchor": "MAD",
        "radiusBefore": 1,
        "radiusAfter": 1.8721926586277164
      },
      {
        "airport": "PEN",
        "anchor": "HKG",
        "radiusBefore": 1,
        "radiusAfter": 1.373439844831265
      },
      {
        "airport": "RGN",
        "anchor": "ICN",
        "radiusBefore": 1,
        "radiusAfter": 1.57889418186849
      }
    ],
    "stressBefore": 1.322390031282886e-16,
    "stressAfter": 1.3342207466540817e-16,
    "radialVariationBefore": 1.4043333874306802e-16,
    "radialVariationAfter": 0.22539704300401495
  },
  "lowDegreeCounts": {
    "1": 9,
    "2": 14,
    "3": 17
  },
  "referenceMissingAirports": [
    "BER",
    "TFU",
    "UBN"
  ],
  "findings": [
    "Previous rendering issue, now corrected: all 21 labeled hubs are north of the equator in an independent reference. The earlier build mistakenly restricted the hull to those hubs. The current hull uses every fitted airport.",
    "The filtered graph has 9 degree-one, 14 degree-two and 17 degree-three airports. Sparse constraints admit multiple point clouds; additional iterations cannot determine missing distances.",
    "The same graph with perfect sphere chord targets reaches about 0.2% distance residual but 12–17% radial variation at 30,000 iterations. The exact degree-one construction proves that different shapes can even share zero edge error.",
    "Flight schedules are not exact Euclidean chords: routing, winds, fixed flight phases and schedule padding alter durations. Averaging directions reduces directional effects but does not remove these differences.",
    "Three random starts at 30,000 iterations give 3.5–4.6% distance residual, 3.2–4.9% shown-hub radial variation and 17.5–24.1% full-cloud radial variation. Different minima persist; none of these runs met the strict stopping condition."
  ],
  "renderingCorrection": "The investigation described the earlier build, which incorrectly limited the points and hull to hubs. The current build renders all fitted airports and uses the top 10% only for scene text labels. The all-airport numerical findings remain applicable.",
  "surfaceRenderingUpdate": "The default all-airport surface now uses every retained airport as a mesh vertex at its exact fitted XYZ coordinates. Direction-based connectivity permits concavity and dents. Convex envelope remains a comparison option. This changes rendering only; all-airport optimization and the numerical findings remain applicable."
}