Return to the reconstruction

Outlier corrections and remaining issues

6 October 2026 · Jets only · 201 airports · 3,880 edges · 41,894 observations

The data corrections and annealing search are included in this version. No geographical coordinates or sphere forces were introduced.

What changed

Five legitimate return records were restored: JD471 Qingdao–Vancouver, matching LY88 Phuket–Tel Aviv records for October 3 and 7, and 4Y202 Frankfurt–Marrakech for October 4 and 6. Five individual duration discrepancies were corrected, including the two 4Y202 return records. Original provider values and independent evidence remain in the inspector and CSV.

The optimizer now perturbs coherent groups, relaxes each proposal and applies a cooling annealing temperature. It also searches one fresh seeded random 3D start. The best fit remains visible throughout; worse accepted proposals stay inside the search. Restart reproduces the same seed. New random start changes it. Annealing can be disabled for comparison.

Measured improvement

Radial variation is a fitted-sphere diagnostic, not an optimization target. The three tests do not establish a global optimum. Plane and random 3D recovery of the exact synthetic benchmark still pass.

What remains

Incompatible time constraints — Unresolved

82 of 34,782 fully observed triangles violate the triangle inequality by more than 0.001h. No arrangement of Euclidean points can satisfy such a triangle exactly. Travel times include route-dependent wind, performance, routing and schedule overhead. The exact cause of each remaining inconsistency has not been measured.

Short-flight overhead — Unresolved

Below three hours: 14.48% normalized error. At least three hours: 3.99%. Average short-edge residual: -12.7 minutes. Short-flight residuals remain proportionately larger. There is no new cutoff or uniform time subtraction.

Verification coverage — Partially corrected

Five return observations recovered using exact dated independent evidence. 10,420 original observations remain quarantined, including ten confirmed stopped journeys. Exclusion means insufficient or conflicting evidence, not necessarily a connecting flight. The independent crowdsourced index can be stale. Unknown records are not assumed nonstop.

Conflicting LY88 October 6 schedule — Still quarantined

Raw source reports departure 13:40 and duration 10h40; the currently published independent dated schedule reports departure 13:25 and duration 10h55. The two matching October 3 and 7 return records are restored. The conflicting source observation is not guessed into the dataset.

Global optimality and ambiguous shape — Mitigated, not guaranteed

All three tested starts reach 4.57–4.59% error with two annealing chains, versus 6.24–6.50% without annealing. Other seeds, datasets and sparse airports can still have worse or ambiguous fits. A settled fit means the bounded search ended and local movement is negligible. It does not certify a global minimum or a sphere.

Largest remaining edge residuals

Positive means the fitted separation is too large for the scheduled-time target; negative means too small. These remain after the data corrections and default annealing run. An individual remaining residual is not automatically a bad flight record.

Current airport rankings

Local distance error across every incident edge. Edge counts mean distinct connected airports.

Full correction and fit report · Airport rankings CSV · Exact dated source reviews