Conformal coordinate intervals (2026-06-07)

A coverage guarantee on where a resolved address actually is. Companion to the isotonic calibration work — calibration tells you how much to trust the label; this tells you the radius the true point sits in.

The question

When the resolver places an address at a locality, it returns that locality's centroid. The honest follow-up question is not "is the name right" but "how far is the real doorstep from the point we returned, and can we put a guaranteed bound on it." A calibrated conf= answers the first kind of question; it says nothing about distance on the ground.

Method

Split conformal regression, no distributional assumption. For every row the resolver placed:

• nonconformity score s = haversine(gold point, resolved locality centroid).
• split the scores into a calibration half and a test half (seeded).
• for a target coverage 1 − α, the radius R(α) is the conformal quantile of the calibration scores — the ceil((1 − α)(n + 1))-th smallest. Output a circle of that radius around the resolved centroid and the true point falls inside it with marginal probability at least 1 − α.
• check it: the fraction of test scores at or under R(α) should land on 1 − α.

It runs offline over an oa-resolver-eval --out-resolved dump plus the admin gazetteer's centroids — no model in the loop. Coverage is conditional on the resolver actually placing the row; rows it declined to place are reported as an abstention rate, not silently dropped.

Results

Three locales off the night's resolved dumps (seed 20260607, 50/50 split). Realized coverage tracks the target everywhere, so the guarantee holds in practice and the radii are honest:

locale   resolved   90% radius (realized)   95% radius (realized)
FR        98.7%       5.49 km  (0.893)        8.16 km  (0.954)
NL        99.0%       4.64 km  (0.903)        7.60 km  (0.949)
DE        65.2%      14.74 km  (0.895)       19.48 km  (0.952)

Read the French row as: when we place a French address at a locality, the real point is within 5.49 km of it nine times in ten — and that "nine times in ten" is measured, not hoped for (0.893).

Two things fall out of the table for free. France and the Netherlands resolve nearly everything (~99%) into tight circles; Germany resolves only 65% and into a circle three times wider. That 34.8% German abstention is not noise — it is the Berlin / Hamburg / Bremen city-state rows where the parser drops the locality entirely (#387), surfacing here a second time through a completely independent lens. The wider German radius is the genuine city-centroid-to-doorstep distance for the rows that do resolve, not a modelling failure.

Where it lives

scripts/eval/conformal-coord.py, with a --self-test that validates the conformal math on synthetic scores (realized coverage within 0.003 of target at 80 / 90 / 95%). The radii are model-version specific — re-run per model. The demo can draw R(α) as a circle, which is also the natural way to show genuine ambiguity ("could be either Berlin") instead of a false-precision pin.