When do coordinates help projection-to-volume learning?

Positional coordinates can resolve spatial ambiguity in learned 3D inverse problems, but their benefit can reverse as measurement coverage increases. We study this in 3D lung segmentation from simulated X-ray projections, separating position from calibrated lifting, attention, and decoder processing. On 24 held-out LCTSC patients under a prospectively locked protocol, coordinates increase source-acquisition Dice by 30.8 percentage points at one view but reduce it by 6.3 at twelve across three initializations. Two-view source acquisitions show a 19.5-point benefit when clustered and a 3.6-point penalty when spread. In our pipeline, sparse-view gains persist without learned attention or the separate geometry-conditioning branch, but accuracy drops substantially without both coordinates and learned spatial slots. Across two development cohorts, along-ray depth exceeds detector-plane coordinates by 9.7 and 3.1 source-acquisition Dice points across three initializations, with advantages persisting under held-out rotations, consistent with difficulty localizing along projection rays. Synthetic coordinate benefits diminish or disappear for uniformly translated populations and depend on sampled frequencies. In a matched context experiment, wider decoder context recovers nearly half of the single-view coordinate advantage without positional input. A scalar acquisition-dependent gate preserves prespecified sparse and broad endpoints in both development cohorts; broader training coverage only partly repairs its intermediate-angle deficit. Coordinate utility therefore depends jointly on measurement ambiguity, population alignment, and decoder processing; neither view count nor geometry alone predicts its benefit.