Localizing from a single base station is a longstanding goal, since it removes the synchronized anchors that geometric methods require. A radio map (RM) answers a position query from this one-station survey, yet classical RMs store coarse received power and match it by correlation, ignoring the small-scale path structure a ray tracer provides. We instead build a small-scale RM and show that cell identification, rather than candidate generation, is its information-limited bottleneck. We propose path-atom localization by matching (PALM), which super-resolves a coarse angle-delay observation into scored atoms and matches them to a ray-traced RM by an exact marginal likelihood. The score marginalizes atom reality inside the logarithm, and we prove that the common posterior-scaled surrogate is a Jensen lower bound whose deficit grows with the number of strong paths. We match on the absolute delay axis under a clock nuisance, since relative delays jump across shadowing boundaries, and we prove a unit-gradient law, a capped miss cost, a minimum-mean-square local centroid, and finite-sample conformal coverage. On the real DeepMIMO campus scenario, PALM localizes to a 1.7 meter median from a single base station, cuts the ninetieth-percentile error of received-power RM matching by 34 to 62 percent, and halves the single-snapshot median to 7 meters.