Recorded source distance had repeated links to British butterfly recovery after local zero counts

We tested whether nearby recorded populations predict butterfly recovery after local zero counts. We used raw UKBMS site indices and public locations, with NOAA temperature data. We tested 38 species in 283 species-site pairs for 2000-2009 and 838 pairs for 2015-2024. Each pair had a positive record before at least three zero baseline years. Greater source distance had a negative adjusted link to persistent reappearance in both periods. Ridge odds ratios per doubling of one plus distance in km were 0.570 and 0.680. Spatial bootstrap ranges were 0.389-0.906 and 0.524-0.776. The direction remained in warmer and cooler affinity groups and several sensitivity checks. Adding distance reduced frozen later-period log loss by 4.15%, but its spatial interval included no gain. At the main penalty, both fitted models were worse than a constant forecast; a stronger penalty reversed that comparison in an exploratory check. Source distance is a repeated recovery marker, but forecast value depends on regularisation. Habitat, range position, detection and record selection can explain the association. We do not identify dispersal limitation or quantify its share of the thermal-tracking gap. The package contains code, aggregate results, a figure, input hashes and retrieval instructions. External raw data and the record-level panel are not bundled.