The authors apologise for two erroneous citations in the following sentence on page 1929, from line 19:
Our choice of a 25-km radius aligns with established norms of spatial analysis, as the evidence suggests that it captures a representative area while maintaining analytical detail (Gould, 1986; Hanson, 2001)
This has been corrected to:
Our choice of a 25-km radius aligns with established norms of spatial analysis, as the evidence suggests that it captures a representative area while maintaining analytical detail (Eurostat, 2024; Neuberger et al., 2021)
Additionally, Gould (1986) and Hanson (2001) have been removed from the reference list and replaced with the following:
Eurostat. (2024). Territorial typologies manual—Border regions. https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Territorial_typologies_manual_-_border_regions
Neuberger, S., Saatkamp, H. W., Oude Lansink, A. G. J. M., & Darr, D. (2021). Can differences in innovativeness between European cross-border regions be explained by factors impeding cross-border business interaction? PLOS ONE, 16(11), e0258591. https://doi.org/10.1371/journal.pone.0258591