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I have a shapefile which I read in via

import geopandas as gpd
shapes_df = gpd.read_file(shp_f)
print(shapes_df.crs)

The output was {'init': 'epsg:3857'}

I then reprojected via

shapes_df = shapes_df.to_crs("epsg:32629")
print(shapes_df.crs)

The output was epsg:32629

What is the meaning of the 'init' value for the CRS in the original CRS? Should I be concerned that there is no 'init' value in my reprojected data? Did the projection not work properly?

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What is the meaning of the 'init' value for the CRS in the original CRS?

It is for PROJ string initialization. That format is deprecated for CRS strings, so it is better to not have it (https://pyproj4.github.io/pyproj/stable/gotchas.html#init-auth-auth-code-should-be-replaced-with-auth-auth-code).

Reference for axis order: https://gis.stackexchange.com/a/326919/144357

Should I be concerned that there is no 'init' value in my reprojected data?

Depends if the axis order is important to you.

Did the projection not work properly?

That depends on the version of geopandas and pyproj. If you have geopandas 6+, then you should be fine.

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