PROJ
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Nicolosi Globular - outer hemisphere seems to be broken
According to Snyder/Voxland, An Album of Map Projections, p. 234, the sign in https://github.com/OSGeo/proj.4/blob/master/src/PJ_nocol.c#L43 should take "the opposite sign of φ times the sign of b" (tb
in your code). Also the "X axis coincides with the Equator, x increasing east".
For comparison, here's my implementation in JS: https://beta.observablehq.com/@toja/nicolosi-globular-projection
There was a typo in the older version of the document, the modern version of it does have "times the sign of b". https://pubs.usgs.gov/pp/1453/report.pdf vs older version on libgen.