Kernel Density output extends beyond raster mask

Question

I've run the Kernel Density tool a bunch of times with the Raster Mask set to a specific layer in the Environments settings yet my output continues to extend beyond the mask.  My troubleshooting has led nowhere (see gis.stackexchange question)...  Any ideas as to why my kernel density output would produce such weird behavior?  See below screenshot, raster mask outlined in red...

DanPatterson_Retired · Answer

When things are a projection issue... all bets on plausible explanations are off

MikeW · Answer

It was definitely a projection issue... specifically the order which I projected then interpolated... but I'm still unclear as to why the output would be so completely outside of the mask?  Thanks for the suggestions.

DanPatterson_Retired · Answer

little things, like

* the cell size used,
* does the mask traverse the -180/+180 line, what's going on over North America? Is that part of the mask since there is no outline around those bands
* where are most of the point? They don't seem spread out over the mask area (or we cant see them
* Are there large tracts of open space where there is no possible observations? (ie over oceans)