OpenGL 4.1 compatibility profile says:
<<
All fragments produced in rasterizing a point sprite are assigned the same as-
sociated data, which are those of the vertex corresponding to the
point. However,
the fragment shader built-in gl_PointCoord contains point sprite texture coor-
dinates. Additionally, for each texture coordinate set where COORD_REPLACE is
TRUE, these texture coordinates are replaced with point sprite texture
coordinates.
>>

I think "texture coordinates" here must refer to gl_TexCoord[i].
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