Read what it actually says. It does not say "The parabolic horn is a rectangular horn with two parallel sides, the two other sides expanding linearly", it says "The parabolic horn is a true 1P horn if it is rectangular with two parallel sides, the two other sides expanding linearly". And the concept of true 1P horns is a different issue that what we are talking about here, and applies mainly to directivity controlling devices (i.e. at HF, not for LF/subwoofers). Also note that it is only the 1P part that depends on the geometry, if it is a parabolic horn or not depends only on how the area changes along the horn.
I get that you want people to model what they build what the model, but that is a different issue from how horn profiles are defined in the equations that are used to simulate them.
I get that you want people to model what they build what the model, but that is a different issue from how horn profiles are defined in the equations that are used to simulate them.
The parabolic horn was never the issue, so that is not the case that you need to rest.
You categorically stated in Post #14,663 that a conical horn has all straight expanding sides (no parallel sides) and that an exponential horn has all curved expanding sides (no parallel sides). This is not necessarily the case, as was clearly demonstrated in examples I posted.
Incidentally, you may be interested to know that a rectangular parabolic horn does not need to have two parallel sides provided that the area expansion remains linear, which it does in the following example.