BUR #6980 has been rejected.
remove alias panting -> heavy_breathing
"To breathe heavily" is one possible meaning of the word "pant", but not the primary one. The primary one refers to a means of thermoregulation involving breathing with the tongue exposed, associated with but not exclusive to dogs. This is a taggable theme.
Not all panting involves heavy breathing: post #3865922, post #4372826, and post #4728853 involve clear heavy breathing; post #3634050, post #3828225, and post #4659870 does not. post #4457618 shows an actual dog doing it. post #4602507 is notable because it shows the distinction between panting and sticking your tongue out for a different reason.
Not all heavy breathing is panting: post #4749683, post #4759755, and post #4736810 are are counterexamples. post #4765775 even shows an example of tongue_out heavy_breathing that isn't panting—the tongue is stuck out as an oral invitation instead.
Panting doesn't even have to involve sticking the tongue all the way out; it just involves exposing the tongue. post #4431427 and post #4431428 are examples of panting with the tongue inside the mouth.
Panting is a typical, but not quite essential feature of an ahegao. The milder examples on the end of the spectrum closer to torogao may not open the mouth wide enough (post #4510000), and the crazier examples of the sort indicative of mind break may have the tongue out but jutting out in a deranged I-don't-have-a-word-for-this-expression rather than lolling out in a pant (post #240870).
Updated