From 7 to 15 [points gets you] an honorable mention (with some judges’ discretion)In fact the scoring is even more straightforwardly rule-based than that. There is no judicial discretion.
Participants who do not win a medal but who score seven points on at least one problem receive an honorable mention.That's from Wikipedia, which I didn't check because I don't trust it. In this case, however, Wikipedia is supported by the data. For example: Anthony Flores of Ecuador got an Honorable Mention with scores 0-0-0-7-0-0, but Matteo Migliorini of Italy with scores 6-6-0-1-0-0 didn't, in spite of having nearly twice Flores' total score. Tough tetrahedra there, Matt.
I apologize for the error.