What is the meaning in a sword being worn curve up v. curve over?

I know this post is devoid of any help.

CPT (Join to see) - I only have experience with the Mameluke. I used it twice in my career: First on the grinder in Quantico; the other time to cut my wedding cake. But, I did have a SgtMaj once tell me: "Business end toward the bad guys." Although there was some merit in that, here's my recollection: Speaking only to the cutlass (curved sword) - When one presents the sharpened edge of the cutlass, you're admitting that you're out of ammo but, it's still "on." To present the back-side of the cutlass indicated that your intent is to either disengage or surrender. Of course, presenting the broad-side was a form of salute.

I'm assuming you mean the regulation sword? If so, then the sword belt and associated hook answers the question (I believe the Army's blade is a "saber"?). The Navy's most recent incarnation of this useless but cool uniform accessory has a straight blade, and follows the same pattern as it has since the Civil War. When walking, or in formation, the sword hangs from the hook with the "D" of the guard facing to aft, and the tip of the scabbard facing forward. I am not certain why...but I assume this is to keep from bumping people behind your line of sight. When 'mounted'...which never happens anymore, the sword hangs freely on the two straps at about mid-thigh, with the scabbard trailing to rear. I know our scabbard is designed for the sword to only go in one way...you simply cannot put it in "upside down" without much, obviously incorrect effort.

I've only had the pleasure and honor of wearing my service blade twice...once for my friend's wedding, and the second time, at my own :)