I mean, from what I know of NLHE cash games to this point, it seems to me that the idea is to make profitable decisions at every point in the hand, regardless of external factors..

If you somehow have $170 of your $200 (unlikely yes) in the pot in a 4 way hand, you may feel you are "pot committed" yet in actually, if you are drawing dead X % of the time (i don't feel like figuring it out) then you should fold...

Am I mistaken, or is the term "pot committed" just another way of saying "getting the correct odds to call an all in wager based on the size of the pot, my remaining stack, and my likelihood to win the hand?"

or am I missing something, can one actually be "pot committed" regardless of the mathematics of the decision at hand?

Once you pass the commitment threshold calling odds are irrelevant. You have already solved the equation. The remainder gets tacked on to the solution like it would in 4th grade long division.

well the thing about it is you never really know what the person has... obvisouly if you saw their crads and yu're drawing dead you need to fold, but in the situation like you described, you might as well put in the last $30 just in case your opponent is on a bluff gone wrong

yeah, i watched a guy last night raise and commit all but the last $50 or so of his stack on the turn, then fold when his opponent shoved. he knew he was drawing dead and saved the $50. it was probably wrong from a commitment standpoint - why not just shove yourself? - but why throw $50 away if you know that's what you are doing? Just reach into your pocket and top up and save that $50.

If you are at the commitment threshold (CT) relative to the effective stacks the next bet will make you committed. At this point calling based on pot odds is irrelevant. Why I say is irrelevant? Well, because the only action you can take at this point is to continue all the way to the river. Pot odds or drawing odds are not part of your decisions. Your decision was made already when you decided to commit. It has to be some very specific extra informations come to you to "uncommit" just to manage the damage. The major decision is if to commit or not. You already know if you need to draw and what odds you've got before crossing the threshold. Once you crossed the CT you cannot go back and start figuring out what odds you've got for some draws or whatever ..., And, don't get committed on a draw, this is the first what you've got to take into consideration. If you make a mistake in regard to commitment and mixing things up with the drawing odds, you will put yourself in a situation of lose/lose no matter what you do after that. Don't do that because any decision after that is gonna be -EV.

AT,

this, you can't call if your pot comitted ever when you know you're beat

There's a deeper question in this OP.

You should be planning your hand such that you aren't in the position of thinking, "4 people in the pot, I'm beat but it only costs me the remaining 15% of my stack." Almost always in this situation there is a calling station moment where the player in question thought, "I could be good here, I can't fold yet." If a draw hit and you had that little left, you should have put it in on the previous street.

The problem is that often people commit themselves with a very marginal hand and that's where situaitons get sticky. Crossing the commitment threshold should really only happen with hands we can easily muck (bluffs) and hands that are very strong vs. opponent's range. If we are uncomfortable playing for stacks with our hand (or the hand our hand is likely to make) then we shouldn't be "commiting" ourselves.