I'm probably not going to be able to convince you of any of this, because of your lack of understanding of physics. This is not meant to be a put-down in any way - there's a lot of vaulters (even some very good vaulters) that don't understand physics well enough that they're willing and able to use it to their personal advantage - so you're not alone.
I appreciate you willingness to listen and learn, and I don't think your lack of understanding is due to having a closed mind. Rather, I think that you truly don't "get" the physics principles involved. I'll TRY to explain some of this to you, but I'm just a little skeptical that I can convince you by what I call "physics logic". To me, there's no other type of logic, but the types of objections that I hear quite often defy physics, and I'm hearing some of this from you too.
But as long as you're open and willing to listen, I will TRY. Here goes ...
Chaebo wrote: My thought and goal with pushing the arms up and back was to create space, and create a high pole bend. My belief was that the high pole bend assisted in the transferring of energy through the system.
I'm not sure what you mean by a HIGH pole bend. You seem to imply that the bend is going to be higher on the pole if you apply pressure on your bottom arm, and that a higher bend is better than a lower bend. Are those your assumptions?
My first point is that the type of bend that's "optimal" (high, low, or middle of the pole) is best controlled by the manufacturing material and process, and the mfrs are quite clever in the way they wrap their poles for optimal bend. Certainly there's been changes in the way the poles are wrapped over the 6 decades that fiber has been used, and there's also differences from brand to brand and from model to model. However, I suggest to you that there's no advantage to you to make the pole bend even MORE optimally - the mfrs already have that issue covered. You are right that the pole WILL bend DIFFERENTLY when pressure is applied by the bottom arm.
However, I doubt very much that it will bend more OPTIMALLY because of any bottom arm pressure. I'm going to stop here on this point, because it's actually a red herring - there is no advantage whatsoever in making the pole bend "higher". If that was the case, the mfrs would simply change their wrapping formula to build that idea into the pole.
Sorry, I don't follow the physics that must exist for your following 4 points to be true.
Chaebo wrote: The advantages of a high pole bend were as follows:
- Increased speed on the down swing. (Due to the upward pressure of the bottom arm)
Any pressure on the bottom arm will SLOW DOWN the swing - according to the laws of physics.
Chaebo wrote: - A continued pole rotation from continuous pressure being pushed toward vertical
You WILL bend the pole more by any bottom arm pressure, and this will allow the pole to roll forwards more/easier. However, bending the pole isn't the objective. The objective is to (a) make the swing as quick and efficient as possible; (b) get the CoG up as quickly and efficiently as possible; (c) invert as early and as efficiently as possible; (d) extend as efficiently as you can, in unison with the straightening of the pole.
So if you just want to roll the pole towards the pit, and you don't care about your body position when the pole is vertical, then just press with the bottom arm and "hang low". In fact, hang low with BOTH legs. This will give you the biggest bend. You will not swing much; your CoG will not raise up much; and your will not invert much. But you WILL roll the pole to vertical, and you CAN get onto bigger poles this way. BUT have you ever seen anyone clear a bar just by rolling the pole to vertical - when their hips and CoG are still under their shoulders, and their legs are even lower? Of course not! Unless you're clearing a bar well under your grip!
Chaebo wrote: - Increased "Lift" from the pole. And an increased "Pop" once in vertical.
This totally defies the laws of physics. Once the takeoff foot leaves the ground, the vaulter-pole system has a fixed amount of energy in the system. There ARE ways of increasing this total/fixed amount of energy, but merely pressing on the pole with the bottom arm isn't one of them. I'm assuming that you feel you get the increased "lift" and "pop" due to being on a bigger pole - or bending it more. As I explained in the previous paragraph, you may very well get more "lift" or "pop" by bending a bigger pole (or bending it more), but your body will NOT be in an ideal inverted position to take advantage of this increased "lift" or "pop" because you will be "behind the pole". That is, you will not have your CoG high enough or your body inverted enough to take advantage of this increased "lift" or "pop". Best case will be that you will have to tuck to wait for the pole to rotate to vertical, and worst case will be that you don't even get into a tuck - so you will have no choice but to flag out.
Chaebo wrote: (Due to the energy being transferred into the pole and being pushed toward the top rather than being lost in the box)
Huh? Once the takeoff foot leaves the ground, there is no energy being "lost in the box". Short of sound, heat and friction, the vaulter-pole system doesn't lose any energy "in the box". And the amount of sound, heat and friction lost by the butt of the pole against the box is negligible - not even worth quantifying.
Chaebo wrote: - Increased space and hips being kept in a neutral position to allow for more room to swing to the I position in turn speeding up the rotation.
By "allow more room to swing" I'm not sure if you mean "room" as in "space" or "room" as in "time". And I'm not sure what you consider a "neutral position" of the hips. If the former (space), then that's not an objective of the swing. The objective is to swing quickly and efficiently. If the latter (time), then all the time in the world isn't going to help you get your hips up if you've killed your swing by bottom arm pressure. Conversely, the quicker you can swing and rotate to an inverted position, the better position you'll be in to take advantage of the pole straightening out. If you can't get to this inverted position in time, then you will either tuck or flag - or both.
Chaebo wrote: A reason I am very open to the idea of not using the bottom hand is because I have played around on short approached 3 to 5 lefts not using the bottom and the pole bent and i was able to swing to vertical.
Cool.

Chaebo wrote: ... i was able to get to roll in the poll and get to vertical through the effects of a powerful swing. But, I was not comfortable with how deep I had my standards so I tried pushing slightly and was able to still get to vertical and have my standards back around 80' jumping 13'6 from 4 lefts.
I'm a bit surprised at this. I'm thinking that there was something else going on that helped you clear the bar with standards at 80 other than pushing slightly. Remember that landing deep into the pit is only one objective. Another is to raise the CoG quickly and efficiently, and another is to get inverted quickly and efficiently. Perhaps you sacrificed one of these other objectives in order to land deeper into the pit? I don't know - just guessing, based on the laws of physics. I see that you say that you were "able to get to vertical" while pushing, but I guess I'd have to see a vid to know what else was different then.
Also, I'm not sure why you weren't comfortable with your standards at 80? That's the ideal setting, as far as I'm concerned.
Chaebo wrote: ... A rigid pole can not be given the initial pop because it doesn't bend. And you would have to revert back to the old straight pole style which I am aware is the basis of petrov's teachings.
Correct.

So what's the problem?
Chaebo wrote: ... where i get confused is the conference in Reno with Petrov discussing the importance of the bottom arm saying the bottom arm should be the focus to generate energy through the system.
I did watch and listen to that Reno vid, but I honestly found Petrov's interpreter VERY hard to understand. So I'll let someone else with better ears and patience reply to this point of yours. My best guess (which might not be a very good one) is that he might have been referring to the role of the bottom arm (both arms, actually) in getting the plant up as high as possible - rather than referring to any post-takeoff role?
Chaebo wrote: I also became confused on reading one of the Continuous Chain Model done by Roman.
This is another whole topic or thread. Due to the length of this reply, I'd prefer to leave the topic of the Continuous Chain Model to another post on another day. It's not that it's unimportant - it's EXTREMELY important. It's just not anything I can do justice to in a couple sentences. Again, I'll leave this for someone else to answer. Maybe even Agapit?!

Sorry for the long reply. I hope we're making progress?
Kirk