I'll respond to your response - I hope it will cover other responses, too.
"Regardless, I would think it would be straightforward to measure. "
You can measure it, but you can't distinguish the VOLUNTARY push-off component from recoil component.
"We've previously seen links to force plate charts from which it is easy to see there are two peaks. The first peak is the maximum force exerted on landing (which is then partially or wholly stored up in the muscles, etc).
The second peak is the maximum force exerted on 'push-off'. If this second peak is less than the first, then it is difficult to say whether it is comprised solely of muscle recoil or includes some conscious effort."
This depends upon who is running in the experiment. It may be a conventional runner, or a runner "instructed to run Pose" - which in fact also means a conventional runner. To get a reliable data you would have to test the same runner pre-Pose, and then test him after he mastered Pose - and he would have to have the same Pose mileage under his belt as he had pre-Pose. Other than that the results will be skewed.
I wrote:
"The energy absorbed upon landing is used:
1. To regain the lost height.
2. Adds to propelling the body forward, the prime mover being gravity. That is - it aids to transform the downward action of gravity to horizontal."
You wrote:
"Here, stated in very clear terms that no one can dispute, you are saying that not only is the body a lossless system (such that everything absorbed from landing due to gravity gets transferred 100% back on recoil), but that the human body is a free energy producer."
I wrote: the energy is USED. Do you have a proof that it is NOT USED?.I wrote: it ADDS to propelling forward. Do you have data that it DOESN'T ADD? The operative words are "used" and "adds". Where do you see about lossless system? Or do you think that muscle recoil can be reduced to recoil of a metal spring? Believe me, in years of surgeon practice I've seen some dead people, and I can assure you - muscle recoil in a corpse is different than that in a live person.
I wrote:
"Yes, this energy is used to regain height and to propel forward. And in my understanding it propels you forward in the following manner: it counters the downward pulling of gravity and enables to transform downward direction of gravity to forward movement."
Read once more: "it transforms downward pulling of gravity to forward movement". Translating for you from English into English: it means gravity is doing the work, and stored energy aids to transform its direction from downward to horizontal. Where do you see me saying that there is is some more enegry left, when you claim that I say that recoil not only gives 100% return to regain the lost height, but produces more energy to propel forward?
I wrote:
"You say: "Whatever it adds on one stride is taken away later". I say: but you have made the stride " for free", that is, you have moved one stride forward ".
The English to English version: the recoil energy brings us to the running pose for the next falling, and on the next falling you again have a portion of "free" energy from gravitational pull. I see it like this: recoil produces energy, when you are in running pose you have lost it, but with the next fall ( which is free) you gain it again, to be used again to get into running pose. And I don't care about vectors and such - all I care is that I don't have to fight against the ground to move forward. English to English: I don't have the feeling of fighting against the ground. Because (let it ingrain into your head), Pose is about perception.
I wrote:
"One thing: Pose doesn't claim that "gravity is enough to continualy drive the system". Pose says that gravity is the prime mover in running."
English to English: without using muscle energy you wouldn't be able to get back into running pose, so you wouldn't be able to use the free gravitational energy for your next stride. Everything uses energy: hamstring pull, core positioning, arms movement.
"If gravity is NOT enough to continually drive the system, then you are saying there is additionaly energy added."
Yes, you must add - and recoil does it by bringing you into previous height. The question what you imagine to be recoil. The difference between the recoil of a bouncing ball and a human leg is that metabolic process takes place in muscles (as you've already understood, contrary to the ball or a metal spring). In a live organism the release of stored energy can't be separated from reflective contraction of miofibrilles. Means, upon foot landing proprioreceptors get impulses from nerves and involuntary contraction of certain groups of miofibrilles takes place. Recoil is divided into recoil of bones, ligaments, tendons and muscles, the more elastic a tissue is - the more force it can generate by recoil. To measure "real recoil" (or recoil like you understand it - in pure physical sense) you would have to measure it in a corpse - but again, nervous impulses travel in tissues for some time after death, and later on the corpse starts to stiffen, thus the recoil of muscular tissue changes due to biochemical changes in miofibriles. In a live organism it's impossible to separate "pure physical recoil" from reflective conraction of muscles reacting to landing impact. So both of these are called "recoil". And contraction is a contraction. So I see no problem about where the energy comes from. You can't influence neither "physical recoil", nor reflective mucular contraction, and you can't separately measure them, so for practical purposes it is called " muscle recoil". Pose is teaching a running technique, and teaching means learning to influence what can be influenced. That's why I don't lose any of my sleep because all of this physics.
"You can't say one thing (no pushing) and then turn around and say you need to add more energy to the system to keep it going"
I can say it, because "no pushing" means NOT PERFORMING PUSHIMG ACTION. (Read my above post about push-off approaching near-zero level). Means "trying to push-off less, striving to achieving no push-off at all". THIS IS ALL ABOUT PERCEPTION.
"So do we need to consciously push-off since gravity is NOT enough to drive the system? Or do we need to just let the muscles recoil after being loaded up by gravity and not do any further pushing?"
No, we needn't to push-off. Let's agree upon terms: when I say "no push-off", I mean "not performing a conscious pushing-off action", it means "trying to reprogram the brain not to send the impulse to the muscles to push-off". And I don't care if there is something that you could call a physical push-off. All I wanna do is try to achieve my push-off to "approach near-zero level". It's a way to teach running technique, and not a work if theoretical physics. And - yes, we need to let the muscles recoil to the highest degree possible, because recoil is energetically more efficient than voluntary muscle contraction.
"You have very clearly stated your belief that POSE professes the human body to be a lossless system and capable of generating free energy."
Please, quote me saying it.
"So, since it is now established explicitly that POSE believes in a lossless human body capable of generating free energy"
Where have you found it written about generating free energy? Pose says that is teaches to harness free energy.