I just would like to focus as much as possible on the information contained in the ICCF3 paper.
Why? So you can pretend the rest of the information does not exist?
The oscilloscope is an unnecessary distraction.
No, it proves they measured all of the power (I*V) at high resolution, which proves you are wrong. It also proved that Morrison was wrong, which got his goat. He claimed they only measured every 10 minutes, as I recall.
If you take foam for liquid, as F&P did in their ICCF3 paper, you can easily produce even higher apparent gains.
If it were foam, unboiled water would leave the cell, and much of the lithium salt would be missing. So you are wrong. Either you do not understand this simple fact, or you will not admit it. I recommend you do some actual electrochemistry with ordinary salt -- and detergent if you like. You need to stop waving your hands and inventing impossible physics. Do some real world observations and you will see that you have not discovered something that other people overlooked since 1867.