I have no idea what you're trying to prove with this diffuse polemic. Deuterons are particles, and if deuterium converts to helium then you have fewer deuterons and more helium nuclei. This does not exclude the participation of electrons, but the number of electrons doesn't change.
It's actually clear, but clear to one who understands the background, I'm sure. I'm surprised to find that Joshua doesn't understand this, if he doesn't.
He is correct. The number of electrons apparently does not change. However, in muon-catalyzed fusion, the number of muons don't change, either. The muon "catalyzes" the fusion. Single electrons don't do that. D2 gas doesn't spontaneously fuse, even if you get if very cold. Has Joshua read Takahashi? I've been pointing out that nobody with the requisite chops has critiqued Takahashi (either way). When I came into the field, I found that hardly anyone understood what Takahashi was saying. He was difficult to read. For example, he doesn't point out that he is essentially considering deuterium molecular fusion, two deuterium molecules. Not four deuterons, as such. So there are four electrons involved, and they must be there, or a collapse could not occur, because of Coulomb forces. No BEC could form without those electrons.
So this is not at all "deuterons fusing," it is deuterium fusing. Even though it is four deuterons (in that theory, we do not know what is actually happening), and results in two helium nuclei, so it is like deuterons fusing, but isn't the same.
Muon-catalyzed fusion was predicted before being observed, yes. Cold fusion wasn't. Pons and Fleischmann were looking for a fusion effect, and would have expected neutrons and tritium (and protons and 3He). And some heat. The thought the effect would be very small, if it was observable at all. That they found something has to be one of the most astonishing pieces of luck in the 20th century. Later, it was found that almost all palladium didn't work! It was many years of work to find out how to enhance results by palladium processing, and it is still not particularly reliable. What they found confused them -- and everyone else.
Nobody predicted cold fusion for very obvious reasons. Suppose something like Takahashi TSC theory is correct. That's an effing complex calculation. Nobody expected that this would allow fusion, so nobody undertook the study, Takahashi has put years into it. Muon-catalyzed fusion was far, far simpler to calculate. What led Takahashi to his study? Well, first of all, he'd seen cold fusion results. There has to be some explanation somewhere. And then his experimental work, which was quite what a hot fusion physicist would do: deuteron bombardment of palladium deuteride, he saw greatly enhanced (I recall 10^23 enhanced) 3-deuteron fusion products. This was hot fusion, but 3-deuterons? Not expected. Something unexpected was happening involving multibody reactions. That has become a widely accepted understanding of cold fusion, in the field, that somehow multibody reactions are involved.