If you want to get technical about the physics, we can do that.

Here are the basics: nothing is 'online', online is not a state of matter, or of anything. Fission produces energy, as does fusion. This guy called einstein even figured out a famous equation to express the released energy, you have probably heard of it. As the names suggest, fission is a split which is easiest done to heavy elements (since their large atomic radius is at a distance where the short range 'strong' force is tapering off, making it inherently more unstable than lighter elements) , and fusion is a joining, done mainly to light elements since they are the easiest/lightest to smash together at speeds high enough to overcome the mutual repulsion and fuse. Both release energy, since the mass after is less than the mass before the reaction. Its the heat that makes bomb explosions hot, that gives the reactor 'coolant' their heat that is used to boil water and run turbines with steam. Easy.

We know of natural fission and fusion reactions, all going on without the aid of people. If fusion were not possible, the stars wouldnt be shining. If fission were not possible, well ive mentioned the reactor power plants, and there are also fission products found in rock formations that demonstrate isotopes typical of uranium reaction products - one such was found in Gabon.

Radiation is provable and measurable, both in EM form and alpha/beta particles. You can detect it, defract it, shield against it, deflect the charged particle types in fields, and so on.

So presumably radioactive decay is something believable, indicating other nuclear reactions like fission and fusion are also possible.

Where are the holes or gaps in the theory?

I just dont think the 'tells' are there that you assert. Supposedly Germany had a quantity of refined weapon grade material that was spirited away to the US after the war, operation-paperclip style. So did Japan, or at least the makings of research projects that would have led them down that same direction.