The mathematical proof of the misdefinition of kinetic energy is simple and unquestionable. The logic is just as unquestionable. Rockets clearly show the error. When they are constant powered, they produce a constant force. Constant force means the product is force times time. Force times time is mathematically equal to mv, momentum, for an accelerating mass. It means rockets transform energy in proportion to mv, not mv².
A closely related proof is even more obvious. Power is defined in physics as rate of energy addition. For ½mv² of a constant mass, power is ½mv² divided by time, which is force times velocity, Fv. Notice what happens with a constant powered rocket (as most are). They increase in velocity, which causes the total Fv to increase. The power of the mass is increasing, while the power of the rocket engine is constant. Eventually, the mass can acquire power at a rate greater than the engine provides, an impossibility.
Where did Einstein get the equation, E=mc²? Physicists say he paralleled the kinetic energy equation, KE=½mv². Since that equation can be proven to be in error, he paralleled an erroneous equation.
Where it matters is hydrogen fusion. Physicists expect to get energy from hydrogen fusion in proportion to E=mc². If that equation were to parallel the correct definition of energy, it would have to be E=mc. There is immensely less energy when not squaring the velocity of light. It means there is very little energy in hydrogen fusion.
A few weeks ago, American physicists discontinued their attempts to create useable energy through hydrogen fusion using lasers due to total failure. They were so sure that the procedure would work that they did no preliminary experiments. Everything worked flawlessly, except there was almost no energy released. Of course there were theories of what might have gone wrong, but nothing concrete enough to continue with the project. The result is another indication that the energy equation is in error, and E does not equal mc².
The counter-argument is that hydrogen bombs show that there is a huge amount of energy in hydrogen fusion. A closer look indicates more wishful thinking than fact. Consider this quote on hydrogen bombs from Wikipedia: "...though in most applications the majority of its destructive energy comes from uranium fission, not hydrogen fusion alone." Physicists cannot determine the difference between most and all. It means there is no verification that hydrogen fusion exists in hydrogen bombs.
The description of how hydrogen bombs work looks like more wishful thinking and hocus pocus than fact. When physicists cannot produce hydrogen fusion with several decades of trying under laboratory conditions, the assumption of it happening in the clutter of an explosion is not credible.
Since the misdefinition of kinetic energy is beyond question, and Einstein created an improper equation for turning mass into energy, the mysteries of hydrogen fusion are beyond doubt due to an absence of significant energy being produced from fusion.
Why would most of the energy in a hydrogen bomb come from fission instead of fusion? Why bother with a small amount of fusion, when it is supposed to be the superior source of energy? It wouldn't happen. It means physicists know they are not getting energy from fusion in a hydrogen bomb, and they are lying about it. The motive would be to sustain the fakery of fusion power and the fraud of Einstein's equation.