Are you arguing that the only fusion that can be known to science is production of He from deuterium? Catalyzed fusion is not dependent on a solid like Pd.
As far as I know, it is dependent on a solid like Pd. I have never heard of catalyzed fusion with a gas or liquid.
However, I did not say it is dependent on a solid. I said that when two deuterons fuse to form a helium atom, they release 24 MeV of energy. Whatever method you use to make them fuse, in a plasma, a solid state, or some state that you know of that I have not heard of, they always produce that much energy. Because of the mass deficit. That is a theory: special relativity. (Apparently, THH does not think special relativity is a theory . . . who knows what he thinks? He won't say.)
This is similar to the fact that when oxygen and carbon combine, they always produce 393.5 kJ/mol. Whether they combine in a fire, or in your cells with metabolism, they always produce that much heat. That was first confirmed by Lavoisier in 1780. He measured the heat of metabolism and the CO2 production from a guinea pig placed inside an ice calorimeter. He compared the results to combustion. (He also reported that the guinea pig was fine. It "did not suffer" at all.)
In other words, when the starting and ending materials in a chemical or nuclear reaction are the same, the heat release or absorption will be the same, even when the reaction paths are different. This is thermodynamics. Which is another theory that THH does not think is a theory.