Jed Rothwell wrote:

I suppose the cathode might have been storing and releasing heat at the same time, but how could you tell with a calorimeter?

One expected effect of an experiment which is both storing and releasing excess heat at the same time would be a period of so-called heat-after-death following shut-down.

Aside from that kind of direct proof, no one understands the mechanism for storage of nuclear changes but a good candidate would be a mechanism which results in "dense hydrogen". (technically this is not nuclear, but it is closer to nuclear than to chemistry)

If we had a rock-solid experiment which was clearly able to show heat-after-death, then perhaps efforts could be made to collect and characterize dense hydrogen.

The problem of course is that there is no rock solid experiment capable of showing heat-after-death.

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