[kosta50]

HIlbert's tenth problem involves Diophantine equations

I suspect it involves 'axiomatic' truth, which is theoretical. I further suspect that maybe it is akin to uncertainty principle, which is a limit imposed by the model and not the true nature of the energy 'particle.'

I am asking for an example of something that is true but cannot be proven in the real world, not in a mathematical model.

[D-fendr]

I suspect it involves 'axiomatic' truth,

Nope. That's a completely different discussion.

This is just math. Diophantine equations are equations of a particular form.

[D-fendr]

I probably should have added that the variables in the equation, the Xs, can represent “real world” things.

[D-fendr]

Matiyasevich's work is available online:

Hilbert's tenth problem