Spectral problem for the interface tensor: fine-tuned constants of physics

We pose a problem for mathematical physicists working at the intersection of spectral theory, quan- tum foundations, and the constants problem. The problem is precisely stated, with preconditions, a candidate mechanism, a falsifiable prediction, and a clear delineation of what would constitute a solution. It is offered not as a theory, but as a well-posed problem. The motivation is structural: if the dimensionless constants of physics are eigenvalues of a self-adjoint operator on the abstraction Hilbert space, then fine-tuning is dissolved rather than solved, and the laws themselves are eigen- modes of a deeper quantum structure. We do not attempt the formalization. We state the problem for those with the expertise to attempt it.