>  Each appendix isolates and resolves one of the classical obstacles to a self-contained Hilbert–Pólya formulation—self-adjointness, trace-class bounds, Paley–Wiener confinement, Weyl normalization, and uniqueness of the arithmetic weights.

Given the nature of the problem and the unsolicited mention of a "confinement manifold" earlier in the abstract, this summary gives very strong vibes of "My corral has six well closed gates, why do you keep asking about the fence?". This is in addition to not trusting complex and unclear proofs.