MATHEMATICAL ANALYSIS Self-Adjointness as System Integrity

ABSTRACT Bender, Brody, and Müller (2017) constructed a Hamiltonian operator Ĥ whose eigenvalues correspond to the non-trivial zeros of the Riemann zeta function ζ (s), and showed that if Ĥ can be proven self-adjoint on a suitable Hilbert space, then the Riemann Hypothesis (RH) follows. This paper proposes that the Universal Balance–Feedback Framework (UBFF) provides a natural dynamical language for this central open gap. The five UBFF laws correspond precisely to five structural operator-theoretic conditions that ĤBBM must satisfy for self-adjointness. A composite Lyapunov-type functional ℒĤ is defined; the UBFF Self-Adjointness Conjecture states that ℒĤ = 0 is equivalent to self-adjointness of Ĥ, and hence to RH. Six required lemmas are enumerated with statuses; the deficiency-index lemma remains the central open problem. This analysis positions UBFF as a falsifiable structural conjecture at the frontier of the spectral approach.