2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227870We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution; this subsequently allows us to formally derive an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and also offer a physical interpretation of the result and discuss the Hilbert-Polya approach.LaTeX, 18 pages; subtleties in convergence and branch cut addedMathematical PhysicsHigh Energy Physics - TheoryNumber Theorytext