The Sub-Leading Weyl Mismatch and the Constant-Term Gap

Research Note 46 in the "Geometry of the Critical Line" programme. The post-quotient Sturm–Liouville counting on the SCT critical sector matches the Riemann–von Mangoldt law at leading order: Nₚost (E) = E log E / (2π) + O (E). The remaining discrepancy lies in the sub-leading linear term. On the geometric side, the Stieltjes–Mellin analysis gives a heuristic sub-leading coefficient of γ/ (2π). On the arithmetic side, the Riemann–von Mangoldt formula has linear coefficient − (1 + log (2π) ) / (2π). This note records the precise form of the gap, documents corrections to two prior geometric estimates (the full-carrier reduction factor and the quarter-lattice Epstein residue), and isolates the remaining analytic task: a rigorous derivation of the geometric sub-leading term and its conversion by the arithmetic extractor.