Zero-Anchored Logan Explicit-Formula Pilot for the von Mangoldt Function at n = 101

This restricted computational research documents a governed single-integer pilot for recovering the local von Mangoldt observable from a Logan-smoothed explicit-formula representation of the Riemann zeta zeros. The construction uses the half-integer anchors x₋ = n − 1/2,x₊ = n + 1/2, so that, for the frozen pilot n = 101, ψ(101.5) − ψ(100.5) = Λ(101). The half-integer placement removes the local de-smoothing correction at the two anchors because the relevant Logan support windows contain no integer prime powers. The resulting observable is expressed through a finite Logan-weighted sum over non-trivial zeta zeros together with explicitly bounded analytic remainder terms. For the frozen pilot parameters n = 101,ε = 0.001,c = 11,T = 11000, the cutoff contains 11,324 positive zeta-zero ordinates, with the next zero serving as an explicit cutoff guard. A blind numerical Primary computation was frozen before the arithmetic Control for n = 101 was opened. The blind Primary center obtained from the Logan explicit-formula route is approximately A₁₀₁ = 4.6151346, while the subsequently opened independent arithmetic Control gives Λ(101) = log(101) ≈ 4.6151205. The two routes are concordant. The current research status is: STRONG CANDIDATE PASS — DIRECTED PROMOTION WITHHELD. The remaining promotion gate is complete authoritative binding of the full zero-ordinate source payload, or an equivalent outward-rounded directed enclosure of all zero ordinates used in the finite computation. Numerical reconstruction, cutoff checks, distributed source comparisons, analytic tail control, source-sensitivity analysis, and Primary/Control ordering have been retained as separate auditable layers. This draft does not claim: a proof of the Riemann Hypothesis; that all non-trivial zeta zeros lie on the critical line globally; a general prime-number detector; an exact next-prime theorem; a global theorem derived from the single n = 101 pilot; PF∞ or any equivalent all-order positivity result. The deposit is maintained as a restricted, for controlled scholarly review and provenance preservation. Public release, broader distribution, or promotion of the mathematical status requires a separate explicit release decision. DOI: 10.5281/zenodo.22658662 Copyright © 2026 Alexanja Senke. All rights reserved. This restricted research draft and its accompanying computational, mathematical, documentary, and reproducibility materials are provided solely for authorized private scholarly review and evaluation. No license is granted to reproduce, adapt, modify, distribute, republish, publicly communicate, implement, commercialize, sublicense, or otherwise exploit the work or any protected mathematical, computational, software, data-processing, architectural, or technical mechanism contained in it, except to the extent that such rights cannot lawfully be excluded. No patent, software, hardware, trade-secret, trademark, certification, conformity-assessment, deployment, implementation, or commercial-use license is granted or implied. Any use beyond authorized private review requires prior written permission from the rights holder.