A p-adic Bridge from Wilson's Theorem to the Riemann Zeta Function
Year: 2026
Type: preprint
Abstract: . This paper provides the formal and unconditional analytical resolution of theYousef-Dirichlet Spectral Positivity Conjecture (formerly Conjecture 14.1). By mappingthe discrete complex denominator lattice into a continuous wave domain, we introduce amicro-local directional perturbation framework (s = ρ0 ± ϵ) to evaluate the continuouswave kernel ψ(x). We prove that the odd-order perturbation terms of the phase modulationoperator Z(n) undergo complete algebraic annihilation under the global cyclotomic reflectionsymmetry. Furthermore, by interfacing these results with the determinants of the 4 × 4Hermitian global matrix operator, we establish that the eigenvalues are strictly invariantand locked. Consequently, secondary non-trivial zeros outside the critical Riemann halfline Re(s) = 1/2 are structurally prohibited, establishing the unconditional stability of theglobal prime density spectrum.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172296381
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