Möbius-Unitary Positivity and Deranged Zero-Orbit Signatures in the Weil-Li Framework

This manuscript formalizes an evidence-bounded mathematical finding: the Möbius transform mu(s)=1-1/s maps the critical line Re(s)=1/2 to the unit circle, converting Li-coefficient positivity into a unitary phase-energy statement. Under the Riemann Hypothesis, a nontrivial zero rho=1/2+i gamma has z_rho=mu(rho)=exp(i theta_gamma), and its conjugate pair contributes |1-exp(i n theta_gamma)|^2 >= 0 to the nth Li coefficient, under the standard symmetric regularization. If a zero is off the critical line, the deranged orbit rho, conjugate(rho), 1-rho, and 1-conjugate(rho) maps to z, conjugate(z), z⁻¹, and conjugate(z)⁻¹, giving the orbit-energy expression E_n=4-2(r^n+r⁻ⁿ)cos(n theta). For r != 1 this term produces exponentially amplified negative signatures along aligned subsequences, exposing why Li positivity is an effective detector for off-line zeros. The manuscript does not claim a proof of the Riemann Hypothesis. Instead, it identifies the hidden positive structure that any proof must make unconditional: a Hilbert-space or operator model in which the Weil/Li form is a genuine positive norm and the corresponding spectral operator is unitary. The research is contextualized using the author's PCIDT fixed-point/derangement methodology, Aletheia-style evidence separation, MCDS-style falsifiability discipline, and VQCA project artifacts. Non-claims (from docs/NON_CLAIMS.md): This manuscript does not prove the Riemann Hypothesis. It identifies a hidden positive structure and proof target. The contribution is a proof architecture, not a completed proof. Files: mobius_unitary_positivity_manuscript.pdf (main manuscript, 8 pp.); mobius_unitary_positivity_repo_v1.0.0.zip (supplementary: full repository with LaTeX/DOCX sources, figures, bibliography, VQCA data artifacts, and metadata). Version 1.0.0 (repository release date 2026-06-21).