Kotlyar–Riemann Postulate, Version 1.51 A Potential Universal Passivity Framework for the Riemann Hypothesis

Version 1.51 — Full-response licensing and remainder correction Retains the passivity-led framework while removing the requirement that every individual remainder be passive. It shows that the prior remainder condition fails at sufficiently large degree, without disproving passivity of the complete response. The target becomes one exact licensed passive realization of the full arithmetic response at each degree. The conditional RH theorem remains intact; independent verification of that arithmetic realization remains outstanding. Version 1.50 — Passivity-led integrated framework Reorganizes the Kotlyar–Riemann Postulate around arithmetic passivity as the primary possible route to RH. It introduces the exact theta-defined degree-extension recurrence, incorporates modified Dorraki circuits and the universal AC passivity license, and presents the complete conditional implication all-degree arithmetic passivity ⇒ RH. Earlier spatial, spectral, disk, and GSRC results are integrated as supporting material. It also proposes passivity of each recurrence remainder as a possible construction route. This work presents a research framework, not a proof of the Riemann Hypothesis. OpenAI’s ChatGPT assisted with organizing prior research material, preliminary mathematical analysis, literature identification and checking, drafting, editing, and typesetting. AI assistance does not constitute independent mathematical verification, peer review, or formal proof certification. AI tools are not credited as authors.