The Prime Structure of Electromagnetic Constants

The Prime Structure of Electromagnetic Constants | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Prime Structure of Electromagnetic Constants Jian Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9143298/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We systematically rewrite eighteen electromagnetic quantities—from the Bohr radius to the quantum Hall conductance—in a canonical form built from the Riemann zeta value ζ(−3) = 1/120 and the primes {2, 3, 5}. Starting from the ζ-Wyler identity α = 3²ζ(−3)^{1/4}/(2⁴π^{11/4}), every quantity Q with mass dimension d decomposes as Q = mₑᵈ × f(2, 3, 5, π, ζ(−3)), requiring only one experimental input (the electron mass) plus pure mathematics. Three structural results emerge: a Rationality Theorem (α⁴π¹¹/ζ(−3) = 3⁸/2¹⁶), a Mirror Theorem linking quantum-vacuum α to thermal-vacuum ζ(4) via the functional equation, and an mₑ-Separation Principle. All eighteen theoretical values match CODATA 2018 to within 0.30–3.05 ppm, governed by a single offset Δα/α = 6.1 × 10⁻⁷. This is the companion paper to "The Arithmetic of Light" [doi:10.6084/m9.figshare.31744981]. fine-structure constant Riemann zeta function functional equation Wyler’s formula prime factorisation me-separation principle quantum electrodynamics thermal–vacuum duality Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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