Exact Symmetries in Discrete Gauge-Gravity Dynamics: A Unified Computational Framework

Exact Symmetries in Discrete Gauge-Gravity Dynamics: A Unified Computational Framework | 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 Article Exact Symmetries in Discrete Gauge-Gravity Dynamics: A Unified Computational Framework Anoop Madhusudanan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7755172/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 present a computational framework unifying discrete exterior calculus, lattice gauge theory, and discrete-time quantum walks, where fundamental symmetries become exact algebraic identities at finite lattice spacing rather than approximate continuum limits. Fields are represented as cochains on oriented cell complexes with a discrete wedge product satisfying the graded Leibniz rule. Dynamics consists of holonomic shifts—permutations decorated by spatial and temporal link variables encoding space-time rectangle holonomies. We prove and verify numerically to∼10 −15 residual - (i) sitewise probability continuity for split-step Dirac walks; (ii) time-dependent non-Abelian (SU(2)) gauge intertwiner identities; (iii) lattice U(1) Ward identities for vac-uum polarization; (iv) exact commutation of class-function plaquette dynamics with Gauss constraints; (v) palindromic Cayley integration preserving Einstein–Cartan vertex closure. The Whitney restriction operator commutes exactly with the coboundary (Rd= dR), enabling symmetry-preserving renormalization. This framework provides structure-preserving numerics for non-perturbative field theory and clarifies how continuum symmetries emerge from discrete structure Physical sciences/Physics/Information theory and computation Physical sciences/Mathematics and computing/Computational science discrete exterior calculus lattice gauge theory quantum walks exact gauge invariance Ward identities structurepreserving integration Full Text Additional Declarations There is NO Competing Interest. 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. 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Fields are represented as cochains on oriented cell complexes with a discrete wedge product satisfying the graded Leibniz rule. Dynamics consists of holonomic shifts—permutations decorated by spatial and temporal link variables encoding space-time rectangle holonomies. We prove and verify numerically to∼10\u003csup\u003e−15\u003c/sup\u003e residual - (i) sitewise probability continuity for split-step Dirac walks; (ii) time-dependent non-Abelian (SU(2)) gauge intertwiner identities; (iii) lattice U(1) Ward identities for vac-uum polarization; (iv) exact commutation of class-function plaquette dynamics with Gauss constraints; (v) palindromic Cayley integration preserving Einstein–Cartan vertex closure. The Whitney restriction operator commutes exactly with the coboundary (Rd= dR), enabling symmetry-preserving renormalization. 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