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oai:figshare.com:article/33604633 2026-09-30T18:00:16Z category_29794 category_29797 item_type_12 month_year_09_2026

<b>Effective Metronic Geometrodynamics: A Computable Field-Theoretic and Variational Modernization of Burkhard Heim’s Unified Physics</b> Mr. Symplex (24499997) Mathematical aspects of general relativity Mathematical aspects of quantum and conformal field theory, quantum gravity and string theory Burkhard Effective field theory (EFT) Discrete Exterior Calculus Kaluza-Klein Theory (KK) Lean 4 Tensor Networks <p dir="ltr">This repository contains the complete open-source research archive for <b>Effective Metronic Geometrodynamics (EMG)</b>, including formal mathematical monographs, computational engines, numerical datasets, concordance tables, and machine-checked proof certificates. EMG presents a computable effective-field-theory and variational extension of Burkhard Heim’s unified geometrodynamic program, with particular reference to <i>Elementarstrukturen der Materie</i> and the 1976 MBB Lectures.</p><p dir="ltr">The mathematical framework reformulates selected elements of Heim’s discrete geometrodynamics using modern <b>Discrete Exterior Calculus (DEC)</b>, simplicial geometry, effective field theory, higher-derivative and non-local operators, Kaluza–Klein reduction, topological soliton constructions, and tensor-network methods. The archive includes an 11-chapter EMG monograph, formal reconstructions of Heim’s Physics volumes and MBB lectures, a Python mass-calculation engine, and a Julia DMRG/MPO soliton solver.</p><p dir="ltr">The <code>/proofs</code> directory contains a <b>Lean 4 / Mathlib formalization</b> of selected mathematical claims, including positivity of the metronic area scale, the non-Leibniz product-rule defect, Faulhaber shell polynomials, mass-ordering relations, nucleon mass-splitting bounds, and the formal treatment of fermion doubling on the metronic lattice. The <code>/data</code> directory provides numerical spectrum tables covering 80 stated hadron and lepton states together with formula concordances linking historical Heim expressions to their modern mathematical formulations.</p><p dir="ltr">The archive also reports numerical comparisons for quantities including the electron, proton, and neutron masses, fine-structure constant, weak mixing angle, elementary charge, hadronic string tension, and a proposed gravitational-wave echo timescale. These comparisons are provided as computational benchmarks rather than independent experimental validation: <b>formal proofs establish the encoded mathematics, while numerical agreement with observations does not by itself establish the physical validity of EMG</b>. The repository is structured to allow the mathematical definitions, computational implementations, numerical results, and verification artifacts to be inspected and reproduced independently.</p> 2026-09-30T18:00:16Z Text Preprint 10.6084/m9.figshare.33604633.v11 https://figshare.com/articles/preprint/_b_Effective_Metronic_Geometrodynamics_A_Computable_Field-Theoretic_and_Variational_Modernization_of_Burkhard_Heim_s_Unified_Physics_b_/33604633 CC BY 4.0