Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology
We present Hypatian Physics, a Lean4-verified framework that unifies quantum gravity, particle physics, and cosmology via a recursive algebraic-geometric formulation. Our approach formalizes fundamental structures such as recursive Jordan algebras, p-adic metric spaces, and recursive renormalization...
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2025
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| _version_ | 1849927625903964160 |
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| author | Del Bel, Julian (21403013) |
| author_facet | Del Bel, Julian (21403013) |
| author_role | author |
| dc.creator.none.fl_str_mv | Del Bel, Julian (21403013) |
| dc.date.none.fl_str_mv | 2025-11-25T18:59:22Z |
| dc.identifier.none.fl_str_mv | 10.5281/zenodo.15219237 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/online resource/Hypatian_Physics_Lean4-Verified_Framework_Recursive_Expansive_Algebraic-Geometric_Quantum_Gravity_Particle_Physics_and_Cosmology/30559529 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical methods and special functions Algebraic structures in mathematical physics Mathematical aspects of general relativity Mathematical physics not elsewhere classified Combinatorics and discrete mathematics (excl. physical combinatorics) Fractal Geometry, Time Irreversibility, Quantum Entangle ment Entropy, Spacetime Phase Transition, Black Hole Thermodynamics Fractal Geometry; Yang-Mills Theory; Mass Gap; Topological Quantum Field Theory; Renormalization Group; Langlands Program Fractal geometry; Laplace operator; Sobolev space; spectral analysis; regu larity; multiscale phenomena Fractal Geometry; Langlands Program; Mass Gap; Yang-Mills Theory; Holographic Dimensionality Reduction Fractal geometry, Cartan formula, holographic emergence, string theory, non-local differential operators, fractal curvature recursive expansive dynamics Hypatian |
| dc.title.none.fl_str_mv | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| dc.type.none.fl_str_mv | Text Online resource info:eu-repo/semantics/publishedVersion text |
| description | We present Hypatian Physics, a Lean4-verified framework that unifies quantum gravity, particle physics, and cosmology via a recursive algebraic-geometric formulation. Our approach formalizes fundamental structures such as recursive Jordan algebras, p-adic metric spaces, and recursive renormalization group flows. The theory yields empirically testable predictions, including gravitational wave echoes, non-zero fermion masses via Yukawa couplings, and fractal spacetime geometries consistent with cosmological observations. Formal Proof of Recursive Topological Vertex, Recursive Mirror Symmetry, and Recursive Renormalization Group Flow. The sequence C(n)λµν converges to a unique limit C(∞)λµν. The convergence of the sequence is established through the geometric decay of the recursive terms and the application of the Banach Fixed-Point.<p></p> |
| eu_rights_str_mv | openAccess |
| id | Manara_99d496b7407ddc0c69d3fc56815fd671 |
| identifier_str_mv | 10.5281/zenodo.15219237 |
| network_acronym_str | Manara |
| network_name_str | ManaraRepo |
| oai_identifier_str | oai:figshare.com:article/30559529 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and CosmologyDel Bel, Julian (21403013)Mathematical methods and special functionsAlgebraic structures in mathematical physicsMathematical aspects of general relativityMathematical physics not elsewhere classifiedCombinatorics and discrete mathematics (excl. physical combinatorics)Fractal Geometry, Time Irreversibility, Quantum Entangle ment Entropy, Spacetime Phase Transition, Black Hole ThermodynamicsFractal Geometry; Yang-Mills Theory; Mass Gap; Topological Quantum Field Theory; Renormalization Group; Langlands ProgramFractal geometry; Laplace operator; Sobolev space; spectral analysis; regu larity; multiscale phenomenaFractal Geometry; Langlands Program; Mass Gap; Yang-Mills Theory; Holographic Dimensionality ReductionFractal geometry, Cartan formula, holographic emergence, string theory, non-local differential operators, fractal curvaturerecursive expansive dynamicsHypatianWe present Hypatian Physics, a Lean4-verified framework that unifies quantum gravity, particle physics, and cosmology via a recursive algebraic-geometric formulation. Our approach formalizes fundamental structures such as recursive Jordan algebras, p-adic metric spaces, and recursive renormalization group flows. The theory yields empirically testable predictions, including gravitational wave echoes, non-zero fermion masses via Yukawa couplings, and fractal spacetime geometries consistent with cosmological observations. Formal Proof of Recursive Topological Vertex, Recursive Mirror Symmetry, and Recursive Renormalization Group Flow. The sequence C(n)λµν converges to a unique limit C(∞)λµν. The convergence of the sequence is established through the geometric decay of the recursive terms and the application of the Banach Fixed-Point.<p></p>2025-11-25T18:59:22ZTextOnline resourceinfo:eu-repo/semantics/publishedVersiontext10.5281/zenodo.15219237https://figshare.com/articles/online resource/Hypatian_Physics_Lean4-Verified_Framework_Recursive_Expansive_Algebraic-Geometric_Quantum_Gravity_Particle_Physics_and_Cosmology/30559529CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/305595292025-11-25T18:59:22Z |
| spellingShingle | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology Del Bel, Julian (21403013) Mathematical methods and special functions Algebraic structures in mathematical physics Mathematical aspects of general relativity Mathematical physics not elsewhere classified Combinatorics and discrete mathematics (excl. physical combinatorics) Fractal Geometry, Time Irreversibility, Quantum Entangle ment Entropy, Spacetime Phase Transition, Black Hole Thermodynamics Fractal Geometry; Yang-Mills Theory; Mass Gap; Topological Quantum Field Theory; Renormalization Group; Langlands Program Fractal geometry; Laplace operator; Sobolev space; spectral analysis; regu larity; multiscale phenomena Fractal Geometry; Langlands Program; Mass Gap; Yang-Mills Theory; Holographic Dimensionality Reduction Fractal geometry, Cartan formula, holographic emergence, string theory, non-local differential operators, fractal curvature recursive expansive dynamics Hypatian |
| status_str | publishedVersion |
| title | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| title_full | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| title_fullStr | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| title_full_unstemmed | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| title_short | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| title_sort | Hypatian Physics Lean4-Verified Framework Recursive Expansive Algebraic-Geometric Quantum Gravity, Particle Physics, and Cosmology |
| topic | Mathematical methods and special functions Algebraic structures in mathematical physics Mathematical aspects of general relativity Mathematical physics not elsewhere classified Combinatorics and discrete mathematics (excl. physical combinatorics) Fractal Geometry, Time Irreversibility, Quantum Entangle ment Entropy, Spacetime Phase Transition, Black Hole Thermodynamics Fractal Geometry; Yang-Mills Theory; Mass Gap; Topological Quantum Field Theory; Renormalization Group; Langlands Program Fractal geometry; Laplace operator; Sobolev space; spectral analysis; regu larity; multiscale phenomena Fractal Geometry; Langlands Program; Mass Gap; Yang-Mills Theory; Holographic Dimensionality Reduction Fractal geometry, Cartan formula, holographic emergence, string theory, non-local differential operators, fractal curvature recursive expansive dynamics Hypatian |