Hypercomplex General Relativity (HGR): A symplectic and geometric reformulation of Weyl, hypercomplex numbers with late cosmological applications.

Hypercomplex General Relativity (HGR): A symplectic and geometric reformulation of Weyl, hypercomplex numbers with late cosmological applications. | Zenodo Skip to main Communities My dashboard Log in Sign up Zenodo is currently experiencing slowness and intermittent outages due to heavy automated traffic from bots and AI crawlers. We are aware of the problem, and our team is focused on stabilizing the service. Thank you for your patience. Advanced Theoretical Physics and Mathematics There is a newer version of the record available. Published May 10, 2026 | Version v32 Journal article Open Hypercomplex General Relativity (HGR): A symplectic and geometric reformulation of Weyl, hypercomplex numbers with late cosmological applications. Authors/Creators Besson, Laurent (Contact person) Description Hypercomplex General Relativity (HGR), also referred to as Relativité Générale Hypercomplexe (HGR) in French, is a unified theoretical framework... This deposit gathers and documents the complete body of work related to Hypercomplex General Relativity (HGR), an extension of General Relativity developed by Laurent Besson. HGR introduces an internal hypercomplex structure within the spacetime metric, allowing a reformulation of gravity that preserves local consistency and the standard relativistic limit while avoiding Ostrogradsky-type instabilities. The present record synthesizes successive versions of the model, including the initial formulation (2015), a comprehensive theoretical update (2025), and recent additions addressing critical discussions. In a cosmological context, the model leads to a holographic-like behavior characterized by a late-time geometric component compatible with current observational constraints from the Cosmic Microwave Background and large-scale structure data. This deposit includes the Lagrangian formulation, the field equations, and numerical implementations based on a modified version of standard cosmology codes, and is released within an open science framework to ensure long-term accessibility, reproducibility, and citation. Keywords: general relativity, modified gravity, hypercomplex geometry, cosmology, theoretical physics. Objective The goal of this development is to refine the internal structure of Hypercomplex General Relativity and determine whether quantization of the internal sector is physically necessary or conceptually supportive. The previous classical formulation introduced a curvature-dependent threshold controlling local gravitational corrections. The present work reinterprets this threshold in terms of a canonical internal gauge structure. 1. Canonical Structure of the Internal Sector The hypercomplex connection is modeled as a non-abelian gauge field. A full Hamiltonian analysis is performed, including: 3+1 decomposition, identification of canonical variables, Gauss constraint implementation, well-defined phase space. The non-commutative structure emerges from the symplectic form and canonical commutation relations, rather than being assumed. This establishes that the internal HGR sector possesses a legitimate gauge-theoretic foundation. 2. Construction of a Gauge-Invariant Internal Observable A scalar observable is constructed from quadratic electric-like and magnetic-like internal invariants. This observable: is locally gauge invariant, is positive definite, can be promoted to an operator, controls the effective gravitational correction threshold. The threshold becomes state-dependent via expectation values, introducing a statistical interpretation of rebound domains. 3. Semi-Classical Regime In a semi-classical approximation, fluctuations of the internal observable modify the effective threshold. This implies that: internal quantum variance may broaden the population of rebound-triggering domains, the mechanism admits a probabilistic interpretation at high curvature. However, the core rebound mechanism does not rely strictly on quantization. 4. Internal Saturation Mechanism A critical issue arises: without regulation, the internal scalar could grow unbounded at high curvature. To ensure stability, a saturation function is introduced: the internal response becomes bounded, corrections remain finite, ultraviolet divergence is avoided, local activation remains possible. This mechanism stabilizes the theory without requiring full quantum gravity. 5. Conceptual Status at the End of This Stage Established: Canonical internal gauge structure. Well-defined observable controlling corrections. Dynamically bounded internal response. Stabilized domain-triggered rebound mechanism. Not yet addressed: Full quantization of gravity. Complete cosmological perturbation analysis. Weak-field post-Newtonian constraints. Strategic Insight Quantization of the internal sector provides micro-structural grounding and theoretical elegance. However, the macroscopic consistency of HGR does not depend on full gravitational quantization. The saturation mechanism alone is sufficient to ensure stability and physical viability. This stage transforms HGR from an intuitive hypercomplex extension into a symplectically structured, dynamically regulated gravitational framework. ========================================== Appendix: HGR: Beginning of quantization. Appendix: Dark matter galaxies or halos and rotation speed, Dark matter-dominated galaxies, Hypercomplex halos in HGR. Weakless interaction between dark matter H0 equation. RGH manuscript hardening Files hgr_complete_symplectic_rewriting_en.pdf Files (25.6 MB) Name Size Download all annexe_conventions_unites_rgh.pdf md5:af9d29416e6c4ddb7452da693cb2424c 193.4 kB Preview Download annexe_rgh_bulle_alcubierre_like.pdf md5:624662d85d716405d3d0ecec84b302c8 320.9 kB Preview Download Application_numerique_hypothetique_rebond_stellaire_RGH.pdf md5:5ec8d4f2647c58ceb9b69b7b8b9f4abd 297.9 kB Preview Download Application_numerique_rebond_domaines_CEN_controlee.pdf md5:8120c7cbc170acc0d1ad17bb2be627d5 313.6 kB Preview Download Application_numerique_rebond_domaines_CEN_controlee_couplage_delta.pdf md5:5c5ea873c8a4a51bc22b75f2909f1ed0 270.8 kB Preview Download Application_numerique_rebond_domaines_inhomogeneite-V2.pdf md5:b45535185d0fc01083219261c003c598 224.7 kB Preview Download Application_numerique_rebond_domaines_inhomogeneite-V3.pdf md5:90e2f609af29cc3e96c7d23ce5f77d34 309.7 kB Preview Download Application_numerique_rebond_domaines_inhomogeneite.pdf md5:b96877ba3a6a8a74f2bfe863d3e66c8a 304.2 kB Preview Download Application_numerique_rebond_domaines_Kretschmann.pdf md5:13dfbabb09967fe68d9fbe2b0c633e93 311.2 kB Preview Download Application_numerique_rebond_domaines_Weyl_conforme.pdf md5:d84f91f0f9198d1ae9db6fd92d40facd 311.9 kB Preview Download Application_numerique_rebond_domaines_Weyl_conforme_cisaillement.pdf md5:72e47f43c0c2902413b970b1ea5406ee 315.4 kB Preview Download Application_numerique_rebond_interne_pur_omega_J.pdf md5:584a671cd9517bfcb3b92ce45c2d9437 279.1 kB Preview Download Application_numerique_rebond_invariant_maitre_mixte.pdf md5:7494ceb8114337962c5145470a7965d5 260.0 kB Preview Download Application_numerique_rebond_invariant_Weyl_conforme.pdf md5:d2191fa39991272bcbacfc72db02f0ca 298.6 kB Preview Download Application_numerique_rebond_Kretschmann.pdf md5:5fde93434dee572499734fbbf761d7c9 265.1 kB Preview Download Application_numerique_rebond_Kretschmann_cisaillement.pdf md5:6bfe5a2aa59df24cb191390ce46dc9be 254.9 kB Preview Download Application_numerique_rebond_NEC_effective_controlee.pdf md5:05f68fcdc8311c2a8456c9278ff3368b 269.6 kB Preview Download Application_numerique_rebond_Ricci.pdf md5:894ff893bc4b4c1d9e468846ff578352 310.9 kB Preview Download Application_numerique_rebond_Weyl_non_integrable.pdf md5:0afb2953df83b2ab854a079e8cfd6b24 261.1 kB Preview Download Application_numerique_rebond_Weyl_rad_vs_stiff.pdf md5:e896f3845e9f1c4972543cf92b366c28 288.9 kB Preview Download Application_numerique_rebond_X_commutateur_hypercomplexe.pdf md5:bd6af4f1a2976ca5c8d53b67d7920644 325.2 kB Preview Download Application_numerique_rebond_X_commutateur_hypercomplexe_conservation_galaxie_MW.pdf md5:77dc43e3685f4b924089cf53411a51dc 291.7 kB Preview Download Application_numerique_rebond_X_commutateur_hypercomplexe_conservation_galaxie_MW_w_0.65.pdf md5:659807dd07e1b3f73193cbcbf19dcdc4 319.1 kB Preview Download associativite_pas_toujours_la_regle.pdf md5:eaa3f11a8a922214198f1e179d1755d9 129.0 kB Preview Download belles_equations.pdf md5:da6ac76038be4781a26c788a842a9d8f 122.2 kB Preview Download champ_repulsif_effectif_et_reduction_flrw_minimale_rgh_fr.pdf md5:247e8a0c1175eebd7bce1f6030ccd85f 276.8 kB Preview Download charge_hypercomplexe_rgh_note_autonome.pdf md5:5c261d6a2cdb168bffd78c4764f343d3 258.5 kB Preview Download condition_minimale_terme_repulsif_local_annulation_du_poids_rgh_fr.pdf md5:04c2cc2915a44f1c6c15cc07adb90269 233.3 kB Preview Download couplage_entre_deux_champs_hypercomplexes_rgh_fr.pdf md5:22c5b0174548c1f0c29927c9c6ddb56b 245.5 kB Preview Download couplage_faible_ou_nul_entre_champ_de_weyl_et_champ_hypercomplexe_rgh_fr.pdf md5:e792fa3ebff23d2a7221c6d0ed1b6197 219.1 kB Preview Download coupling_between_two_hypercomplex_fields_rgh_en.pdf md5:ffeed4ff1b111e64c1c271e996b66e71 246.0 kB Preview Download dark_fluid_vs_rgh_flrw_bilingue.pdf md5:517a91e591cdf13ca10573125138033b 96.7 kB Preview Download effective_repulsive_field_and_minimal_flrw_reduction_rgh_en.pdf md5:aeea30d61160949739c10d5d540ef4c7 278.5 kB Preview Download feedback_stellaire_et_distribution_baryonique_rgh_fr.pdf md5:8bd0b6b12b99bb0cbe73ab5e82ef52f9 144.3 kB Preview Download fermeture_semi_quantique_minimale_de_h0_rgh_fr.pdf md5:3ad9863beeeb160207d3a9b4396de5f4 277.4 kB Preview Download flux_baryonique_galactique_et_ejection_par_feedback_stellaire_rgh_fr.pdf md5:d71dba00965d24a8d8566ba0bb6813c5 144.4 kB Preview Download galaxies_dominees_par_matiere_noire_et_halos_hypercomplexes_rgh_fr.pdf md5:92076b39ae106c439b52b990381faeef 166.1 kB Preview Download gravite_artificielle_1g_RGH.pdf md5:415ecfa0c09d9019b6ab466f73d970a9 209.7 kB Preview Download GROS_DOCUMENT_RGH.pdf md5:915af15fe6ba5aa04c268dc1e714e7f8 11.2 MB Preview Download hgr_complete_symplectic_rewriting_en.pdf md5:09aa681fec2b7892e58e051084dc98b2 579.7 kB Preview Download hgr_unit_conventions.pdf md5:8ca033fde6e7f2f31475a4c34e3c0076 191.2 kB Preview Download hypercomplex_structures_in_relativistic_spacetime_geometry_rgh_en.pdf md5:9a1530abbd32797e4d680ee1f00cb20e 251.9 kB Preview Download mini_bi_weyl_sector_compatible_with_hgr_en.pdf md5:e66cad8e945e960d578925b381a2c97c 237.9 kB Preview Download mini_secteur_bi_weyl_compatible_avec_la_rgh_fr.pdf md5:3f9275c89ea5ab3dd1bc5f76f2a663f9 236.1 kB Preview Download minimal_condition_for_a_local_repulsive_term_canceling_weight_rgh_en.pdf md5:6fafcc4928d5606de6bbbfc4c1800ac9 235.3 kB Preview Download minimal_semiquantum_closure_of_h0_in_hgr_en.pdf md5:6265b5e42865e76f1ee3cf0efbfc332f 278.7 kB Preview Download phenomenological_suppression_of_the_crossed_hypercomplex_term_in_the_halo_regime_code_rgh_en.pdf md5:a68dbbb6a08a9895cee021f130022cc9 187.6 kB Preview Download phenomenological_suppression_of_the_crossed_hypercomplex_term_in_the_halo_regime_rgh_en.pdf md5:bbe13104bed7f4c666a2fe0e4c993d89 217.6 kB Preview Download prepapier_neutrinos_sources_charge_hypercomplexe_rgh.pdf md5:12613d61192db410a7f1ef7ce0e47be6 248.4 kB Preview Download production_locale_statique_dun_champ_hypercomplexe_antipesanteur_rgh_fr.pdf md5:42ee4a62d1f324b4eca98a4332a7405a 244.9 kB Preview Download rgh_reecriture_symplectique_complete_fr.pdf md5:f3d1388d2801e0aefa2c2d394e0f7e35 582.3 kB Preview Download rgh_transition_H_O_lambda_activation.pdf md5:cbc79ff48240ee76350ff4c92a83e442 264.3 kB Preview Download rgh_transition_H_O_lambda_activation_en.pdf md5:56abb9e8bd11184fd19877fe374f65e9 266.4 kB Preview Download static_local_production_of_an_antigravity_hypercomplex_field_rgh_en.pdf md5:662e82a0bbfc0c8c74c0cfc145c18f7d 244.9 kB Preview Download structures_hypercomplexes_en_geometrie_de_lespace_temps_relativiste_rgh_fr.pdf md5:fa0324e54ba78fbcc0421104dcaf0796 255.4 kB Preview Download weak_or_vanishing_coupling_between_weyl_field_and_hypercomplex_field_rgh_en.pdf md5:a79364e3d54626e8bfac4cfcc7581f1b 219.1 kB Preview Download Additional details Dates Accepted 2026-02-15 Software Programming language Python Development Status Active 4K Views 16K Downloads Show more details All versions This version Views Total views 3,926 54 Downloads Total downloads 16,004 910 Data volume Total data volume 15.9 GB 581.3 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords Hypercomplex and quaternionic geometric structures General relativity extension Symplectic formulation of gravity Weyl geometry and scale invariance Hamiltonian consistency of modified gravity Geometric stability of higher-order theories Cosmological solutions in extended relativistic frameworks Dark matter Hubble calculation Details DOI DOI Badge DOI 10.5281/zenodo.20106777 Markdown [](https://doi.org/10.5281/zenodo.20106777) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.20106777.svg :target: https://doi.org/10.5281/zenodo.20106777 HTML <a href="https://doi.org/10.5281/zenodo.20106777"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.20106777.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.20106777.svg Target URL https://doi.org/10.5281/zenodo.20106777 Resource type Journal article Publisher Zenodo Published in Hypercomplex General Relativity (HGR): A symplectic and geometric reformulation of Weyl, hypercomplex numbers with late cosmological applications., 2026. Conference 371 Relativité générale hypercomplexe (RGH) : une reformulation symplectique et géométrique de Weyl, nombres hypercomplexes et applications cosmologiques récentes. Annexe : RGH : début de la quantification. Annexe : Galaxies ou halos de matière noire et vitesse de rotation, galaxies dominées par la matière noire et halos hypercomplexes en RGH. Interaction faible entre la matière noire et l'équation H₀. Languages French Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Citation Export Technical metadata Created May 10, 2026 Modified May 11, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies

Related documents

• Operational Meaning of the Cosmological Evolution of Dimensional Quantities: A Generalized Cosmological Time Framework for Cross-Epoch Comparisons#1130745
• Publication of the Universal Equation#717715
• Breaking de Sitter Symmetry with Cosmic Topology: Cosmological Role of Infrared Vacuum Freedom#1076293
• Theoretical necessity of the Accelerating Universe#1121362
• Dynamical systems in quadratic teleparallel cosmology#985728