Treatise on Geometric Unification via 17-Layer Modular Foliation: Analytical Derivation, Tensorial Ranks, and Global Empirical Falsifiability

A formal treatise is presented on the analytical formulation and phenomenological validation of a five-dimensional warped geometry governed by a 17-sublayer modular foliation (epsilon = 1/(68*pi), kL ~ 44.547). This framework addresses both the electroweak hierarchy problem and the origin of fermion mass hierarchies without requiring fine-tuning of Yukawa couplings. We provide the analytical derivation of the physical electron mass (m_e ~ 0.511 MeV, c_e ~ 0.6277) and the resulting kinematic decoupling of its first Kaluza-Klein excitation e_1 at 10.79 TeV. Model phenomenology is categorized across tensorial ranks of geometric response: Rank 0 (scalar/unitarity, Delta kappa_V = -2.61e-4), Rank 1 (vector/chiral, Delta sin^2 theta_W ~ +1.96e-6), and Rank 2 (tensorial/evanescent, Delta a_e ~ 1.53e-17). The neutrino sector, governed by SO(8) triality at the modular Majorana scale M_R ~ 15.61 TeV, yields sum m_nu ~ 60.1 meV (fully compliant with combined Planck and DESI 2024 cosmological bounds) and predicts leptonic non-unitarity in the muon channel eta_mumu ~ 3.17e-4, directly probing the NuFIT 5.2 and DUNE discovery threshold. Confronting the model against high-mass dilepton collision datasets from ATLAS Run 2 (139 fb^-1, HEPData ins1827025) yields Delta chi^2 = -0.0105 relative to the Standard Model background. Finally, a Bayesian model selection evaluation demonstrates decisive statistical preference (Delta BIC = 51.45, Delta AIC = 48.06) for the 17-layer modular foliation over the Standard Model.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-08
DOI
https://doi.org/10.5281/zenodo.23245909
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Treatise on Geometric Unification via 17-Layer Modular Foliation: Analytical Derivation, Tensorial Ranks, and Global Empirical Falsifiability

albert cruañas pardo
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Treatise on Geometric Unification via 17-Layer Modular Foliation: Analytical Derivation, Tensorial Ranks, and Global Empirical Falsifiability

albert cruañas pardo
preprint en

Abstract

A formal treatise is presented on the analytical formulation and phenomenological validation of a five-dimensional warped geometry governed by a 17-sublayer modular foliation (epsilon = 1/(68*pi), kL ~ 44.547). This framework addresses both the electroweak hierarchy problem and the origin of fermion mass hierarchies without requiring fine-tuning of Yukawa couplings. We provide the analytical derivation of the physical electron mass (m_e ~ 0.511 MeV, c_e ~ 0.6277) and the resulting kinematic decoupling of its first Kaluza-Klein excitation e_1 at 10.79 TeV. Model phenomenology is categorized across tensorial ranks of geometric response: Rank 0 (scalar/unitarity, Delta kappa_V = -2.61e-4), Rank 1 (vector/chiral, Delta sin^2 theta_W ~ +1.96e-6), and Rank 2 (tensorial/evanescent, Delta a_e ~ 1.53e-17). The neutrino sector, governed by SO(8) triality at the modular Majorana scale M_R ~ 15.61 TeV, yields sum m_nu ~ 60.1 meV (fully compliant with combined Planck and DESI 2024 cosmological bounds) and predicts leptonic non-unitarity in the muon channel eta_mumu ~ 3.17e-4, directly probing the NuFIT 5.2 and DUNE discovery threshold. Confronting the model against high-mass dilepton collision datasets from ATLAS Run 2 (139 fb^-1, HEPData ins1827025) yields Delta chi^2 = -0.0105 relative to the Standard Model background. Finally, a Bayesian model selection evaluation demonstrates decisive statistical preference (Delta BIC = 51.45, Delta AIC = 48.06) for the 17-layer modular foliation over the Standard Model.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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Treatise on Geometric Unification via 17-Layer Modular Foliation: Analytical Derivation, Tensorial Ranks, and Global Empirical Falsifiability — albert cruañas pardo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS