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.