Jean Florent Romaric GNAYORO

PROOF OF EXISTENCE AND MASS GAP FOR YANG-MILLS IN FOUR DIMENSIONAL SPACE-TIME : Via Quantum Coherence Metric, Tube Diagonalization, Stochastic Forcing and Finite Wilsonian Iteration — Unconditional for All g>0

We construct the Euclidean Yang-Mills measure μ on ℝ⁴ for any compact simple Lie group G and any bare coupling g>0. Existence, uniqueness of infinite volume limit, Osterwalder-Schrader axioms OS0-OS4 and mass gap Δ(g)≥c₀ m_dyn(g) >0 with m_dyn(g)=Λ_QCD=μ exp(-8π²/b₀g²) are proved...

p-ADIC CONSTRUCTION OF THE HODGE CYCLE - p-ADIC HODGE THEORY AND BORCHERDS PRODUCTS

We construct the algebraic cycle attached to a Hodge class. For divisor Hodge loci we use Borcherds products where the Frobenius unit satisfies u=1. In general we use integrality, Kedlaya unit-root extension, Crew, Fontaine-Laffaille, rigid maximum principle and norm descent to o...

THE β-COHERENT QUARTIC METAMATERIALS: VISCOUS REGULARIZATION, FROBENIUS FILTERING, AND EFFECTIVE METRIC

We prove global well-posedness, uniform hyperbolicity τcoh≈0.061 s, ℱ≥0.999669, Q=49.92 and H-convergence for the viscosity-regularized quartic system ρ(∂tv+v·∇v)−μΔv+∇p=βcut∇·(|∇Φ|²∇Φ)χδ, ∂tΦ+v·∇Φ−βcutΔ̂β(Φ)+γradΦ=−S′p(Φ)+J, Δ̂β(Φ)=−β∇·(|∇Φ|²∇Φ). Geometry Ωshape=Ωcav∪Ωthroat∪Ωti...