Gluon Elastic Lattice Theory: The Complete Mathematical Derivations(GELT)

Gluon Elastic Lattice Theory: The Complete Mathematical Derivations (GELT) This dataset presents a first-principles theoretical framework in which the fundamental structures of the Standard Model — including gauge symmetries, confinement, chiral symmetry breaking, and fermion flavor structure — emerge from the nonlinear elastic dynamics of a discrete lattice with global coupling. All derivations are conducted in a strict [L][T] dimensional system without introducing mass as a fundamental dimension. The framework provides: (i) an analytical derivation of the linear confinement potential and the Yang-Mills mass gap from lattice geometry; (ii) a geometric origin for SU(3) color symmetry via point-group triple tensor products, yielding exactly three fermion generations; (iii) an analytical running coupling α_s(Q²) consistent with asymptotic freedom; (iv) a resolution of the strong CP problem without an axion; (v) a unified description of electroweak symmetry breaking, fermion mass hierarchies, and CKM flavor mixing from a single microscopic interaction function. All measurable parameters — including the string tension σ, mass gap Δ, QCD scale Λ_MS, and strong coupling α_s — are expressed in terms of lattice geometry (lattice spacing d₀, geometric factors from Ewald sums) and the microscopic interaction function φ(s). This collection contains the complete mathematical derivations, numerical lattice calculations, and connections to experimental observables. Human core contribution:All results presented in this framework originate from a single decision made by the human author: to treat space as a globally coupled simple cubic lattice whose nonlinear elastic response fully determines all physical phenomena. This choice of axioms — one entity, one structure, one relation — is not derived from any deeper principle; it is the author's physical intuition. Every subsequent derivation is a rigorous mathematical consequence of these axioms, but the axioms themselves are human insight. The entire theoretical edifice rests on this foundational act of human creativity.