Field Vortex Theory (TVF): A Geometric Framework Toward the Unification of General Relativity and Quantum Mechanics

The Field Vortex Theory (TVF) is a geometric framework in which the elementary particles of the Standard Model emerge as topological solitons of a single non-linear field defined on a nested chain of complex projective spaces CP⁰ ⊂ CP¹ ⊂ CP² ⊂ CP³. The full action combines the Einstein–Hilbert term in the metric sector with a Faddeev–Skyrme functional in the internal sector, so that General Relativity is recovered as the low-energy metric limit and Quantum Mechanics emerges from canonical quantisation of the soliton collective coordinates around the vacuum. The framework is fixed by one physical scale — the electroweak vacuum expectation value vEW = 246 GeV — and two geometric integers, k₁ = c₁ (CP¹) = 2 and k₂ = c₁ (CP²) = 3. From these inputs, 24 closed-form theorems for Standard Model parameters are derived, with typical sub-percent agreement with PDG 2024 data: sin²θW = 3/8 (Δ ≈ 0%), mₚ/mₑ = 6π⁵ (Δ ≈ 0. 002%), Koide K = 2/3 (Δ ≈ 0. 001%), the full CKM matrix at the percent level, the EW–Planck hierarchy in closed form, and the QCD junction scale ΛTVF = √ (mₑ · vEW). The corpus includes 52 falsifiable predictions across particle physics, atomic structure, nuclear physics, industrial catalysis and primordial cosmology, with applications to green hydrogen via PEM electrolysis, advanced industrial catalysis, molecular design through a topological reading of the periodic table, controlled D–D nuclear fusion, and synthetic non-Abelian photonics. Three structural fronts are explicitly declared open. TVF positions itself as complementary to the Standard Model — extending it, not replacing it — and is falsifiable in the strongest sense: a confirmed sub-percent disagreement on any of the 24 theorems refutes the corresponding closed-form prediction. This deposit represents a working draft of a much more articulated theory, currently in preparatio