DDT Stage-2: Particle Emergence, the Koide Ratio, and CKM Matrix Derived Strictly from Stage-1 Primitives

This Stage-2 document is strictly Stage-1 native: every construction reduces to the single substrate field X₂, its vacuum X₂ᵛᵃᶜ = ln 2, and the topology of the 2 → 3 deployment front — with no additional free parameters.

Starting from the stiffness-completed filament action, we derive: the Koide mass ratio as a deployment-angle theorem; the Borromean equilibrium equation and its two-scale structure; an analytic proof that the mass gap Δ > 0; a geometric mechanism for CP-odd phases via framed-ribbon writhe at filament intersections; and the origin of physical spin from Kelvin modes on quantized flux tubes.

Three points of the construction merit brief advance notice. First, the transverse Gaussian core profile is used as a variational closure in the defect interior (ρ → 0); it is not asserted as the exact asymptotic solution in free space, and all overlap integrals are evaluated where this closure is controlled. Second, the CP-odd phase arises from an intersection holonomy on the overlap manifold of two defect world-sheets, not from the winding number of a single isolated defect; the distinction is essential for surviving topological quantization. Third, physical angular momentum in the filament sector comes from Kelvin-mode excitations of quantized flux tubes, which carry transverse helical polarization despite X₂ being a scalar field.

A reproducibility appendix provides closed-form expressions and executable code for all numerical outputs. The scope of this document is the derivation of Stage-2 predictions from Stage-1 primitives; formal extensions such as the quantization of the filament sector lie outside the present scope and represent natural directions for subsequent work. Observations and suggestions from readers are welcome and will be considered in future revisions.