Into the vortex.

Implemented: solve Q − Z²Q²ʰ = 1, set q = τQ, η = Z/Qᴰ, X = R²/(2Q), then evaluate the Cartesian velocity in (4.5). Radial flux follows (4.7). The profiles are Taylor series in X with Chebyshev coefficients in η, generated by the recurrences from (4.13).

Chosen data: h = 0.005, j₀ = 0.025, Λ = 2, σ* = 1, C = 1.5. U(0,η) = 4η + j₀ and F(0,η) use (B.1), (B.3). Π(0,η) = −2/(1+η²)² is experimental; it is not the matched exterior datum (A.21). These parameter values are not certified to meet the global construction’s thresholds.

Truncation: radial order 10; Chebyshev degree 64; display/integration chart 0 ≤ X ≤ 0.08, |η| ≤ 0.6. The boundary cage marks this chart. Exiting particles are reseeded; scrubbing reseeds the ensemble. Only motion after seeding is a trajectory.

Diagnostics: centred second-order differences use steps δ√τ in the transverse directions, δτᴰ axially, and δτ in time. The momentum metric divides the RMS of ∂ₜu + (u·∇)u − Δu + ∇p by the root-sum-square RMS of those four terms. Energy uses midpoint quadrature and the exact cylindrical coordinate Jacobian. Finite-grid maxima and step-doubling differences are estimates, not rigorous error bounds.

Not implemented: the matched pressure/exterior construction, stress-cone certification, high-order background corrections, oscillatory pulses, compact forcing and localization, and the start-from-rest transition. This is a local numerical profile experiment, not a reconstruction or validation of the paper’s blowup solution.