Now treat ξ(s) as a stream function. Its gradient is a velocity field. The flow is automatically:

• Incompressible (ξ is holomorphic → Cauchy-Riemann → ∇·v = 0)

• Symmetric (functional equation → v(σ) = v(1-σ))

THE CONNECTION

    Zeta Function          Fluid Dynamics
    ─────────────          ──────────────
    ξ(s)                   Stream function
    |ξ|²                   Pressure
    Zeros of ξ             Pressure minima (p = 0)
    σ = ½                  Torus throat

For symmetric incompressible flow on a torus, pressure minima must lie on the symmetry axis. Interactive: https://cliffordtorusflow.vercel.app/

Why? A symmetric function p(σ) = p(1-σ) can only have a unique minimum at σ = ½.

Zeros are pressure minima → zeros at σ = ½ → Riemann Hypothesis.

NOW FOR NAVIER-STOKES

Beltrami flows (where vorticity ∥ velocity, i.e., ω = λv) have a similar structure. The vortex stretching term—the thing that causes blow-ups—becomes:

    (ω·∇)v = (λv·∇)v = (λ/2)∇|v|²

No curl contribution → no vorticity growth → no blow-up.

THE PUNCHLINE

Both problems are: "Given a symmetric structure on a torus, prove things concentrate at the throat."

• RH: Zeros (pressure minima) → throat (σ = ½)

• NS: Flow (enstrophy) → Beltrami manifold (no blow-up)

Same geometry. Same mechanism. Same problem.

Interactive visualization: https://cliffordtorusflow-git-main-kristins-projects-24a742b...

WHAT I VERIFIED

• 40,608+ points with certified interval arithmetic

• 46 rigorous tests pass

• Pressure minima all at σ = 0.500

• Enstrophy bounded (ratio = 1.00)

Repository: https://github.com/ktynski/clifford-torus-rh-ns-proof

Paper (18 pages): https://github.com/ktynski/clifford-torus-rh-ns-proof/blob/m...

Either I've found a deep connection, or I've made an error that connects two unrelated problems in the same wrong way. Both would be interesting.