As someone who knows the Navier-Stokes fairly well ( https://scholar.google.ca/citations?user=--UmWDUAAAAJ&hl=en ) I have to admit I this is completely impenetrable for me. I don't understand why there is a Pressure minima nor a Torus throat on the Fluid Dynamics side of things. Why does it jump to Beltrami flows off of a sudden? I have no clue how to interpret this. Maybe the issue is that I understand Navier-Stokes from an engineering/application standpoint rather than the theoretical side?
Verifying a limited set of points does not count as a mathematical proof, unless you have some proof that by verifying these points it implies to be true for all points.
The paper/codebase contain more than numerical verification, let me clarify the actual proof structure.
The proof is analytic, with numerical verification as a sanity check:
1. Anchoring lower bound (Hadamard product + zero density):
A(s) ≥ c₁ · (σ-½)² · log³(t)
Uses only: N(T) ~ (T/2π)log(T) [Riemann-von Mangoldt, unconditional - doesn't assume RH]
2. Curvature upper bound (growth estimates):
|K| ≤ c₂ · log²(t)
Uses only: Standard bounds on |ζ'/ζ| [Titchmarsh, unconditional]
3. Dominance (algebra):
log³(t) >> log²(t), so A dominates |K| asymptotically
Therefore E'' = E(K + A) > 0
The numerical verification checks that the argument works in the finite regime (low t) where asymptotic bounds may not apply. It's a sanity check, not the proof.
The full circularity audit is in the repo - every dependency traces back to unconditional results (functional equation, zero density, growth estimates), never to RH itself.
As someone who knows the Navier-Stokes fairly well ( https://scholar.google.ca/citations?user=--UmWDUAAAAJ&hl=en ) I have to admit I this is completely impenetrable for me. I don't understand why there is a Pressure minima nor a Torus throat on the Fluid Dynamics side of things. Why does it jump to Beltrami flows off of a sudden? I have no clue how to interpret this. Maybe the issue is that I understand Navier-Stokes from an engineering/application standpoint rather than the theoretical side?
If you don't like this proof of the RH, the same author has four others to try: https://independent.academia.edu/KristinTynski
Verifying a limited set of points does not count as a mathematical proof, unless you have some proof that by verifying these points it implies to be true for all points.
The paper/codebase contain more than numerical verification, let me clarify the actual proof structure.
The proof is analytic, with numerical verification as a sanity check: 1. Anchoring lower bound (Hadamard product + zero density): A(s) ≥ c₁ · (σ-½)² · log³(t) Uses only: N(T) ~ (T/2π)log(T) [Riemann-von Mangoldt, unconditional - doesn't assume RH]
2. Curvature upper bound (growth estimates): |K| ≤ c₂ · log²(t) Uses only: Standard bounds on |ζ'/ζ| [Titchmarsh, unconditional]
3. Dominance (algebra): log³(t) >> log²(t), so A dominates |K| asymptotically Therefore E'' = E(K + A) > 0
The numerical verification checks that the argument works in the finite regime (low t) where asymptotic bounds may not apply. It's a sanity check, not the proof. The full circularity audit is in the repo - every dependency traces back to unconditional results (functional equation, zero density, growth estimates), never to RH itself.
Interactive Torus: https://cliffordtorusflow.vercel.app/