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by kristintynski
174 days ago
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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. |
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