From da3c56855c03c1ada23468c5715b87b35eb5ea59 Mon Sep 17 00:00:00 2001 From: teahubxyz Date: Wed, 28 Oct 2026 00:10:12 +0000 Subject: [PATCH] Landing: add "Sphere, plane, sphere" (the four Wick turns) Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_01FAqjv3n4yABxvJPJHFRhVA --- index.html | 3 +++ 1 file changed, 3 insertions(+) diff --git a/index.html b/index.html index 9eb5c6e..82639d4 100644 --- a/index.html +++ b/index.html @@ -56,6 +56,9 @@ a.card p{margin:0;color:var(--muted);font-size:12.5px}

From Riemann to ζ

The plane is a ball with a lamp on top. Feed ζ a grid and it draws latitude and longitude of a globe lying on its side: the usual stereographic picture tipped a quarter turn, halved, and slid by ½, so the poles land on 0 and 1. The equator casts the critical line; its two ends are ½ and ∞; the functional equation is the half-turn that swaps the poles and keeps the equator. The Riemann hypothesis, on the ball: every zero lives on the equator, climbing toward the lamp.

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Sphere, plane, sphere

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The pattern underneath. Unit quaternions projected from −1; the pure imaginaries are a sphere. Multiply on both sides (locked) and it only spins. Multiply on one side, q = eiθ, and it drifts through the projection point: sphere, plane, inside-out sphere, plane, sphere — the four Wick turns. The plane is a chart missing one point; the sphere is projective; putting the point back is analytic continuation. In the plane phase the grid about j is zeta's grid, poles on 0 and 1, and the gamma factor is what dresses the far hemisphere so ξ lives on the sphere cleanly.

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The same ball in two explorers: put ½ at the centre and the critical line becomes the strut through 0 and ∞, the functional equation a sign flip through the centre. Swap ζ for a function with the same symmetry and no Euler product (Davenport–Heilbronn) and the zeros step off the strut: symmetry alone does not pin them, the arithmetic is the extra incidence.