From 08662dd36bdd77bc9ed1a5132242ad570d98da58 Mon Sep 17 00:00:00 2001 From: teahubxyz Date: Wed, 28 Oct 2026 06:15:45 +0000 Subject: [PATCH] index: card for "One sphere, four turns" (the base case), first among the explorers Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_01FAqjv3n4yABxvJPJHFRhVA --- index.html | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/index.html b/index.html index bbc1716..6e5c484 100644 --- a/index.html +++ b/index.html @@ -64,6 +64,11 @@ a.card p{margin:0;color:var(--muted);font-size:12.5px}

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.

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One sphere, four turns

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The base case. ζ painted on the Riemann sphere, 0 at the bottom, ∞ at the top, and 0, 1, ∞, −1 a quarter turn apart — 1 is half way to ∞. Three sliders turn it about its three struts; the tip about ±i has four stops whose shadows are the charts s/(1 − s), 2s − 1 (zeta’s orientation), 1 − 1/s (Li) and 1/(1 − 2s). The ball beside its shadow, with the six frame points and the zeros as beads.

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The zeta strut

ζ, ξ and Davenport–Heilbronn painted in the s-plane, in w = 1/(s − ½), and on the Riemann sphere with ½ in front; Hardy's Z(t) along the strut, with the off-line zero at t ≈ 85.7 marked.