From 2d55b24bdfc703c1fa3c34d70249954e1f113b28 Mon Sep 17 00:00:00 2001 From: teahubxyz Date: Tue, 27 Oct 2026 19:32:31 +0000 Subject: [PATCH] Landing: add the zeta ball and the zeta strut Co-Authored-By: Claude Fable 5.1 --- index.html | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/index.html b/index.html index 9d7191d..b134a54 100644 --- a/index.html +++ b/index.html @@ -53,6 +53,20 @@ a.card p{margin:0;color:var(--muted);font-size:12.5px}

Symmetry costs a line

Force up–down mirror symmetry on the yantra while keeping all 29 triple points exact, and two of its bases are pulled into one line, carrying one point on the axis and a mirror pair: 1 + 2.

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The same move on ζ

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Put ½ at the centre instead of the bindu. 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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The zeta strut

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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.

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Zeta ball

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The earlier picture: ζ on a ball of diameter ½ resting at ½, turned by quaternion quarter-turns; 3b1b's grid as the ball's own latitude–longitude, bent by η.

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four upward triangles · five downward · the bindu

Triangle coordinates follow a numerical solution of the yantra's concurrency conditions (after Kulaichev and Huet), drawn as 27 lines with 29 triple points.