Landing: add the zeta ball and the zeta strut

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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teahubxyzandClaude Fable 5.1 committed 2026-10-27 19:32:31 +00:00
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<h2 style="font-family:var(--display);font-weight:500;font-size:28px;margin:8px 0 0">Symmetry costs a line</h2>
<p class="lede">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.</p>
<video controls playsinline preload="none" src="https://teahub.xyz/maths/videos/raw/commit/a7601b040a95725e40e58f6ac214a2fe096a3a3e/yantra-symmetry.mp4"></video>
<h2 style="font-family:var(--display);font-weight:500;font-size:28px;margin:8px 0 0">The same move on ζ</h2>
<p class="lede">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.</p>
<div class="cards">
<a class="card" href="strut/">
<h2>The zeta strut</h2>
<p>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.</p>
<span class="go">open explorer →</span>
</a>
<a class="card" href="zeta/">
<h2>Zeta ball</h2>
<p>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.</p>
<span class="go">open explorer →</span>
</a>
</div>
<section class="notes">
<p><span class="dot" style="background:var(--up)"></span>four upward triangles · <span class="dot" style="background:var(--down)"></span>five downward · <span class="dot" style="background:var(--bindu)"></span>the bindu</p>
<p>Triangle coordinates follow a numerical solution of the yantra's concurrency conditions (after Kulaichev and Huet), drawn as 27 lines with 29 triple points.</p>