Landing: add "Sphere, plane, sphere" (the four Wick turns)
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FAqjv3n4yABxvJPJHFRhVA
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<h2 style="font-family:var(--display);font-weight:500;font-size:28px;margin:8px 0 0">From Riemann to ζ</h2>
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<p class="lede">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.</p>
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<video controls playsinline preload="none" src="https://teahub.xyz/maths/videos/raw/commit/4c7ac00ce465abf403b9caf270e14bc1b8688a53/zeta-ball.mp4"></video>
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<h2 style="font-family:var(--display);font-weight:500;font-size:28px;margin:8px 0 0">Sphere, plane, sphere</h2>
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<p class="lede">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 = e<sup>iθ</sup>, 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.</p>
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<video controls playsinline preload="none" src="https://teahub.xyz/maths/videos/raw/commit/27b71220c27a652f449057e0d5f123e194f8b438/wick.mp4"></video>
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<p class="lede">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.</p>
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<div class="cards">
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<a class="card" href="strut/">
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