lamp: link the video from the explorer

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01FAqjv3n4yABxvJPJHFRhVA
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teahubxyzandClaude Fable 5.1 committed 2026-10-28 05:13:26 +00:00
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<div class="eyebrow">maths · <a href="../">two poles</a> · <a href="../zeta/">zeta ball</a> · <a href="../strut/">strut</a> · <a href="../dial/">dial</a> · <a href="../flow/">flow</a> · lamp at ½</div>
<h1>Lamp at <i>½</i></h1>
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<p class="lede" style="margin-top:-6px">Three-minute narrated version on the <a href="../#lamp" style="color:var(--up)">front page</a>: two lamps, the swap, the zeros falling in, and ξ’s light cone.</p>
<p class="lede">The zeta ball, projected from the other pole. Put the lamp at the touch point ½ and the screen at the top, tangent at ∞: the chart is <b>u = ¼ / (s − ½)</b>. The frame does not move — the poles still sit at ±½, the third strut at ±i/2, the circle |u| = ½ is where both charts agree — only the two ends of the ½–∞ strut have swapped. The old lamp, ∞, is now the centre; the old touch point, ½, is now at infinity. In this chart the functional equation is u ↦ −u and the whole dial is a rotation about the centre. And every zero, trivial and critical, falls into the origin: the trivial ones along the real axis from one side, the critical ones along the strut from both.</p>
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