Radial speed
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Vertical speed
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Closing velocity
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Traces the real geometry from hdgl_hourglass_manifold.py: 3 shells × 3 threads × 2 branches (hot = warm, climbing +z; cold = cool, descending −z), all sharing one drain at progress = 0. Radial speed decays toward zero as a particle nears the drain; vertical speed holds near pitch_base·Ω ≈ 64.7 — so hot and cold arrive at the shared point still moving, and collide rather than coast to a stop.