About this episode

This episode explores the mathematical and spiritual significance of the spherical realizations of the Śrī Yantra.

A certified atlas of 968 spherical realizations of the Śrī Yantra, one of the oldest and most studied sacred geometry figures, reconstructed under Rao’s 1998 spherical constraint system. Every figure is a mathematically certified root. The viewer displays what was certified; it does not compute anything itself. The two-layer census * Layer 1 (certification): 968 roots across 3044 possible constraint subsets. Each root verified by Krawczyk interval arithmetic — a rigorous numerical proof of existence and local uniqueness. * Layer 2 (Gate-4 metadata): 525 valid / 443 rejected under Rao’s registered ordering-containment test. This is metadata only — it does not affect certification. * 949 drawable figures; 19 degenerate (constraints satisfied but figure collapses). Why spherical? The familiar plane Śrī Yantra is a special case. Rao showed the constraints generalize naturally to the sphere, producing a much richer solution landscape. Some roots look traditional; others are wildly different. All are valid solutions of the same equations. The topology correction Early renders used truncated corners, interior construction points rather than Rao’s intended produced corners (18, 16, 17…

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