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Moki&Julio: new best-known packings of equal circles, spheres and hyperspheres (Packomania tables), each with an exact certificate

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Zenodo2026-09-26 更新2026-10-01 收录
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Packings that improve the best-known records of Eckard Specht's Packomania tables (www.packomania.com): equal circles in the isosceles right triangle, the circular quadrant, eight fixed rectangles, the semicircle, the unit square and regular polygons; equal spheres in the unit cube and in the unit sphere; and equal balls in the unit ball of dimension 4, 5 and 6. Every record is an exact certificate (a radius and the centres as exact decimals) that two independently written exact checkers verify; results already surpassed in the literature are excluded by a data-level prior-art gate. Also included: Packomania submission files (.pck), local-optimality certificates, the search code, and proofs of optimality for some table entries (Füredi's bound for thin rectangles; exact computer-assisted proofs). The README lists the current count, the claim policy and how to verify every record with one command.

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2026-09-26
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