Coloring, diameter coverings, and packings combine geometric constraints with discrete choices.
6 records · Includes focused interests · How we rate progress
Math, Inc. reports Lean formalizations of sphere-packing optimality for the E₈ lattice in dimension eight and the Leech lattice in dimension 24, with uniqueness among periodic packings in dimension 24. The human maintainers report checking definitions, axiom dependencies and the supplied code.
Read original source Math, Inc.: reported formalization and scopemath.inc
Original report: 2026-03-02The artifact reports exact optimal radii and classifications of optimal packings for one through seven freely rotated unit squares in a disk.
Read original source Original researchgithub.com
Original report: 2026-10-02The human-verified writeup gives a fixed ε>0 and growing planar point sets with at least n^(1+ε) unit distances.
Original report: 2026-05-20The manuscript reports a nine-dimensional counterexample using rank-one orthogonal projectors on R⁴ with the Frobenius metric.
Read original source Original manuscript · family 156github.com
Original report: 2026-10-06The manuscript reports that five colors cannot suffice, implying that the plane’s chromatic number is six or seven if the result holds.
Read original source Original manuscript · family 158github.com
Original report: 2026-10-06The authors report configurations packing 11 and 12 unit regular hexagons inside regular hexagons of approximate side lengths 3.931 and 3.942, respectively.
Read original source Georgiev, Gómez-Serrano, Tao, and Wagner paperarxiv.org
Original report: 2025-11-03Coloring, diameter coverings, and packings combine geometric constraints with discrete choices. Constructions supply examples; universal impossibility claims need arguments covering every allowed case.
This topic groups related mathematical questions across publishers. Each focused problem carries its own baseline and each contribution retains its original source. Results are compared only when their assumptions, optimization target, and computation model agree.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
Gauss: AI-assisted sphere-packing formalization in dimensions 8 and 24
OpenAI reports: Borsuk’s covering question in dimension nine
AlphaEvolve: improved hexagon-packing configurations reported
OpenAI reports: Borsuk’s covering question in dimension nine
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