packing-records: candidate improvements to five record tables for packing and energy problems
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1,154 explicit configurations that improve entries in five public record tables: 747 in Henry Cohn's table of Grassmannian packings, 52 on the Game of Sloanes leaderboard of complex line packings, 108 (equal 4-D spheres in a 4-D sphere) and 216 (equal spheres in a cube) in Eckard Specht's Packomania tables, and 31 in Henry Cohn's table of harmonic energies of points on a sphere. Each Grassmannian file beats the table's printed value in its last digit and stays below any listed bound. Game of Sloanes and Packomania files beat their entries by at least 1e-7 in the table's own measure, and the Packomania results also beat a floor: a local LP polish of the posted configuration and, for spheres in a cube, the posted N-1 configuration plus one sphere after the same polish and the public Moki & Julio collection. Each harmonic file is below the table and the 2021 data set by at least max(1e-9, 1e-12 E) and below a polish of the posted 2021 configuration. Version 1.2.0 adds the 57 spheres-in-a-cube cells that pass those floors and the 31 harmonic cells. Henry Cohn lists the 731 Grassmannian cells of version 1.0.0 in his table as reference [24]. The archive contains the coordinate files in each table's own format, cells.csv (values, margins, floors, sha256, and the author of any posted configuration a search started from), fact extracts of the five tables, and a Python standard-library checker that recomputes every value with exact rational arithmetic (sh check/check_all.sh), with check/mutate.py to confirm that it fails on planted defects. Found by Benjamin Meadows with Claude AI, using numerical optimization (smoothed-maximum descent, Riesz-energy relaxation, L-BFGS with Newton steps, basin hopping, large-neighborhood search and sequential LP polish) run on cloud machines. Snapshot of https://github.com/TheBenMeadows/packing-records at commit 451fc71 (merged as 06594af).



