Changelog

• T-301 Ono's packing at 228, five band periods cut from Couzo's 404, 4.76e-03 below T-300n = 228 · V3 C3 S3 · Ono
• T-302 Ono's packing at 147, one band period cut from Daniel's 229, 5.81e-03 below 7 + 4*sqrt(2)n = 147 · V3 C3 S3 · Ono
• T-301 is now the record packing at 228
• T-302 is now the record packing at 147

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• T-298 s(k² − 5) = k for every integer k from 7 up; k = 7…18 are the cases held here12 counts from 44 to 319 · V0 C1 S4 · Khalili, Gharabaghi
• T-299 De Winter's double-step staircases in T-174's layout at 297, a new arrangement 9.62e-04 below itn = 297 · V3 C3 S3 · de Winter
• T-300 Özden's column-band packing at 228, a new arrangement 3.80e-03 below T-174n = 228 · V3 C3 S3 · Ozden · superseded
• T-299 is now the record packing at 297
• 2 upper bounds beyond n = 324n = 332–409 · Joost de Winter
• Khalili and Gharabaghi Report s(k² − 5) = k for Every k ≥ 7S4 · Issue #973 · PR #974

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• T-297 Özden's column-band packing at 269, 9.74e-03 below his T-296 and 1.13e-02 below his T-290n = 269 · V3 C3 S3 · Ozden
• T-297 is now the record packing at 269

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• T-292 De Winter's pinwheel at 132 from Samanyu-dev's 109, a new arrangement 9.63e-03 below T-174n = 132 · V3 C3 S3 · de Winter
• T-293 De Winter's pinwheel at 157 from Samanyu-dev's 109, the first below the grid's 13, by 6.70e-03n = 157 · V3 C3 S3 · de Winter
• T-294 Özden's further arrangement of his T-291 band at 179, 4.07e-04 below it, 2.645e-12 above s(70) + 5n = 179 · V3 C3 S3 · Ozden
• T-295 Özden's packing at 237, a band from two copies of the registry's 70, 8.80e-03 below T-190n = 237 · V3 C3 S3 · Ozden
• T-296 Özden's band at 269 from tilted squares of the 207, the 70 and his 179, 1.53e-03 below his T-290n = 269 · V3 C3 S3 · Ozden · superseded
• T-292 is now the record packing at 132
• T-293 is now the record packing at 157
• T-294 is now the record packing at 179
• T-295 is now the record packing at 237

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• T-287 Özden's packing at 156, seeded from the registry's 182, 2.11e-03 below the house, T-186n = 156 · V3 C3 S3 · Ozden
• T-288 Özden's packing at 180, seeded from the registry's 154, 1.38e-03 below the house, T-174n = 180 · V3 C3 S3 · Ozden
• T-289 Özden's packing at 268, seeded from the registry's 302, 4.40e-04 below his own T-276n = 268 · V3 C3 S3 · Ozden
• T-290 Özden's packing at 269, seeded from the registry's 304, 5.19e-04 below the house, T-174n = 269 · V3 C3 S3 · Ozden · superseded
• T-291 Özden's packing at 179, a band built from the registry's 70, 2.43e-03 below the house, T-174n = 179 · V3 C3 S3 · Ozden · superseded
• T-285 De Winter's re-solve of T-284's packing at 199, 1.0399 of its margin through the L step; heldn = 199 · V0 C1 S1 · de Winter
• T-286 De Winter's re-solve of T-282's packing at 172, T-285's core, 1.0399 of T-282's margin; heldn = 172 · V0 C1 S1 · de Winter
• T-287 is now the record packing at 156
• T-288 is now the record packing at 180
• T-289 is now the record packing at 268
• 16 upper bounds beyond n = 324n = 632–989 · Joost de Winter
• 14 upper bounds beyond n = 324n = 413–910 · Joost de Winter
• 6 upper bounds beyond n = 324n = 597–991 · Joost de Winter

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• T-284 Özden's T-282 packing plus an L of 27 squares at 199, 2.88e-3 below the housen = 199 · V3 C3 S3 · Ozden
• T-284 is now the record packing at 199

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• T-275 Özden's further arrangement at 232 of Couzo's T-256 packing, one to one, 2.52e-4 below itn = 232 · V3 C3 S3 · Ozden
• T-276 Özden's further arrangement at 268 of Daniel's T-270 packing, one to one, 2.96e-5 below itn = 268 · V3 C3 S3 · Ozden · superseded
• T-277 Özden's further arrangement at 299 of his own T-263 packing, after Daniel, 2.34e-4 below itn = 299 · V3 C3 S3 · Ozden
• T-278 Özden's further arrangement at 303 of Daniel's T-272 packing, one to one, 4.35e-5 below itn = 303 · V3 C3 S3 · Ozden
• T-279 Özden's further arrangement at 307 of Couzo's T-256 packing, one to one, 2.03e-5 below itn = 307 · V3 C3 S3 · Ozden
• T-282 Özden's further arrangement at 172 of Daniel's T-257 packing, 3.25e-3 below itn = 172 · V3 C3 S3 · Ozden
• T-283 Özden's further arrangement at 270 of Daniel's T-224 packing, one to one, 1.36e-5 below itn = 270 · V3 C3 S2 · Ozden
• T-280 Yim's re-solves of Özden's T-277 and T-278 at 299 and 303, within their padding; heldn = 299, 303 · V0 C1 S1 · Yim
• T-281 Yim's translation of T-259's certificate at 130, 1.96e-14 below it at the same print; heldn = 130 · V0 C1 S1 · Yim
• T-275 is now the record packing at 232
• T-277 is now the record packing at 299
• T-278 is now the record packing at 303
• T-279 is now the record packing at 307
• T-282 is now the record packing at 172
• T-283 is now the record packing at 270
• 11 upper bounds beyond n = 324n = 553–700 · Yim

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• T-274 s(12) ≥ 9929/2500 = 3.9716, T-095's points dilated with 3,260 moren = 12 · V3 C3 S3 · unnir

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• T-267 Daniel's new packing of 175 squares, from gadgets of T-186's, 1.24e-4 below itn = 175 · V3 C3 S3 · Daniel
• T-268 Daniel's new packing of 204 squares, 3.26e-3 below T-264n = 204 · V3 C3 S3 · Daniel
• T-269 Daniel's new packing of 260 squares, T-257's tilted island recomposed, 4.62e-4 below T-265n = 260 · V3 C3 S3 · Daniel
• T-270 Daniel's new packing of 268 squares, 1.86e-3 below T-242n = 268 · V3 C3 S3 · Daniel · superseded
• T-271 Daniel's new packing of 293 squares, 1.09e-2 below his T-257n = 293 · V3 C3 S3 · Daniel
• T-272 Daniel's new packing of 303 squares, 5.15e-3 below T-240n = 303 · V3 C3 S3 · Daniel · superseded
• T-273 Daniel's new packing of 304 squares, 5.95e-3 below T-242n = 304 · V3 C3 S3 · Daniel
• T-267 is now the record packing at 175
• T-268 is now the record packing at 204
• T-269 is now the record packing at 260
• T-271 is now the record packing at 293
• T-273 is now the record packing at 304

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• T-266 s(94) ≥ 2493/250 verified, T-091's measure dilated onto a 4,972-direction netn = 94 · V3 C3 S3 · Ozden
• T-265 Yim's further arrangement at 260 of Daniel's T-257 packing, one to one, 1.99e-10 below itn = 260 · V3 C3 S2 · Yim · superseded

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• T-263 Özden's further arrangement at 299 of Daniel's T-258 packing, one to one, 1.54e-8 below itn = 299 · V3 C3 S2 · Ozden · superseded
• T-264 Özden's further arrangement at 204 of Daniel's T-257 packing, one to one, 6.48e-6 below itn = 204 · V3 C3 S2 · Ozden · superseded

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• T-262 s(94) ≥ 1993/200 verified, T-091's measure dilated onto a 600-direction netn = 94 · V3 C3 S3 · Ozden · superseded

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• T-252 s(44) = 7, by a closed mixed cover of points and grid-line segmentsn = 44 · V3 C3 S3 · Khalili, Gharabaghi
• T-254 Couzo's new packing of 130 squares from PR #574's, 2.05e-3 below T-174n = 130 · V3 C3 S3 · Couzo · superseded
• T-255 Couzo's certificates of ntumlnoob's Kaggle packings at 260 and 307, below T-225 and T-174n = 260, 307 · V3 C3 S3 · Couzo · superseded
• T-256 Couzo's packings from Kaggle notebook packings at 232, 260 and 307, below T-186, T-225 and T-174n = 232, 260, 307 · V3 C3 S3 · Couzo · superseded
• T-257 Daniel's new packings of 172, 204, 260 and 293 squares, 1.64e-4 to 1.18e-2 below each housen = 172, 204, 260, 293 · V3 C3 S3 · Daniel · superseded
• T-258 Daniel's lower packing of 299 squares from his T-248 packing, 2.46e-3 below itn = 299 · V3 C3 S3 · Daniel · superseded
• T-261 Reported grade-C local minima for 233 source configurations of field degree at most 4233 counts from 1 to 324 · V3 C1 S2 · Daniel
• T-253 Polkovskyi's sub-print re-certifications of nine house packings, 1.3e-19 to 1.7e-19 below each9 counts from 154 to 271 · V0 C1 S1 · Polkovskyi
• T-259 Polkovskyi's re-solve of Couzo's packing of 130 squares, 2.08e-12 below T-254n = 130 · V3 C3 S1 · Polkovskyi
• T-260 Polkovskyi's sub-print re-certifications at 105, 146, 156, 229 and 308, 1e-41 to 1e-21 below eachn = 105, 146, 156, 229, 308 · V0 C1 S1 · Polkovskyi
• T-259 is now the record packing at 130
• Daniel’s, Couzo’s and Polkovskyi’s Certificates Become the House Best Packings at Eight CountsS3 · Issue #824 · Issue #843 · Issue #844 · Issue #845 · Issue #846 · PR #852

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• T-248 Daniel's new arrangement at 299, 1.92e-2 below the catalogue's constructionn = 299 · V3 C3 S3 · Daniel · superseded
• T-250 Hosono reports a Lean kernel proof of Daniel's Valid7, and so of s(k² − 3) = k for every k ≥ 613 counts from 33 to 321 · V0 C0 S3 · Hosono
• T-251 Hosono reports a Lean kernel proof of Daniel's ValidTilt9, so s(k² − 4) = k for every k ≥ 811 counts from 60 to 320 · V0 C0 S3 · Hosono
• T-247 Kim's exact degree-21 side at 297, as reported, of the packing the record creditsn = 297 · V3 C3 S2 · Kim · superseded
• T-249 Daniel reports a Lean kernel proof that s(12) ≥ 15680/3951, the bound T-049 holdsn = 12 · V0 C0 S2 · Daniel
• 1 upper bound beyond n = 324n = 344 · Amund Kristiansen
• A Concise Changelog, and News for the StoriesS2 · PR #840
• The Project Changelog Gets a Page, Under a Project MenuS2 · PR #837 · The site design record

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• T-245 Jatloe reports a Lean proof that the 4 × 3 grid is optimal, s(12) = 4n = 12 · V0 C0 S5 · jatloe, Gurevitch, ctjlewis, Ahmed
• T-243 Daniel's new arrangement at 182, 3.17e-3 below T-174n = 182 · V3 C3 S3 · Daniel
• T-246 Reported degree-7213 minimal polynomial of the s(29) record siden = 29 · V0 C0 S3 · Daniel
• T-244 Kim's exact algebraic sides at 172 and 263, as reported, of packings the record creditsn = 172, 263 · V3 C3 S2 · Kim
• T-243 is now the record packing at 182
• 122 upper bounds beyond n = 324n = 330–997 · Francisco Couzo · 21 since superseded
• 13 upper bounds beyond n = 324n = 365–970 · Francisco Couzo · 9 since superseded
• 12 upper bounds beyond n = 324n = 334–504 · Amund Kristiansen
• Couzo’s Packings Become the House Best Packings at 268 and 303S3 · Issue #763 · PR #794
• Daniel’s New Arrangement Becomes the House Best Packing at 182S3 · Issue #806 · PR #814
• Jatloe Reports a Lean Proof for 12 SquaresS5 · Issue #810 · PR #812

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• T-232 Mixed rectangle-measure lower bound s(31) ≥ 2391/400 verified, on a 2,073-direction declared netn = 31 · V3 C3 S3 · Hosono
• T-233 Mixed rectangle-measure lower bounds verified at n = 19, 20, 26, 27, on a 2,073-direction netn = 19, 20, 26, 27 · V3 C3 S3 · Hosono
• T-236 Daniel reports Lean proofs of Fang's Theorems 1 and 2, s(n² − n + 1) < n for n ≥ 15n = 211, 241, 273, 307 · V0 C0 S3 · Daniel
• T-237 s(2), s(3), s(4) = 2 and s(5) = 2 + 1/√2 = 2.70710678…, the classical first casesn = 2–5 · V3 C3 S3 · Göbel; Friedman
• T-240 Couzo's 268 and 303 of #763, below T-174 and T-239, from Kaggle notebook packingsn = 268, 303 · V3 C3 S3 · Couzo · superseded
• T-241 Couzo's certificate at 304 of Tymchishin's Kaggle notebook packing, 2.53e-3 below T-186n = 304 · V3 C3 S3 · Couzo · superseded
• T-231 Polkovskyi's lower re-solve at 204 of Couzo's packing, 1.48e-11 below T-229n = 204 · V3 C3 S2 · Polkovskyi · superseded
• T-234 Hosono reports a hypothesis-free Lean proof that s(21) = 5, by the point-only routen = 21 · V0 C0 S2 · Hosono
• T-235 Hosono reports a Lean kernel proof that s(59) = 8, on Daniel's mixed-measure checkern = 59 · V0 C0 S2 · Hosono
• T-238 chelokot reports Lean proofs of s(2), s(3), s(4) = 2, s(5) = 2.707…; Daniel, rectangle theoremsn = 2–5 · V0 C0 S2 · Vlasenko; Daniel
• T-239 Kristiansen's smaller n303 packing, found from Daniel's packing, certified exactlyn = 303 · V3 C3 S2 · Kristiansen · superseded
• T-242 Daniel's exact descents of public Kaggle packings at 268 and 304, below the reports before themn = 268, 304 · V3 C3 S2 · Daniel · superseded
• T-174 is now the record packing at 70, 153 and 207
• T-193 is now the record packing at 102, 123, 258, 259, 295 and 302
• 184 upper bounds beyond n = 324n = 333–997 · Francisco Couzo · 94 since superseded
• 138 upper bounds beyond n = 324n = 328–989 · Mykhailo Polkovskyi · 131 since superseded
• 42 upper bounds beyond n = 324n = 327–975 · Kirill Tymchishin · 17 since superseded
• 37 upper bounds beyond n = 324n = 377–994 · Francisco Couzo · all since superseded
• 35 upper bounds beyond n = 324n = 377–984 · Francisco Couzo · all since superseded
• 18 upper bounds beyond n = 324n = 377–981 · kyleluecke · 11 since superseded
• 15 upper bounds beyond n = 324n = 376–984 · Kirill Tymchishin · 6 since superseded
• 11 upper bounds beyond n = 324n = 338–875 · alexchilton · 7 since superseded
• 11 upper bounds beyond n = 324n = 330–816 · Vladislav Lavrentev · all since superseded
• 10 upper bounds beyond n = 324n = 335–998 · Francisco Couzo · 3 since superseded
• 9 upper bounds beyond n = 324n = 364–994 · aqibrazadev · 8 since superseded
• 7 upper bounds beyond n = 324n = 653–923 · Vladislav Lavrentev · 4 since superseded
• Daniel Reports Lean Proofs of Fang’s Theorems, and the Register Takes In $s(2)$s(2) to $s(5)$s(5)S3 · Issue #784 · Issue #785 · PR #750
• Hosono Raises the Lower Bound for 31 Squares to 5.9775S3 · Issue #446 · Issue #534 · PR #745

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• T-230 Daniel's smaller n303 packing, started from Ostashev's packing, certified exactlyn = 303 · V3 C3 S3 · Daniel · superseded
• T-229 is now the record packing at 105
• 253 upper bounds beyond n = 324n = 325–994 · Francisco Couzo · 214 since superseded
• 77 upper bounds beyond n = 324n = 372–995 · Mykhailo Polkovskyi · all since superseded
• 21 upper bounds beyond n = 324n = 547–997 · Francisco Couzo · all since superseded
• 20 upper bounds beyond n = 324n = 409–997 · Francisco Couzo · all since superseded
• 12 upper bounds beyond n = 324n = 332–379 · Francisco Couzo · 7 since superseded
• 4 upper bounds beyond n = 324n = 340–380 · Francisco Couzo · all since superseded
• 2 upper bounds beyond n = 324n = 338–340 · Francisco Couzo · all since superseded
• 2 upper bounds beyond n = 324n = 344–378 · Francisco Couzo · all since superseded
• 2 upper bounds beyond n = 324n = 703–994 · Kevin Fang · all since superseded
• 1 upper bound beyond n = 324n = 378 · Francisco Couzo · all since superseded
• 1 upper bound beyond n = 324n = 344 · Francisco Couzo · all since superseded
• 1 upper bound beyond n = 324n = 343 · Evan Daniel · all since superseded
• Couzo’s and Polkovskyi’s Certificates at Four Counts ConfirmedS3 · Issue #670 · Issue #672 · Issue #675 · Issue #719 · PR #725
• Daniel’s Smaller Packing of 303 Squares AdoptedS3 · Issue #728 · PR #731
• The Visual Atlas Follows the ScrollS2 · PR #746 · The site design record

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• T-226 Couzo's 204 of #670, below Polkovskyi's T-186, since superseded by his own #675 and #678n = 204 · V3 C3 S3 · Couzo · superseded
• T-227 Couzo's refinements of de Winter's 227 and 229, below T-196 at bothn = 227, 229 · V3 C3 S3 · Couzo · superseded
• T-225 Daniel's solved, regularized views at 204, 227, 229 and 260, each the smallest side reported theren = 204, 227, 229, 260 · V3 C3 S2 · Daniel
• T-228 Couzo's 204 of #675, below his #670, since superseded by his #678n = 204 · V3 C3 S2 · Couzo · superseded
• T-229 Polkovskyi's re-solves of the house packings at 105 and 204, below T-174 and T-225n = 105, 204 · V3 C3 S2 · Polkovskyi
• T-225 is now the record packing at 227 and 229
• 111 upper bounds beyond n = 324n = 330–997 · Mykhailo Polkovskyi · 109 since superseded
• 109 upper bounds beyond n = 324n = 328–996 · Francisco Couzo · all since superseded
• 78 upper bounds beyond n = 324n = 419–998 · Francisco Couzo · all since superseded
• 72 upper bounds beyond n = 324n = 330–993 · Francisco Couzo · all since superseded
• 44 upper bounds beyond n = 324n = 330–996 · Francisco Couzo · all since superseded
• 11 upper bounds beyond n = 324n = 464–998 · Joost de Winter · all since superseded
• Contributor Profiles With Records, Results and CreditsS3 · PR #578 · Contributor records · Attribution rules

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• T-223 Couzo's smaller packings at 204 and 260, the two in the corpus of issue 678's 85 boundsn = 204, 260 · V3 C3 S3 · Couzo · superseded
• T-224 Daniel's smaller n270 packing, another arrangement found from Chaoweeraprasit's, certified exactlyn = 270 · V3 C3 S3 · Daniel · superseded
• 100 upper bounds beyond n = 324n = 328–998 · Darius Muglich · 97 since superseded
• 83 upper bounds beyond n = 324n = 330–998 · Francisco Couzo · all since superseded
• 1 upper bound beyond n = 324n = 343 · Evan Daniel · all since superseded
• Couzo’s Smaller Packings of 204 and 260 Squares AdoptedS3 · Issue #678 · PR #706
• Daniel’s Smaller Packing of 270 Squares AdoptedS3 · Issue #703 · PR #708
• De Winter’s Smaller Packings of 227 and 260 Squares AdoptedS3 · Issue #668 · PR #704

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• T-218 Daniel's smaller n236 packing, after Chaoweeraprasit's composition, certified exactlyn = 236 · V3 C3 S3 · Daniel
• T-219 Daniel's smaller n271 packing, continuing Couzo's arrangement, certified exactlyn = 271 · V3 C3 S3 · Daniel
• T-220 Daniel's finite sub-grid upper bound for 183 squares, after Couzo's n182 packingn = 183 · V3 C3 S3 · Daniel
• T-221 Daniel's smaller n308 packing, started from Chaoweeraprasit's 307 packing, certified exactlyn = 308 · V3 C3 S3 · Daniel
• T-222 Daniel's smaller n154 packing, continuing Couzo's #586 arrangement, certified exactlyn = 154 · V3 C3 S3 · Daniel
• T-197 is now the record packing at 155
• T-218 is now the record packing at 236
• T-219 is now the record packing at 271
• T-220 is now the record packing at 183
• T-221 is now the record packing at 308
• T-222 is now the record packing at 154
• Daniel’s Smaller Packings at 155, 229, 236 and 271 Squares AdoptedS3 · Issue #659 · Issue #664 · Issue #669 · Issue #674 · PR #676 · PR #692
• Daniel’s Packing of 183 Squares Below Side 14S3 · Issue #680 · PR #687
• Daniel’s Smaller Packings of 154 and 308 Squares AdoptedS3 · Issue #689 · Issue #694 · PR #699
• Hosono Reports Stronger Lower Bounds at 18 Counts, Four VerifiedS3 · Issue #446 · PR #671 · PR #688

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• T-196 de Winter reports three smaller rational upper bounds at 227, 229 and 260n = 227, 229, 260 · V3 C3 S3 · de Winter · superseded
• T-197 Daniel's smaller n155 packing, started from Ostashev's packingn = 155 · V3 C3 S3 · Daniel
• T-200 Mixed rectangle-measure lower bound s(38) ≥ 2631/400 reported, on a 2,073-direction declared netn = 38 · V0 C0 S3 · Hosono
• T-201 Mixed rectangle-measure lower bound s(40) ≥ 1347/200 reported, on a 2,073-direction declared netn = 40 · V0 C0 S3 · Hosono
• T-202 Mixed rectangle-measure lower bound s(41) ≥ 2721/400 reported, on a 2,073-direction declared netn = 41 · V0 C0 S3 · Hosono
• T-203 Mixed rectangle-measure lower bound s(43) ≥ 2777/400 reported, on a 2,073-direction declared netn = 43 · V0 C0 S3 · Hosono
• T-204 Mixed rectangle-measure lower bound s(51) ≥ 3011/400 reported, on a 2,073-direction declared netn = 51 · V0 C0 S3 · Hosono
• T-205 Mixed rectangle-measure lower bound s(68) ≥ 853/100 verified, on the 201-direction netn = 68 · V3 C3 S3 · Hosono
• T-206 Mixed rectangle-measure lower bound s(84) ≥ 3769/400 verified, on the 201-direction netn = 84 · V3 C3 S3 · Hosono
• T-207 Mixed rectangle-measure lower bound s(85) ≥ 379/40 verified, on the 201-direction netn = 85 · V3 C3 S3 · Hosono
• T-208 Mixed rectangle-measure lower bound s(86) ≥ 3811/400 reported, on the 201-direction netn = 86 · V0 C0 S3 · Hosono
• T-209 Mixed rectangle-measure lower bound s(88) ≥ 3853/400 reported, on the 201-direction netn = 88 · V0 C0 S3 · Hosono
• T-210 Mixed rectangle-measure lower bound s(89) ≥ 1937/200 reported, on the 201-direction netn = 89 · V0 C0 S3 · Hosono
• T-211 Mixed rectangle-measure lower bound s(91) ≥ 783/80 reported, on the 201-direction netn = 91 · V0 C0 S3 · Hosono
• T-212 Mixed rectangle-measure lower bound s(90) ≥ 489/50 reported, on the 201-direction netn = 90 · V0 C0 S3 · Hosono
• T-213 Mixed rectangle-measure lower bound s(92) ≥ 493/50 reported, on the 201-direction netn = 92 · V0 C0 S3 · Hosono
• T-214 Mixed rectangle-measure lower bound s(106) ≥ 10503/1000 reported, on the 201-direction netn = 106 · V0 C0 S3 · Hosono
• T-215 Mixed rectangle-measure lower bound s(107) ≥ 529/50 reported, on the 201-direction netn = 107 · V0 C0 S3 · Hosono
• T-216 Mixed rectangle-measure lower bound s(108) ≥ 531/50 verified, on the 201-direction netn = 108 · V3 C3 S3 · Hosono
• T-217 Mixed rectangle-measure lower bound s(110) ≥ 1073/100 reported, on the 201-direction netn = 110 · V0 C0 S3 · Hosono
• T-198 Daniel's opening n229 dilation certificate, after Couzo and de Wintern = 229 · V3 C3 S2 · Daniel · superseded
• T-199 Daniel's smaller n229 update, replacing the opening certificaten = 229 · V3 C3 S2 · Daniel · superseded
• T-195 A tighter rational certificate of Schadt and Ellsworth's 29-square packing, 1.57e-36 below T-155n = 29 · V3 C3 S1 · PingYou Ltd
• T-174 is now the record packing at 68, 84, 86, 103, 108, 110, 127, 131, 181, 206, 208, 209, 210, 238, 239, 240, 261, 263, 272, 273, 305 and 306
• T-195 is now the record packing at 29
• Fitzharding’s Reported 17-Square Proof Admitted on Its Own BuildS3 · Issue #565 · PR #645

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• T-186 is now the record packing at 129, 176 and 264
• T-187 is now the record packing at 146
• T-188 is now the record packing at 211
• Smaller Confirmed Packings Adopted at 15 Square CountsS3 · Issue #506 · Issue #593 · Issue #606 · Issue #607 · PR #657

• T-194 Fitzharding reports a Lean proof that Wainwright's packing is optimal, s(19) = 3 + 4√2/3n = 19 · V0 C1 S5 · Fitzharding
• T-189 Couzo's refinement of Polkovskyi's 237, and fifteen beyond-horizon boundsn = 237 · V3 C3 S3 · Couzo · superseded
• T-191 s(95) = 10, by a mixed cover of points and grid-line segmentsn = 95, 96 · V3 C3 S3 · Greff
• T-192 Continuous-pose lower bound s(28) > 1149/200 reported, by two of the source's programsn = 28 · V0 C1 S3 · Hosono
• T-188 A tighter exact certificate for 211 squares from Couzo, of Ostashev's arrangementn = 211 · V3 C3 S2 · Couzo
• T-190 A tighter exact certificate for 237 squares from Couzo, below his issue-607 certificaten = 237 · V3 C3 S2 · Couzo · superseded
• T-193 Exact algebraic sides at sixteen counts from Daniel, of packings the record credits16 counts from 88 to 302 · V3 C3 S2 · Daniel
• 252 upper bounds beyond n = 324n = 339–991 · Francisco Couzo · all since superseded
• 15 upper bounds beyond n = 324n = 339–804 · Francisco Couzo · all since superseded
• Fitzharding Reports a Lean Proof for 19 SquaresS5 · Issue #640 · PR #651
• Greff Reports an Optimum for 95 SquaresS3 · Issue #610 · PR #627
• Hosono Reports a Stronger Lower Bound for 28 SquaresS3 · PR #627
• Regularized Drawings for Six Re-Housed Counts, Including 176S3 · PR #644

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• T-185 A tighter packing of 175 squares from Couzo, superseded by Ostashev's compositionn = 175 · V3 C3 S2 · Couzo · superseded
• T-187 A smaller packing of 146 squares from Daniel's chain search, started from Xu's packingn = 146 · V3 C3 S2 · Daniel
• T-186 Exact certificates at twelve counts from Polkovskyi, tightening the smallest reported there12 counts from 129 to 304 · V3 C3 S1 · Polkovskyi
• T-182 is now the record packing at 241
• Atlas Posters Include the October Packing ResultsS2 · PR #619 · Current 1–100 packing infographic · Current 1–324 packing poster · Lower-bounds paper · Publication evidence · Atlas and downloadable editions · Published release and verification · Site v0.7.7; Infographics v0.6.1; New Lower Bounds for Square Packing for n = 11 v0.4.7
• Every Selected Validation Check Now RunsS3 · PR #620 · Validation tiers
• Smaller Verified Packings for 18 Square CountsS3 · Issue #503 · Issue #504 · Issue #561 · Issue #562 · Issue #564 · Issue #566 · Issue #567 · Issue #568 · Issue #569 · Issue #570 · Issue #573 · Issue #574 · Issue #575 · Issue #583 · Issue #586 · Issue #593 · PR #614
• Significance Levels for News and Pull RequestsS3 · PR #621 · The significance rubric · Maintaining the project changelog

Show these 3 in the table

• T-163 s(n² − n + 1) < n for every n ≥ 15, and n² − n + F(n) squares below side n, from Fangn = 211, 241, 273, 307 · V3 C1 S4 · Fang · superseded
• T-180 Closed-form lower bound s(N) ≥ a(N) for every non-square N ≥ 49, reported264 counts from 50 to 323 · V0 C1 S4 · Hosono
• T-157 s(40) > 3359/500 = 6.718, by T-145's continuous-pose kernel on a density with 163 new supportsn = 40 · V3 C3 S3 · Guzhou0806
• T-158 New packings of 175, 232 and 264 squares built on a new 38-square rectangle, each certified exactlyn = 175, 232, 264 · V3 C3 S3 · Ostashev · superseded
• T-160 A smaller packing of 154 squares from Daniel's size-chaining explorer, certified exactlyn = 154 · V3 C3 S3 · Daniel · superseded
• T-161 Exact rational certificates at 156, 176, 237 and 271 from Couzon = 156, 176, 237, 271 · V3 C3 S3 · Couzo · superseded
• T-162 New packings of 129, 204 and 303 squares, a cut-out and two compositions, each certified exactlyn = 129, 204, 303 · V3 C3 S3 · Ostashev · superseded
• T-164 A packing of 302 squares from four boundary patches of Xu's packing of 70 and two upright banksn = 302 · V3 C3 S3 · PingYou Ltd · superseded
• T-172 A packing of 154 squares from Couzo, continuing Daniel's arrangementn = 154 · V3 C3 S3 · Couzo · superseded
• T-175 New packings of 211, 241 and 304 squares, two with merged tilted bands, each certified exactlyn = 211, 241, 304 · V3 C3 S3 · Ostashev · superseded
• T-176 Mixed rectangle-measure lower bound s(39) ≥ 533/80 verified, on a 2,073-direction declared netn = 39 · V3 C3 S3 · Hosono
• T-177 Mixed rectangle-measure lower bound s(44) ≥ 2799/400 reported, on a 2,073-direction declared netn = 44 · V0 C1 S3 · Hosono · superseded
• T-178 Mixed rectangle-measure lower bound s(37) ≥ 2599/400 verified, on a 2,073-direction declared netn = 37 · V3 C3 S3 · Hosono
• T-179 Linear-measure lower bound s(n) ≥ 306/25 = 12.24 for n = 145…149, replayedn = 145–149 · V3 C3 S3 · Hosono
• T-181 Exact rational certificates at 211, 241 and 302 from Couzon = 211, 241, 302 · V3 C3 S3 · Couzo · superseded
• T-182 Exact rational certificates at 154, 211 and 241 from Couzon = 154, 211, 241 · V3 C3 S3 · Couzo
• T-183 Polkovskyi's certificate for 237 squares, the smallest known side there when registeredn = 237 · V3 C3 S3 · Polkovskyi · superseded
• T-184 s(76) = 9, by a mixed cover of points and grid-line segmentsn = 76 · V3 C3 S3 · Greff
• T-159 Another arrangement of Xu's design for 102 squares, certified exactly from its decimal layoutn = 102 · V3 C3 S2 · Calle · superseded
• T-165 A tighter certificate at 176 from Couzo, published with no issuen = 176 · V3 C3 S2 · Couzo · superseded
• T-167 A tighter rational realization of PingYou Ltd's packing of 207 squaresn = 207 · V3 C3 S2 · PingYou Ltd · superseded
• T-168 A further exact refinement of Xu's packing of 146 squares, after Barnett'sn = 146 · V3 C3 S2 · PingYou Ltd · superseded
• T-169 A further exact refinement of Xu's packing of 261 squares, after Barnett'sn = 261 · V3 C3 S2 · PingYou Ltd · superseded
• T-173 Polkovskyi's packings of 153 and 207 squares, each below the earlier refinements theren = 153, 207 · V3 C3 S2 · Polkovskyi · superseded
• T-155 Exact regularized sides at 59 counts, 5.4e-20 to 9.9e-15 below the ceilings they replace59 counts from 28 to 300 · V3 C3 S1 · Levy
• T-156 s(290) ≤ 17.5355339059327376…, by monotonicity from T-155, with its own exact certificaten = 290 · V3 C3 S1 · Levy
• T-166 A tighter rational realization of PingYou Ltd's packing of 153 squaresn = 153 · V3 C3 S1 · PingYou Ltd · superseded
• T-170 An exact contact refinement of Xu's packing of 105 squares, after Couzo'sn = 105 · V3 C3 S1 · PingYou Ltd · superseded
• T-171 An exact contact refinement of SQUISH's packing of 272 squaresn = 272 · V3 C3 S1 · PingYou Ltd · superseded
• T-174 Tighter certificates at 68 counts from PingYou Ltd, of others' packings and its own68 counts from 68 to 308 · V3 C3 S1 · PingYou Ltd
• 14 upper bounds beyond n = 324n = 380–814 · Kevin Fang · all since superseded
• 9 upper bounds beyond n = 324n = 339–382 · Francisco Couzo · 8 since superseded
• 5 upper bounds beyond n = 324n = 338–378 · Francisco Couzo · 3 since superseded
• 4 upper bounds beyond n = 324n = 339–382 · Francisco Couzo · all since superseded
• 3 upper bounds beyond n = 324n = 339–375 · Evan Daniel · all since superseded
• 3 upper bounds beyond n = 324n = 365–460 · Evan Daniel · all since superseded
• 1 upper bound beyond n = 324n = 932 · Kevin Fang · all since superseded
• Basic and Advanced Tutorials Under ExplanationsS4 · PR #604
• Initial Reviews of the 17-Square Proof ReportsS3 · Issue #557 · Issue #565 · PR #592 · PR #595
• Audit Covers Every Open Upper-Bound ReportS3 · PR #601
• Fang and Hosono Report New Bound FamiliesS4 · Issue #446 · Issue #503 · Issue #504 · Issue #561 · Issue #562 · Issue #564 · Issue #566 · Issue #567 · Issue #568 · Issue #569 · Issue #570 · Issue #573 · Issue #574 · Issue #575 · Issue #583 · Issue #586 · Issue #593 · Issue #594 · Issue #600 · Issue #603 · PR #602
• A Stronger 40-Square Bound and Four Smaller PackingsS3 · Issue #485 · Issue #528 · Issue #529 · Issue #552 · PR #598
• Release Histories for the Site, Papers and PostersS4 · PR #590 · Current About changelog · Current 1–100 packing infographic · Current 1–324 packing poster · Current lower-bounds explainer · Publication evidence · GitHub changelog · Component release rules · Site v0.6.0; Infographics v0.6.0; New Lower Bounds for Square Packing for n = 11 v0.4.6
• Regularized Packings With Originals for ComparisonS4 · PR #511 · PR #530 · PR #548 · PR #549 · PR #559 · PR #580 · PR #585 · PR #587 · PR #591
• Seventeen Close Packing Comparisons Resolved ExactlyS2 · PR #605 · Publication evidence · The intake runbook · The decided comparisons · Site v0.6.3
• Result Ratings and Verification Evidence AuditedS3 · Issue #238 · Issue #256 · PR #563

Show these 30 in the table

• T-153 Candidate proof that Bidwell's 1998 packing is optimal, s(17) = 4.67553009360455…n = 17 · V0 C1 S5 · Overbeck
• T-154 Fitzharding reports a Lean proof that s(17) = 4.67553009360455…n = 17 · V3 C1 S5 · Fitzharding
• Verification Gaps in 92 Packing RecordsS3 · PR #581
• Fitzharding Reports a Lean Proof for 17 SquaresS5 · Issue #565 · PR #588
• Overbeck Reports a Candidate Proof for 17 SquaresS5 · Issue #557 · PR #560
• A Second Review of Overbeck’s 17-Square Candidate ProofS3 · Issue #557 · PR #577
• Rules for Verifying Regularized DrawingsS2 · PR #497 · PR #509 · Regularization policy · Assessment · Retained regularizer

Show these 2 in the table

• T-147 A packing of 207 squares from two placed patches of Xu's packing of 70n = 207 · V3 C3 S3 · PingYou Ltd · superseded
• T-148 A packing of 153 squares built from Xu's packing of 70, its contacts reclosed at a new anglen = 153 · V3 C3 S3 · PingYou Ltd · superseded
• T-149 New packings of 155, 156 and 211 squares, each with an exact rational certificaten = 155, 156, 211 · V3 C3 S3 · Ostashev · superseded
• T-151 Nine exact rational packings from SQUISH's fourth requestn = 176, 181, 238, 239, 270–272, 304, 305 · V3 C3 S3 · Chaoweeraprasit · superseded
• T-152 Exact rational refinements of SQUISH's Mondrian packings of 304 and 305 squaresn = 304, 305 · V3 C3 S3 · Couzo · superseded
• T-150 Exact rational refinements of Xu's packings of 146 and 261 squaresn = 146, 261 · V3 C3 S2 · Barnett · superseded
• T-134 is now the record packing at 267
• T-139 is now the record packing at 126
• T-146 is now the record packing at 292
• 9 upper bounds beyond n = 324n = 338–381 · Francisco Couzo · 7 since superseded
• Corrections to Result Reports Stay VisibleS2 · PR #531 · Intake workflow
• Smaller Certified Packings for 42 Square CountsS3 · Issue #501 · Issue #503 · Issue #504 · Issue #505 · PR #512 · PR #516 · PR #518
• PingYou Names PY as Its AI AssistantS2 · Issue #503 · Issue #504 · PR #558 · Current 207-square PingYou record · Current 153-square PingYou record · Publication evidence
• Publication Checks Follow Code DependenciesS2 · PR #507 · Publication and validation workflow
• Nine Smaller Packings From Chaoweeraprasit and CouzoS3 · Issue #500 · Issue #506 · PR #553

Show these 6 in the table

• T-132 Mixed rectangle-measure lower bound s(29) ≥ 291/50 reported, on a 2,073-direction declared netn = 29 · V0 C0 S3 · Hosono
• T-133 s(40) > 335427/50000 = 6.70854, by a clipped-corner transfer on a 401-direction netn = 40 · V3 C3 S3 · Guzhou0806 · superseded
• T-134 Six exact rational certificates from Couzon = 132, 237, 263, 267, 270, 303 · V3 C3 S3 · Couzo
• T-135 A packing of 308 squares below the grid, from Fangn = 308 · V3 C3 S3 · Fang · superseded
• T-136 Seventeen exact rational packings from SQUISH's third request17 counts from 131 to 307 · V3 C3 S3 · Chaoweeraprasit · superseded
• T-138 Exact witnesses at Mishapolk's printed ceilings, the smallest known at 103 and 258 when registered16 counts from 84 to 306 · V3 C3 S3 · Polkovskyi · superseded
• T-140 Six more exact rational certificates from Couzon = 132, 175, 209, 237, 270, 305 · V3 C3 S3 · Couzo · superseded
• T-141 Exact rational certificates at 132 and 308 from Daniel's third record huntn = 132, 308 · V3 C3 S3 · Daniel · superseded
• T-142 Mixed rectangle-measure lower bound s(28) ≥ 2297/400 reported, on a 2,073-direction declared netn = 28 · V0 C0 S3 · Hosono
• T-143 Mixed rectangle-measure lower bound s(30) ≥ 2357/400 reported, on a 2,073-direction declared netn = 30 · V0 C0 S3 · Hosono
• T-144 Linear-measure lower bound s(n) ≥ 563/50 = 11.26 for n = 122…126, reportedn = 122–126 · V0 C0 S3 · Hosono
• T-145 s(40) > 1340000/199529 = 6.7158157…, by a continuous-pose interval kerneln = 40 · V3 C3 S3 · Guzhou0806 · superseded
• T-137 An exact rational refinement of Xu's packing of 70 squaresn = 70 · V3 C3 S2 · Deleeuw · superseded
• T-139 A more precise certificate of Xu's 126-square arrangement, from Danieln = 126 · V3 C3 S2 · Daniel
• T-146 Exact rational certificates at fifteen counts from Daniel's regularized record lists15 counts from 70 to 303 · V3 C3 S2 · Daniel
• 2 upper bounds beyond n = 324n = 343–344 · Evan Daniel · all since superseded
• 2 upper bounds beyond n = 324n = 343–344 · Kevin Fang · all since superseded
• Publication Audits Show Progress and FailuresS2 · PR #496 · Publication and validation workflow
• Fuller Credit for Daniel’s ResultsS2 · Issue #256 · Issue #296 · Issue #316 · PR #508 · Current contributor and result overview · Publication evidence
• Exact Certificates and a Stronger 40-Square BoundS3 · Issue #375 · Issue #446 · Issue #451 · Issue #465 · Issue #470 · Issue #476 · Issue #481 · Issue #483 · Issue #484 · Issue #485 · Issue #488 · Issue #489 · PR #487
• Narrower Text Columns and Responsive NavigationS2 · PR #513 · Current project overview · Current About page · Publication evidence · Front-door prose review · Reader-document prose review
• Shared Navigation Connects the Atlas, Results and PapersS4 · PR #462 · Overview · Atlas · Results · Papers and downloads · Publication evidence
• Share a Result With the Squares ProjectS2 · PR #502 · Project homepage · Reporting results on About · Publication evidence

Show these 15 in the table

• T-131 s(132) ≤ 11.987099332245063… from Daniel's record huntn = 132 · V3 C3 S3 · Daniel · superseded
• 2 upper bounds beyond n = 324n = 375–378 · Francisco Couzo · 1 since superseded
• Daniel’s Exact Certificates for 132 and 155 SquaresS3 · Issue #451 · Issue #465 · PR #478
• Couzo Reports Smaller Packings at 375 and 378 SquaresS3 · PR #479
• Five Illustrations of Packing Search and CertificationS3 · PR #477
• Consistent Typography Across the PapersS2 · PR #492 · Current Part I paper · Current Part I PDF · Current Part II paper · Current Part II PDF · Current Part III paper · Current Part III PDF · Current methods tutorial · Current methods tutorial PDF · Publication evidence · New Lower Bounds for Square Packing for n = 11 v0.4.5; How Record Square Packings Are Found v0.2.1
• Compare Packings on Screen and on PaperS4 · PR #474

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• T-119 Three exact feasible upper bounds at n=266,270,272 from new source arrangementsn = 266, 270, 272 · V3 C3 S3 · Daniel
• T-125 Complete rational construction reports at 25 counts25 counts from 51 to 295 · V3 C3 S3 · Xu · superseded
• T-126 Undilated n51 construction over Q(sqrt2)n = 51 · V3 C3 S3 · Xu
• T-127 Fourteen rational refinements, seventeen complete source cases17 counts from 88 to 239 · V3 C3 S3 · Gupta
• T-128 Eight complete rational refinements from Couzon = 105, 108, 127, 131, 155, 180, 228, 306 · V3 C3 S3 · Couzo · superseded
• T-130 Five follow-up rational refinements from Couzon = 84, 86, 105, 175, 270 · V3 C3 S3 · Couzo · superseded
• T-117 Exact rational ceiling refinements at n = 105, 292n = 105, 292 · V3 C3 S2 · Rehwaldt · superseded
• T-118 Exact rational ceiling refinements at n = 68n = 68 · V3 C3 S2 · Rehwaldt · superseded
• T-120 Reported s(102) ≤ alpha_102 with a degree-8 exact side formn = 102 · V0 C0 S2 · Daniel · superseded
• T-121 Reported s(106) ≤ alpha_106 with a degree-32 exact side formn = 106 · V0 C0 S2 · Daniel
• T-122 Reported s(152) ≤ alpha_152 with a degree-40 exact side formn = 152 · V0 C0 S2 · Daniel
• T-123 Reported s(177) ≤ alpha_177 with a degree-32 exact side formn = 177 · V0 C0 S2 · Daniel
• T-124 Reported non-strict local minima for 178 source configurations178 counts from 1 to 324 · V0 C0 S2 · Daniel
• T-129 Three dated Daniel certificate reports with historical source custodyn = 105, 130, 292 · V0 C0 S1 · Daniel · superseded
• 20 upper bounds beyond n = 324n = 327–379 · Francisco Couzo · 17 since superseded
• Couzo Reports Eight Smaller Exact PackingsS3 · Issue #451 · Issue #465 · PR #460
• Couzo Reports Five Further Exact PackingsS3 · Issue #451 · PR #469
• Couzo Reports Packings Beyond 324 SquaresS3 · PR #466
• Daniel’s Smaller Packings at 266, 270 and 272 SquaresS3 · Issue #399 · Issue #419 · Issue #420 · PR #441
• Gupta’s Refinements Improve 14 Packing BoundsS3 · Issue #438 · PR #448 · PR #459
• Hosono Reports Seven Stronger Lower BoundsS3 · Issue #446 · PR #450
• Hosono’s Twelve Certificates Narrow the 17-Square SearchS3 · Issue #472 · PR #475
• A Survey of How Square Packings Are FoundS4 · PR #458
• Ryu Reports Polynomial Deficiency BoundsS4 · Issue #414 · PR #439 · PR #440
• Xu’s Verified Packings Include an Exact 51-Square ConstructionS3 · Issue #432 · PR #442

Show these 14 in the table

• T-116 s(n) ≤ S_n at nine counts, from the second SQUISH update’s new rational packings9 counts from 88 to 302 · V3 C3 S3 · Chaoweeraprasit · superseded
• Readable Formulas in the Frontier TablesS2 · PR #456 · Frontier table · Static rendering and deployment work

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• T-113 s(n) ≤ S_n at ten counts, n = 108 to 303, from new SQUISH rational packings10 counts from 108 to 303 · V3 C3 S3 · Chaoweeraprasit · superseded
• T-114 s(153) ≤ 7250614903299225/562949953421312, from a SQUISH rational packingn = 153 · V3 C3 S3 · Chaoweeraprasit · superseded
• T-115 s(n) ≤ S_n at twelve counts, from the SQUISH update’s new and smaller rational packings12 counts from 123 to 263 · V3 C3 S3 · Chaoweeraprasit · superseded

Show these 3 in the table

• T-095 s(12) ≥ 7943/2000 = 3.9715, Daniel's points dilated and re-weightedn = 12 · V3 C3 S3 · Ryu · superseded
• T-096 Mixed rectangle-measure lower bound replayed at n = 18, on a net the certificate declaresn = 18 · V3 C3 S3 · Hosono · superseded
• T-097 Mixed rectangle-measure lower bound verified at n = 66n = 66 · V3 C3 S3 · Hosono
• T-099 Mixed rectangle-measure lower bound verified at n = 18, on a finer declared netn = 18 · V3 C3 S3 · Hosono · superseded
• T-100 Mixed rectangle-measure lower bound verified at n = 19, past the best 18-square packingn = 19 · V3 C3 S3 · Hosono · superseded
• T-102 Mixed rectangle-measure lower bound verified at n = 18, on the finest declared net yetn = 18 · V3 C3 S3 · Hosono
• T-103 Mixed rectangle-measure lower bound verified at n = 19, on the finest declared net yetn = 19 · V3 C3 S3 · Hosono · superseded
• T-104 Mixed rectangle-measure lower bound verified at n = 20, on a declared netn = 20 · V3 C3 S3 · Hosono · superseded
• T-105 Mixed rectangle-measure lower bound verified at n = 26, on a declared netn = 26 · V3 C3 S3 · Hosono · superseded
• T-106 Mixed rectangle-measure lower bound verified at n = 27, on a declared netn = 27 · V3 C3 S3 · Hosono · superseded
• T-107 Mixed rectangle-measure lower bound verified at n = 28, on a declared netn = 28 · V3 C3 S3 · Hosono
• T-108 Mixed rectangle-measure lower bound verified at n = 29, on a declared netn = 29 · V3 C3 S3 · Hosono
• T-109 Mixed rectangle-measure lower bound verified at n = 30, on a declared netn = 30 · V3 C3 S3 · Hosono
• T-110 Mixed rectangle-measure lower bound verified at n = 39, on a declared netn = 39 · V3 C3 S3 · Hosono · superseded
• T-111 Mixed rectangle-measure lower bound verified at n = 41, on a declared netn = 41 · V3 C3 S3 · Hosono
• T-112 Trump's packing is the only optimal packing of eleven squares, up to symmetryn = 11 · V3 C2 S3 · Levy
• T-098 Exact optima of 48 known-best packings: s(n) ≤ S', 3.5e-13 to 5.0e-11 below each printed side48 counts from 68 to 307 · V3 C3 S2 · Daniel
• T-101 Exact certificates of 77 catalogue packings: s(n) ≤ S', 1.2e-16 to 9.8e-15 above each side77 counts from 28 to 300 · V3 C3 S2 · Daniel

Show these 18 in the table

• T-090 Mixed rectangle-measure lower bounds verified at 17 counts in n = 42…9617 counts from 42 to 96 · V3 C3 S3 · Hosono
• T-091 Mixed rectangle-measure lower bounds verified at 17 counts in n = 53…95n = 53, 54, 58, 70–73, 76, 87–95 · V3 C3 S3 · Hosono
• T-092 Smaller packings again at seven counts from n = 208 to 306, each certified two independent waysn = 208, 209, 228, 263, 272, 303, 306 · V3 C3 S3 · Couzo · superseded
• T-094 Mixed rectangle-measure lower bounds verified at n = 67 and 84n = 67, 84 · V3 C3 S3 · Hosono
• T-088 s(69) ≤ 8.82719465572975, Ellsworth's degree-38 packing, certified exactly from its picturen = 69 · V3 C3 S2 · Ellsworth · superseded
• T-089 s(83) ≤ 9.63475764863195 and s(87) ≤ 9.83881526994915, Chang's packings, certified exactlyn = 83, 87 · V3 C3 S2 · Chang, Ellsworth · superseded
• T-093 s(17) > 18641771/4000000 = 4.66044275n = 17 · V3 C3 S2 · Guzhou0806

Show these 7 in the table

• T-083 s(n) ≥ 1/2 + √(n − ⌊√n⌋ + 1/4) for every nonsquare 8 ≤ n ≤ 324301 counts from 8 to 323 · V3 C3 S3 · Karakuş
• T-084 s(k² − 1) = k for every integer k ≥ 3; k = 3…18 are the cases held here16 counts from 8 to 323 · V3 C3 S3 · Karakuş
• T-085 Nagamochi 2005, Lemma 1 is false for every container with a > 3 and b > 2n = 10–324 · V3 C3 S3 · Karakuş; Vlasenko
• T-086 s(k² − 2) = k for every integer k ≥ 2; k = 3…18 are the cases held here16 counts from 7 to 322 · V3 C3 S3 · Vlasenko
• T-087 s(37) ≥ 5√3/2 + 2√2 − 1 and s(61) ≥ 7√3/2 + 2√2 − 1, by optimal piercingn = 37, 61 · V3 C1 S3 · Bašić, Slivková · superseded

Show these 5 in the table

• T-081 s(k² − 4) = k for every integer k from 5 up; k = 5…18 are the cases held here14 counts from 21 to 320 · V0 C1 S4 · Daniel
• T-066 s(59) = 8, by a mixed cover of points and grid-line segmentsn = 59 · V3 C3 S3 · Hosono
• T-067 s(77) = 9, by a mixed cover extended from Daniel's s(60) covern = 77, 78 · V3 C3 S3 · Hosono
• T-068 Rectangle-density lower bounds verified at 34 counts in n = 19…9534 counts from 19 to 95 · V3 C3 S3 · Hosono
• T-069 Mixed rectangle-measure lower bounds replayed at n = 37, 65, 66, 90, 92n = 37, 65, 66, 90, 92 · V3 C3 S3 · Hosono
• T-070 Rectangle-density lower bounds replayed at 25 counts in n = 29…9525 counts from 29 to 95 · V3 C3 S3 · Hosono · superseded
• T-071 Mixed rectangle-measure lower bounds replayed at n = 84…87n = 84–87 · V3 C3 S3 · Hosono · superseded
• T-072 Mixed rectangle-measure lower bound replayed at n = 76n = 76 · V3 C3 S3 · Hosono · superseded
• T-073 Linear-measure lower bounds replayed at n = 83 and n = 101…105n = 83, 101–105 · V3 C3 S3 · Hosono
• T-074 Rectangle-density lower bounds replayed at 31 counts in n = 19…9531 counts from 19 to 95 · V3 C3 S3 · Hosono
• T-075 Mixed rectangle-measure lower bounds replayed at nine counts in n = 83…96n = 83, 85–88, 91–93, 96 · V3 C3 S3 · Hosono
• T-076 Linear-measure lower bound replayed at n = 82n = 82 · V3 C3 S3 · Hosono
• T-077 Rectangle-density lower bounds replayed at n = 20, 42 and 70n = 20, 42, 70 · V3 C3 S3 · Hosono · superseded
• T-079 s(12) ≥ 15680000/3949423 = 3.9702002…, Daniel's points re-weightedn = 12 · V3 C3 S3 · Levy · superseded
• T-080 Linear-measure lower bound replayed at n = 101…105n = 101–105 · V3 C3 S3 · Hosono
• T-082 Mixed rectangle-measure lower bounds verified at 22 counts in n = 51…96n = 51, 52, 55, 58, 69–71, 73–76, 86–96 · V3 C3 S3 · Hosono
• T-078 s(12) ≥ 31360/7901 = 3.9691178…, Daniel's certificate rescaled by 7902/7901n = 12 · V3 C3 S2 · Ryu · superseded

Show these 17 in the table

• T-064 s(k² − 3) = k for every integer k from 6 up; k = 6…18 are the cases held here13 counts from 33 to 321 · V3 C3 S4 · Daniel
• T-062 s(60) = 8, by a mixed cover of points and grid-line segmentsn = 60 · V3 C3 S3 · Daniel
• T-063 s(61) = 8, by monotonicity from T-062n = 61 · V3 C3 S3 · Daniel
• T-061 s(11) > 3875000000/999999999 = 3.875000003875…, 3.9e-9 above 31/8n = 11 · V3 C3 S2 · Wang, Li · superseded
• T-065 s(17) ≤ 4.6755300936045509…, Bidwell's packing certified exactlyn = 17 · V3 C3 S2 · Overbeck

Show these 5 in the table

• T-060 Trump's eleven-square packing is globally optimaln = 11 · V3 C3 S5 · Ahmed
• T-058 Rectangle-certificate ceiling α·UB(n) proved for n = 1..100; B·UB(n) on 64 grid rowsn = 1–100 · V3 C3 S2 · Hosono
• T-059 Reported equality of 12028 n11 row minima reproduced by a complete bound replayn = 11 · V3 C3 S2 · Hosono
• Ahmed Proves Trump’s Eleven-Square Packing OptimalS5 · PR #246

Show these 3 in the table

• T-037 s(11) > 31/8 = 3.875n = 11 · V3 C3 S5 · Overbeck · superseded
• T-047 s(11) ≥ 381/100; s(n) ≥ 1377/250 for n = 26…28; s(n) ≥ 571/100 for n = 29…31n = 11, 26–31 · V3 C3 S4 · Tokoharu · superseded
• T-051 s(32) = 6n = 32 · V3 C3 S4 · Daniel
• T-052 s(21) = 5, by a mixed cover of points and grid-line segmentsn = 21 · V3 C3 S4 · Daniel
• T-038 s(17) > 461300/99853 = 4.6197910929…n = 17 · V3 C3 S3 · Overbeck · superseded
• T-039 s(17) > 231001/50000 = 4.62002n = 17 · V3 C3 S3 · Guzhou0806 · superseded
• T-040 s(17) > 232001/50000 = 4.64002n = 17 · V3 C3 S3 · Overbeck · superseded
• T-041 s(17) > 466001/100000 = 4.66001n = 17 · V3 C3 S3 · Overbeck · superseded
• T-043 s(17) > 116511/25000 = 4.66044n = 17 · V3 C3 S3 · Guzhou0806 · superseded
• T-044 Weighted point lower bounds for ten counts in n = 26…72, plus seven from the same filesn = 26, 29, 39–41, 52–57, 68–73 · V3 C3 S3 · Hosono · superseded
• T-045 Rectangle-density lower bounds replayed at 15 counts in n = 18…78n = 18–20, 26–28, 30–32, 40, 61, 75–78 · V3 C3 S3 · Hosono · superseded
• T-046 Rectangle-density lower bounds verified at 48 counts in n = 18…9548 counts from 18 to 95 · V3 C3 S3 · Hosono · superseded
• T-048 s(50) ≥ 37/5 = 7.4n = 50, 51 · V3 C3 S3 · Hosono
• T-049 s(12) ≥ 15680/3951 = 3.9686155…n = 12 · V3 C3 S3 · Daniel · superseded
• T-050 s(21) ≥ 5000/1001 = 4.995004995…n = 21 · V3 C3 S3 · Daniel · superseded
• T-053 s(45) = 7, by a mixed cover of points and grid-line segmentsn = 45 · V3 C3 S3 · Daniel
• T-056 Smaller packings for 49 counts from n = 68 to 307, each certified two independent ways49 counts from 68 to 307 · V3 C3 S3 · Couzo · superseded
• T-057 s(211) ≤ 14.99796070496771500150 < 15, the first packing of 211 squares below the grid on recordn = 211 · V3 C3 S3 · de Winter · superseded
• T-042 s(17) > 233009/50000 = 4.66018n = 17 · V3 C3 S2 · Guzhou0806 · superseded
• T-054 s(45) = 7 by a second, point-only routen = 45 · V3 C3 S2 · Hosono
• T-055 s(21) = 5 by a point-only routen = 21 · V3 C3 S2 · Hosono

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• T-034 s(21) ≥ 122/25 = 4.88n = 21 · V3 C3 S3 · Levy · superseded
• T-035 Six-plus-five packings near Trump's tilt with side ≤ U_hi lie within rho of his posen = 11 · V3 C3 S3 · Levy
• T-036 Trump's pose is optimal among six-plus-five packings near its tilt, unique up to symmetryn = 11 · V3 C2 S3 · Levy

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• T-033 s(11) ≥ 955000√(2073600042893309449)/359341754646249 = 3.8269975…n = 11 · V3 C3 S3 · Levy · superseded

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• T-032 s(17) ≥ 461300/99999 = 4.61304613…, and beneath it Mira's s(17) ≥ 4613/1000n = 17 · V3 C3 S3 · Guzhou0806, Mira-acc · superseded
• T-031 The octagon corner class (threshold 1/2) holds no eleven-square packing at side 96/25n = 11 · V3 C3 S2 · Levy · superseded

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• T-027 s(18) ≥ 467/100 = 4.67n = 18 · V3 C3 S3 · Levy · superseded
• T-028 s(18) ≥ 187/40 = 4.675n = 18 · V3 C3 S3 · Levy · superseded
• T-029 s(18) ≥ 1871/400 = 4.6775n = 18 · V3 C3 S3 · Levy · superseded
• T-030 s(18) ≥ 4679/1000 = 4.679n = 18 · V3 C3 S3 · Levy · superseded

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• T-024 s(11) ≥ 3175000√(518400042893309449)/598960960743657 = 3.8166095…n = 11 · V3 C3 S5 · Levy · superseded
• T-025 s(11) ≥ 191/50 = 3.82, by a threshold certificaten = 11 · V3 C3 S5 · Levy · superseded
• T-026 s(11) ≥ 955000√(518400042893309449)/179696714646249 = 3.8264474…n = 11 · V3 C3 S5 · Levy · superseded
• T-023 Conditional exclusion: no eleven-square packing in the four-owner branch at q = 96/25n = 11 · V3 C3 S3 · Levy

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• T-022 s(11) ≥ 38100√(8100042893309449)/899996306539 = 3.8100257…n = 11 · V3 C3 S5 · Levy · superseded

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• T-018 s(11) ≥ 381/100 = 3.81n = 11 · V3 C3 S5 · Levy · superseded
• T-017 s(12) ≥ 99/25 = 3.96n = 12 · V3 C3 S4 · Levy · superseded
• T-019 s(n) ≥ 459/100 = 4.59 for n = 17, 18, 19n = 17–19 · V3 C3 S4 · Levy · superseded
• T-020 s(n) ≥ 24/5 = 4.80 for n = 19, 20, 21n = 19–21 · V3 C3 S4 · Levy · superseded
• T-021 s(n) ≥ 97/20 = 4.85 for n = 20, 21n = 20, 21 · V3 C3 S3 · Levy · superseded

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• T-014 Goebel's n = 5 optimum is rigid at fixed side: its pose is an isolated feasible pointn = 5 · V3 C3 S3 · Levy
• T-015 s(17) ≥ 22529/5000 = 4.5058n = 17 · V3 C3 S3 · Massaccesi · superseded
• T-016 s(n) ≥ 22529/5000 for n = 18, 19, by monotonicity from T-015n = 18, 19 · V3 C3 S3 · Massaccesi · superseded

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• T-010 s(11) ≥ 2 + 4/√5, by a repair of Stromquist 2003's Figure 14 point setn = 11 · V3 C3 S4 · Levy · superseded
• T-001 s(17) ≥ 4426213/1000000 = 4.426213, from a sixteen-point unavoidable setn = 17 · V3 C3 S3 · Levy · superseded
• T-002 s(18) ≥ 4426213/1000000, by monotonicity from T-001n = 18 · V3 C3 S3 · Levy · superseded
• T-004 Bentz 2010, Theorem 8 (s(46) ≥ 7) is correct as printed, machine-audited in fulln = 46 · V3 C3 S3 · Bentz
• T-006 s(13) = 4n = 13 · V3 C3 S3 · Bentz; Daniel
• T-007 s(n) ≥ min(⌈√n⌉, √(n - 2⌊√n⌋ + 1) + 1) for 4 ≤ n ≤ 324n = 4–324 · V0 C1 S3 · Nagamochi
• T-008 s(46) = 7n = 46 · V3 C3 S3 · Bentz
• T-009 s(29) ≤ 5.93383346267692918974…, by a Krawczyk interval certificaten = 29 · V3 C3 S3 · Levy · superseded
• T-012 Goebel's n = 5 packing is second-order rigid at fixed siden = 5 · V3 C3 S3 · Levy
• T-013 Goebel's n = 40 packing: seven verified first-order flexes, each refused at second ordern = 40 · V3 C3 S3 · Levy
• T-003 The sixteen-point set's unavoidability ceiling lies in [4426213/1000000, 4427/1000)n = 17, 18 · V3 C3 S2 · Levy
• T-005 Bentz 2010, Lemma 10 is false as printed and true as corrected to (1.74, 1)n = 13 · V3 C3 S2 · Levy
• T-011 Trump's 1979 packing is exactly valid, so s(11) ≤ 3.877083590022814…n = 11 · V3 C3 S2 · Trump

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