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Verification Confirmation Kind Status Hide supersededSource Case n Max age daysAdded within daysProject 261 results

Date	Result	n	Credit	Rungs	Status	ID
2026-10-30 published	Polkovskyi's sub-print re-certifications at 105, 146, 156, 229 and 308, 1e-41 to 1e-21 below each	105, 146, 156, 229, 308	Polkovskyi after Couzo, Xu, Daniel, Ostashev, Levy	V0 C1Upper bound	reviewed	T-260
2026-10-30 published	Polkovskyi's re-solve of Couzo's packing of 130 squares, 2.08e-12 below T-254	130	Polkovskyi after Couzo, Xu, Daniel, Ostashev, Levy	V3 C3Upper bound	confirmed	T-259
2026-10-29 published	Daniel's lower packing of 299 squares from his T-248 packing, 2.46e-3 below it	299	Daniel after Deotte	V3 C3Upper bound	confirmed	T-258
2026-10-29 published	Daniel's new packings of 172, 204, 260 and 293 squares, 1.64e-4 to 1.18e-2 below each house	172, 204, 260, 293	Daniel after Chaoweeraprasit, Gupta, Ostashev, kirilltym, Friedman	V3 C3Upper bound	confirmed	T-257
2026-10-28 published	Couzo's packings from Kaggle notebook packings at 232, 260 and 307, below T-186, T-225 and T-174	232, 260, 307	Couzo after Chilton, ntumlnoob, Lavrentev, Ellsworth, Daniel, Levy	V3 C3Upper bound	confirmed	T-256
2026-10-28 published	Couzo's certificates of ntumlnoob's Kaggle packings at 260 and 307, below T-225 and T-174	260, 307	Couzo after ntumlnoob, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-257 and others	T-255
2026-10-27 published	Couzo's new packing of 130 squares from PR #574's, 2.05e-3 below T-174	130	Couzo after Chaoweeraprasit, Gupta, PingYou Ltd, Levy	V3 C3Upper bound	confirmed superseded by T-259	T-254
2026-10-26 published	$s (44) = 7$ , by a closed mixed cover of points and grid-line segments	44	Khalili, Gharabaghi after Daniel	V3 C3Optimality	confirmed	T-252
2026-10-26 published	Daniel's new arrangement at 299, 1.92e-2 below the catalogue's construction	299	Daniel after Deotte	V3 C3Upper bound	confirmed superseded by T-258	T-248
2026-10-25 published	Kim's exact degree-21 side at 297, as reported, of the packing the record credits	297	Kim after Couzo, Daniel, PingYou Ltd, Levy	V3 C3Upper bound	confirmed	T-247
2026-10-25 published	Kim's exact algebraic sides at 172 and 263, as reported, of packings the record credits	172, 263	Kim after Couzo, Chaoweeraprasit, Daniel, PingYou Ltd, Levy	V3 C3Upper bound	confirmed	T-244
2026-10-25 published	Daniel's new arrangement at 182, 3.17e-3 below T-174	182	Daniel after Couzo, Ostashev, Levy	V3 C3Upper bound	confirmed	T-243
2026-10-24 published	Daniel's exact descents of public Kaggle packings at 268 and 304, below the reports before them	268, 304	Daniel after Lavrentev, Tymchishin	V3 C3Upper bound	confirmed	T-242
2026-10-23 published	Polkovskyi's sub-print re-certifications of nine house packings, 1.3e-19 to 1.7e-19 below each	154, 155, 183, 211, 227, 236, 237, 241, 271	Polkovskyi after Daniel, Couzo, Ostashev, de Winter, Chaoweeraprasit, Levy	V0 C1Upper bound	reviewed	T-253
2026-10-23 published	Couzo's certificate at 304 of Tymchishin's Kaggle notebook packing, 2.53e-3 below T-186	304	Couzo after Tymchishin, Levy	V3 C3Upper bound	confirmed superseded by T-242	T-241
2026-10-23 published	Couzo's 268 and 303 of #763, below T-174 and T-239, from Kaggle notebook packings	268, 303	Couzo after Lavrentev, Tymchishin, Muglich, Polkovskyi, Daniel, Fang, de Winter, Levy	V3 C3Upper bound	confirmed	T-240
2026-10-23 published	Kristiansen's smaller n303 packing, found from Daniel's packing, certified exactly	303	Kristiansen after Daniel, Ostashev, Levy	V3 C3Upper bound	confirmed superseded by T-240	T-239
2026-10-22 published	Polkovskyi's lower re-solve at 204 of Couzo's packing, 1.48e-11 below T-229	204	Polkovskyi after Couzo, Ostashev, PingYou Ltd, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-257	T-231
2026-10-22 published	Daniel's smaller n303 packing, started from Ostashev's packing, certified exactly	303	Daniel after Ostashev, Levy	V3 C3Upper bound	confirmed superseded by T-240	T-230
2026-10-22 published	Polkovskyi's re-solves of the house packings at 105 and 204, below T-174 and T-225	105, 204	Polkovskyi after Couzo, Muglich, Daniel, Xu, Ostashev, PingYou Ltd, Levy	V3 C3Upper bound	confirmed	T-229
2026-10-20 published	Daniel's solved, regularized views at 204, 227, 229 and 260, each the smallest side reported there	204, 227, 229, 260	Daniel after Couzo, de Winter, Polkovskyi, Ostashev, PingYou Ltd, Levy	V3 C3Upper bound	confirmed	T-225
2026-10-20 published	Daniel's smaller n270 packing, another arrangement found from Chaoweeraprasit's, certified exactly	270	Daniel after Chaoweeraprasit, Levy	V3 C3Upper bound	confirmed	T-224
2026-10-20 published	Daniel's smaller n154 packing, continuing Couzo's #586 arrangement, certified exactly	154	Daniel after Couzo, Ostashev, Levy	V3 C3Upper bound	confirmed	T-222
2026-10-19 published	Daniel's smaller n308 packing, started from Chaoweeraprasit's 307 packing, certified exactly	308	Daniel after Chaoweeraprasit, Levy	V3 C3Upper bound	confirmed	T-221
2026-10-19 published	Daniel's finite sub-grid upper bound for 183 squares, after Couzo's n182 packing	183	Daniel after Couzo; register seed data from Levy	V3 C3Upper bound	confirmed	T-220
2026-10-18 published	Daniel reports Lean proofs of Fang's Theorems 1 and 2, $s (n^{2} - n + 1) < n$ for $n \geq 15$	211, 241, 273, 307	Daniel after Fang, Arslanov, Mustafin, Shangitbayev, Levy	V0 C0Formalization	recorded	T-236
2026-10-18 published	Couzo's 204 of #675, below his #670, since superseded by his #678	204	Couzo after Polkovskyi, Ostashev, PingYou Ltd, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-257	T-228
2026-10-18 published	Couzo's smaller packings at 204 and 260, the two in the corpus of issue 678's 85 bounds	204, 260	Couzo after de Winter, Polkovskyi, Ostashev, Daniel, Fang, PingYou Ltd, Levy	V3 C3Upper bound	confirmed superseded by T-257	T-223
2026-10-18 published	Daniel's smaller n229 update, replacing the opening certificate	229	Daniel after Couzo, de Winter, Levy	V3 C3Upper bound	confirmed superseded by T-225	T-199
2026-10-17 published	Hosono reports a Lean kernel proof of Daniel's Valid7, and so of $s (k^{2} - 3) = k$ for every $k \geq 6$	33, 46, 61, 78, 97, 118, 141, 166, 193, 222, 253, 286, 321	Hosono after Daniel, Burns, Massaccesi; Hosono after Daniel, Levy, Burns, Massaccesi	V0 C0Formalization	recorded	T-250
2026-10-17 published	Couzo's refinements of de Winter's 227 and 229, below T-196 at both	227, 229	Couzo after de Winter, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-225	T-227
2026-10-17 published	Couzo's 204 of #670, below Polkovskyi's T-186, since superseded by his own #675 and #678	204	Couzo after Polkovskyi, Ostashev, PingYou Ltd, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-257	T-226
2026-10-17 published	Daniel's smaller n271 packing, continuing Couzo's arrangement, certified exactly	271	Daniel after Couzo, Chaoweeraprasit, Levy	V3 C3Upper bound	confirmed	T-219
2026-10-17 published	Daniel's opening n229 dilation certificate, after Couzo and de Winter	229	Daniel after Couzo, de Winter, Levy	V3 C3Upper bound	confirmed superseded by T-225	T-198
2026-10-17 published	Daniel's smaller n155 packing, started from Ostashev's packing	155	Daniel after Ostashev, Levy	V3 C3Upper bound	confirmed	T-197
2026-10-17 published	de Winter reports three smaller rational upper bounds at 227, 229 and 260	227, 229, 260	de Winter after Levy	V3 C3Upper bound	confirmed superseded by T-257 and others	T-196
2026-10-16 published	Hosono reports a Lean kernel proof of Daniel's ValidTilt9, so $s (k^{2} - 4) = k$ for every $k \geq 8$	60, 77, 96, 117, 140, 165, 192, 221, 252, 285, 320	Hosono after Daniel, Levy, Burns, Massaccesi	V0 C0Formalization	recorded	T-251
2026-10-16 published	Jatloe reports a Lean proof that the 4 × 3 grid is optimal, $s (12) = 4$	12	jatloe, Gurevitch, ctjlewis, Ahmed	V0 C0Optimality	recorded	T-245
2026-10-16 published	Daniel's smaller n236 packing, after Chaoweeraprasit's composition, certified exactly	236	Daniel after Chaoweeraprasit, Levy	V3 C3Upper bound	confirmed	T-218
2026-10-16 published	Mixed rectangle-measure lower bound $s (110) \geq 1073 / 100$ reported, on the 201-direction net	110	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-217
2026-10-16 published	Mixed rectangle-measure lower bound $s (108) \geq 531 / 50$ verified, on the 201-direction net	108	Hosono after Tokoharu and Levy	V3 C3Lower bound	confirmed	T-216
2026-10-16 published	Mixed rectangle-measure lower bound $s (107) \geq 529 / 50$ reported, on the 201-direction net	107	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-215
2026-10-16 published	Mixed rectangle-measure lower bound $s (106) \geq 10503 / 1000$ reported, on the 201-direction net	106	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-214
2026-10-16 published	Mixed rectangle-measure lower bound $s (92) \geq 493 / 50$ reported, on the 201-direction net	92	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-213
2026-10-16 published	Mixed rectangle-measure lower bound $s (90) \geq 489 / 50$ reported, on the 201-direction net	90	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-212
2026-10-16 published	Mixed rectangle-measure lower bound $s (91) \geq 783 / 80$ reported, on the 201-direction net	91	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-211
2026-10-16 published	Mixed rectangle-measure lower bound $s (89) \geq 1937 / 200$ reported, on the 201-direction net	89	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-210
2026-10-16 published	Mixed rectangle-measure lower bound $s (88) \geq 3853 / 400$ reported, on the 201-direction net	88	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-209
2026-10-16 published	Mixed rectangle-measure lower bound $s (86) \geq 3811 / 400$ reported, on the 201-direction net	86	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-208
2026-10-16 published	Mixed rectangle-measure lower bound $s (85) \geq 379 / 40$ verified, on the 201-direction net	85	Hosono after Tokoharu and Levy	V3 C3Lower bound	confirmed	T-207
2026-10-16 published	Mixed rectangle-measure lower bound $s (84) \geq 3769 / 400$ verified, on the 201-direction net	84	Hosono after Tokoharu and Levy	V3 C3Lower bound	confirmed	T-206
2026-10-16 published	Mixed rectangle-measure lower bound $s (68) \geq 853 / 100$ verified, on the 201-direction net	68	Hosono after Tokoharu and Levy	V3 C3Lower bound	confirmed	T-205
2026-10-16 published	Mixed rectangle-measure lower bound $s (51) \geq 3011 / 400$ reported, on a 2,073-direction declared net	51	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-204
2026-10-16 published	Mixed rectangle-measure lower bound $s (43) \geq 2777 / 400$ reported, on a 2,073-direction declared net	43	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-203
2026-10-16 published	Mixed rectangle-measure lower bound $s (41) \geq 2721 / 400$ reported, on a 2,073-direction declared net	41	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-202
2026-10-16 published	Mixed rectangle-measure lower bound $s (40) \geq 1347 / 200$ reported, on a 2,073-direction declared net	40	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-201
2026-10-16 published	Mixed rectangle-measure lower bound $s (38) \geq 2631 / 400$ reported, on a 2,073-direction declared net	38	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-200
2026-10-16 published	Fitzharding reports a Lean proof that Wainwright's packing is optimal, $s (19) = 3 + 4 \sqrt{2} / 3$	19	Fitzharding after Levy, Ahmed	V0 C1Optimality	reviewed	T-194
2026-10-16 published	Exact algebraic sides at sixteen counts from Evan Daniel, of packings the record credits	88, 102, 123, 126, 175, 199, 204, 232, 258, 259, 266, 267, 292, 295, 301, 302	Daniel after Xu, Chaoweeraprasit, Ostashev, Couzo, PingYou Ltd, Gupta, Polkovskyi, Levy	V3 C3Upper bound	confirmed	T-193
2026-10-15 published	A tighter rational certificate of Schadt and Ellsworth's 29-square packing, `1.57e-36` below T-155	29	PingYou Ltd after Schadt, Ellsworth, Daniel, Levy	V3 C3Upper bound	confirmed	T-195
2026-10-15 published	Continuous-pose lower bound $s (28) > 1149 / 200$ reported, by two of the source's programs	28	Hosono after Guzhou0806, Tokoharu, Levy	V0 C1Lower bound	reviewed	T-192
2026-10-15 published	$s (95) = 10$ , by a mixed cover of points and grid-line segments	95, 96	Greff after Daniel, Hosono	V3 C3Optimality	confirmed	T-191
2026-10-15 published	A tighter exact certificate for 237 squares from Francisco Couzo, below his issue-607 certificate	237	Couzo after Polkovskyi, Chaoweeraprasit, Daniel, Levy	V3 C3Upper bound	confirmed	T-190
2026-10-14 published	Francisco Couzo's refinement of Mykhailo Polkovskyi's 237, and fifteen beyond-horizon bounds	237	Couzo after Polkovskyi, Fang, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-190	T-189
2026-10-14 published	A tighter exact certificate for 211 squares from Francisco Couzo, of Daniil Ostashev's arrangement	211	Couzo after Ostashev, Daniel, Levy	V3 C3Upper bound	confirmed	T-188
2026-10-14 published	A smaller packing of 146 squares from Daniel's chain search, started from Xu's packing	146	Daniel after Xu	V3 C3Upper bound	confirmed	T-187
2026-10-14 published	Exact certificates at twelve counts from Mykhailo Polkovskyi, tightening the smallest reported there	129, 154, 156, 175, 176, 204, 232, 264, 271, 302–304	Polkovskyi after Ostashev, Couzo, PingYou Ltd, Levy	V3 C3Upper bound	confirmed	T-186
2026-10-14 published	$s (76) = 9$ , by a mixed cover of points and grid-line segments	76	Greff after Daniel, Hosono	V3 C3Optimality	confirmed	T-184
2026-10-13 published	Mykhailo Polkovskyi's certificate for 237 squares, the smallest known side there when registered	237	Polkovskyi after Friedman, Daniel, Xu, Chaoweeraprasit, Barnett, Couzo, Ostashev, Ellsworth, Fang, Levy	V3 C3Upper bound	confirmed superseded by T-190	T-183
2026-10-13 published	Exact rational certificates at 154, 211 and 241 from Couzo	154, 211, 241	Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy	V3 C3Upper bound	confirmed	T-182
2026-10-13 published	Exact rational certificates at 211, 241 and 302 from Couzo	211, 241, 302	Couzo after Daniel, Ostashev, Fang, Ellsworth, Levy; Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-193 and others	T-181
2026-10-13 published	Closed-form lower bound $s (N) \geq a (N)$ for every non-square $N \geq 49$ , reported	50–63, 65–80, 82–99, 101–120, 122–143, 145–168, 170–195, 197–224, 226–255, 257–288, 290–323	Hosono	V0 C1Lower bound	reviewed	T-180
2026-10-13 published	Linear-measure lower bound $s (n) \geq 306 / 25 = 12.24$ for $n = 145 \dots 149$ , reported	145–149	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V0 C1Lower bound	reviewed	T-179
2026-10-13 published	Mixed rectangle-measure lower bound $s (37) \geq 2599 / 400$ verified, on a 2,073-direction declared net	37	Hosono after Tokoharu and Levy	V3 C3Lower bound	confirmed	T-178
2026-10-13 published	Mixed rectangle-measure lower bound $s (44) \geq 2799 / 400$ reported, on a 2,073-direction declared net	44	Hosono after Tokoharu and Levy	V0 C1Lower bound	reviewed superseded by T-252	T-177
2026-10-13 published	Mixed rectangle-measure lower bound $s (39) \geq 533 / 80$ reported, on a 2,073-direction declared net	39	Hosono after Tokoharu and Levy	V0 C1Lower bound	reviewed	T-176
2026-10-13 published	New packings of 211, 241 and 304 squares, two with merged tilted bands, each certified exactly	211, 241, 304	Ostashev after Nakajima, Daniel, de Winter, Couzo, Levy, Xu	V3 C3Upper bound	confirmed superseded by T-242 and others	T-175
2026-10-13 published	Tighter certificates at 68 counts from PingYou Ltd, of others' packings and its own	68, 70, 84, 86, 88, 102, 103, 105, 108, 110, 123, 126, 127, 129–132, 146, 153, 155, 156, 172, 175, 176, 179–182, 199, 204, 206–211, 228, 232, 236–241, 258, 259, 261, 263, 264, 266–273, 292, 295, 297, 301–308	PingYou Ltd after Friedman, Ellsworth, Daniel, Xu, Barnett, Couzo, Ostashev, Chaoweeraprasit, Gupta, Fang, Polkovskyi, Levy	V3 C3Upper bound	confirmed	T-174
2026-10-13 established	$s (290) \leq 17.5355339059327376 \dots$ , by monotonicity from T-155, with its own exact certificate	290	Levy after Daniel	V3 C3Upper bound	confirmed	T-156
2026-10-12 published	Reported grade-C local minima for 233 source configurations of field degree at most 4	1–10, 12–16, 18–27, 30–36, 38, 40, 42–50, 52–54, 56–67, 70, 72–82, 84–86, 89–101, 104, 107, 109, 111–122, 124, 125, 127, 133–145, 147–151, 153, 157–171, 173, 175, 176, 178, 183–198, 200, 202, 203, 212–227, 229, 230, 232, 233, 242–256, 258, 260, 261, 264, 265, 267, 276–291, 293, 294, 298, 313–324	Daniel after Schadt, Ellsworth, Levy	V3 C1Restricted optimality	incomplete	T-261
2026-10-12 published	Mykhailo Polkovskyi's packings of 153 and 207 squares, each below the earlier refinements there	153, 207	Polkovskyi after Xu, Chaoweeraprasit, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-173
2026-10-12 published	A packing of 154 squares from Couzo, continuing Daniel's arrangement	154	Couzo after Daniel, Ostashev, Fang, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-222	T-172
2026-10-12 published	An exact contact refinement of SQUISH's packing of 272 squares	272	PingYou Ltd after Chaoweeraprasit, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-171
2026-10-12 published	An exact contact refinement of Xu's packing of 105 squares, after Couzo's	105	PingYou Ltd after Xu, Couzo, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-229	T-170
2026-10-12 published	A further exact refinement of Xu's packing of 261 squares, after Barnett's	261	PingYou Ltd after Xu, Barnett, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-169
2026-10-12 published	A further exact refinement of Xu's packing of 146 squares, after Barnett's	146	PingYou Ltd after Xu, Barnett, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-187	T-168
2026-10-12 published	A tighter rational realization of PingYou Ltd's packing of 207 squares	207	PingYou Ltd after Xu, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-167
2026-10-12 published	A tighter rational realization of PingYou Ltd's packing of 153 squares	153	PingYou Ltd after Xu, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-166
2026-10-12 published	A tighter certificate at 176 from Couzo, published with no issue	176	Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-186	T-165
2026-10-12 published	A packing of 302 squares from four boundary patches of Xu's packing of 70 and two upright banks	302	PingYou Ltd after Xu, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-193	T-164
2026-10-12 published	s(n² − n + 1) < n for every n ≥ 15, and n² − n + F(n) squares below side n, from Kevin Fang	211, 241, 273, 307	Fang after Arslanov, Mustafin, Shangitbayev, Ellsworth, Stead, de Winter, Daniel, Couzo	V3 C1Upper bound	reviewed superseded by T-256 and others	T-163
2026-10-12 published	New packings of 129, 204 and 303 squares, a cut-out and two compositions, each certified exactly	129, 204, 303	Ostashev after Nakajima, Chaoweeraprasit, Daniel, Xu, Levy	V3 C3Upper bound	confirmed superseded by T-257 and others	T-162
2026-10-12 published	Exact rational certificates at 156, 176, 237 and 271 from Couzo	156, 176, 237, 271	Couzo after Ostashev, Chaoweeraprasit, Fang, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-219 and others	T-161
2026-10-12 published	A smaller packing of 154 squares from Daniel's size-chaining explorer, certified exactly	154	Daniel after Couzo, Levy	V3 C3Upper bound	confirmed superseded by T-222	T-160
2026-10-12 published	New packings of 175, 232 and 264 squares built on a new 38-square rectangle, each certified exactly	175, 232, 264	Ostashev after Nakajima, Ellsworth, Schadt, Friedman, de Winter, Daniel, Levy, Xu	V3 C3Upper bound	confirmed superseded by T-256 and others	T-158
2026-10-12 established	Exact regularized sides at 59 counts, `5.4e-20` to `9.9e-15` below the ceilings they replace	28, 29, 37, 39, 41, 50, 53–55, 69, 71, 83, 87, 101, 104, 107, 109, 122, 124, 125, 128, 145, 147–149, 151, 170, 171, 173, 174, 178, 197, 198, 200–205, 226, 227, 229–231, 233–235, 257, 260, 262, 264, 265, 291, 293, 294, 296, 298–300	Levy after Daniel	V3 C3Upper bound	confirmed	T-155
2026-10-12 published	Fitzharding reports a Lean proof that $s (17) = 4.67553009360455 \dots$	17	Fitzharding after Levy, Ahmed, MacIver	V3 C1Formalization	reviewed	T-154
2026-10-12 published	Candidate proof that Bidwell's 1998 packing is optimal, $s (17) = 4.67553009360455 \dots$	17	Overbeck after Levy, Ahmed, Mira-acc, Guzhou0806, Maaz	V0 C1Optimality	reviewed	T-153
2026-10-11 published	Reported degree-7213 minimal polynomial of the $s (29)$ record side	29	Daniel after Schadt, Ellsworth, Levy	V0 C0Exact side	recorded	T-246
2026-10-11 published	Hosono reports a Lean kernel proof that $s (59) = 8$ , on Daniel's mixed-measure checker	59	Hosono after Daniel, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V0 C0Formalization	recorded	T-235
2026-10-11 published	Mixed rectangle-measure lower bound $s (31) \geq 2391 / 400$ verified, on a 2,073-direction declared net	31	Hosono after Tokoharu and Levy	V3 C3Lower bound	confirmed	T-232
2026-10-11 published	A tighter packing of 175 squares from Couzo, superseded by Ostashev's composition	175	Couzo after Xu, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-186	T-185
2026-10-11 published	Another arrangement of Xu's design for 102 squares, certified exactly from its decimal layout	102	Calle after Xu, Levy	V3 C3Upper bound	confirmed superseded by T-193	T-159
2026-10-11 published	$s (40) > 3359 / 500 = 6.718$ , by T-145's continuous-pose kernel on a density with 163 new supports	40	Guzhou0806 after Hosono, Tokoharu, Levy, Stromquist, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-157
2026-10-11 published	Exact rational refinements of SQUISH's Mondrian packings of 304 and 305 squares	304, 305	Couzo after Chaoweeraprasit, Fang, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-242 and others	T-152
2026-10-11 published	Nine exact rational packings from SQUISH's fourth request	176, 181, 238, 239, 270–272, 304, 305	Chaoweeraprasit after Couzo, Gupta, Ellsworth, Friedman, Levy	V3 C3Upper bound	confirmed superseded by T-242 and others	T-151
2026-10-11 published	Exact rational refinements of Xu's packings of 146 and 261 squares	146, 261	Barnett after Xu, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-187 and others	T-150
2026-10-11 published	New packings of 155, 156 and 211 squares, each with an exact rational certificate	155, 156, 211	Ostashev after Nakajima, Levy, Xu	V3 C3Upper bound	confirmed superseded by T-197 and others	T-149
2026-10-11 published	A packing of 153 squares built from Xu's packing of 70, its contacts reclosed at a new angle	153	PingYou Ltd after Xu, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-148
2026-10-11 published	A packing of 207 squares from two placed patches of Xu's packing of 70	207	PingYou Ltd after Xu, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-147
2026-10-10 published	Exact rational certificates at fifteen counts from Daniel's regularized record lists	70, 102, 103, 123, 129, 146, 153, 236, 258, 263, 269, 292, 295, 302, 303	Daniel after Xu, Chaoweeraprasit, Polkovskyi, Levy	V3 C3Upper bound	confirmed	T-146
2026-10-10 published	$s (40) > 1340000 / 199529 = 6.7158157 \dots$ , by a continuous-pose interval kernel	40	Guzhou0806 after Hosono, Tokoharu, Levy, Stromquist, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-157	T-145
2026-10-10 published	Linear-measure lower bound $s (n) \geq 563 / 50 = 11.26$ for $n = 122 \dots 126$ , reported	122–126	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V0 C0Lower bound	recorded	T-144
2026-10-10 published	Mixed rectangle-measure lower bound $s (30) \geq 2357 / 400$ reported, on a 2,073-direction declared net	30	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-143
2026-10-10 published	Mixed rectangle-measure lower bound $s (28) \geq 2297 / 400$ reported, on a 2,073-direction declared net	28	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-142
2026-10-10 published	Exact rational certificates at 132 and 308 from Daniel's third record hunt	132, 308	Daniel after Fang, Arslanov, Mustafin, Shangitbayev, Couzo, Levy	V3 C3Upper bound	confirmed superseded by T-221 and others	T-141
2026-10-10 published	Six more exact rational certificates from Couzo	132, 175, 209, 237, 270, 305	Couzo after Chaoweeraprasit, Polkovskyi, Xu, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-224 and others	T-140
2026-10-10 published	An exact rational refinement of Xu's packing of 70 squares	70	Deleeuw after Xu, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-137
2026-10-10 published	A packing of 308 squares below the grid, from Fang	308	Fang after Arslanov, Mustafin, Shangitbayev, Ellsworth, Stead	V3 C3Upper bound	confirmed superseded by T-221	T-135
2026-10-10 published	$s (40) > 335427 / 50000 = 6.70854$ , by a clipped-corner transfer on a 401-direction net	40	Guzhou0806 after Hosono, Tokoharu, Levy, Stromquist, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-157	T-133
2026-10-10 published	Mixed rectangle-measure lower bound $s (29) \geq 291 / 50$ reported, on a 2,073-direction declared net	29	Hosono after Tokoharu and Levy	V0 C0Lower bound	recorded	T-132
2026-10-09 published	A more precise certificate of Xu's 126-square arrangement, from Daniel	126	Daniel after Xu, Chaoweeraprasit	V3 C3Upper bound	confirmed	T-139
2026-10-09 published	Exact witnesses at Mishapolk's printed ceilings, the smallest known at 103 and 258 when registered	84, 86, 103, 105, 108, 127, 131, 132, 175, 180, 258, 267, 270, 302, 303, 306	Polkovskyi after Stenlund, Friedman, Ellsworth, Chaoweeraprasit, Couzo, Xu, Gupta, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-240 and others	T-138
2026-10-09 published	Seventeen exact rational packings from SQUISH's third request	131, 153, 154, 207, 209, 232, 236, 237, 259, 263, 269, 270, 292, 302, 303, 305, 307	Chaoweeraprasit after Couzo, Xu, Göbel, Schadt, Ellsworth, Hajba, Levy	V3 C3Upper bound	confirmed superseded by T-256 and others	T-136
2026-10-09 published	Six exact rational certificates from Couzo	132, 237, 263, 267, 270, 303	Couzo after Polkovskyi, Chaoweeraprasit, Gupta, Xu, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed	T-134
2026-10-09 published	$s (132) \leq 11.987099332245063 \dots$ from Daniel's record hunt	132	Daniel after Couzo, Chaoweeraprasit, Levy	V3 C3Upper bound	confirmed superseded by T-174	T-131
2026-10-08 published	Mixed rectangle-measure lower bounds reported at $n = 19, 20, 26, 27$ , on a 2,073-direction net	19, 20, 26, 27	Hosono after Tokoharu and Levy	V0 C1Lower bound	reviewed	T-233
2026-10-08 published	Five follow-up rational refinements from Couzo	84, 86, 105, 175, 270	Couzo after Xu, Daniel, Ellsworth, Levy	V3 C3Upper bound	confirmed superseded by T-229 and others	T-130
2026-10-08 published	Eight complete rational refinements from Couzo	105, 108, 127, 131, 155, 180, 228, 306	Couzo after Xu, Chaoweeraprasit, Gupta, Ellsworth, Daniel, Levy	V3 C3Upper bound	confirmed superseded by T-229 and others	T-128
2026-10-08 published	Fourteen rational refinements, seventeen complete source cases	88, 108, 123, 129, 130, 153, 154, 179, 180, 199, 207–209, 236–239	Gupta after Chaoweeraprasit, Daniel	V3 C3Upper bound	confirmed	T-127
2026-10-08 published	Undilated n51 construction over Q(sqrt2)	51	Xu	V3 C3Upper bound	confirmed	T-126
2026-10-08 published	Complete rational construction reports at 25 counts	51, 70, 84, 86, 88, 102, 103, 105, 108, 123, 126, 127, 129–131, 146, 153, 175, 179, 236, 258, 261, 263, 267, 295	Xu	V3 C3Upper bound	confirmed superseded by T-259 and others	T-125
2026-10-07 published	Three dated Daniel certificate reports with historical source custody	105, 130, 292	Daniel after Couzo, Levy	V0 C0Upper bound	recorded superseded by T-259 and others	T-129
2026-10-07 published	Reported non-strict local minima for 178 source configurations	1–4, 6–9, 11–16, 20–25, 28, 30–36, 42–49, 56–64, 72–81, 90–100, 111–121, 133–144, 157–169, 183–196, 212–225, 242–256, 274–289, 308–324	Daniel after Couzo	V0 C0Restricted optimality	recorded	T-124
2026-10-07 published	Reported `s(177) ≤ alpha_177` with a degree-32 exact side form	177	Daniel after Couzo	V0 C0Upper bound	recorded	T-123
2026-10-07 published	Reported `s(152) ≤ alpha_152` with a degree-40 exact side form	152	Daniel after Couzo	V0 C0Upper bound	recorded	T-122
2026-10-07 published	Reported `s(106) ≤ alpha_106` with a degree-32 exact side form	106	Daniel after Couzo	V0 C0Upper bound	recorded	T-121
2026-10-07 published	Reported `s(102) ≤ alpha_102` with a degree-8 exact side form	102	Daniel after Couzo	V0 C0Upper bound	recorded superseded by T-193	T-120
2026-10-07 published	Three exact feasible upper bounds at n=266,270,272 from new source arrangements	266, 270, 272	Daniel after Levy, Ellsworth, Couzo, Stead	V3 C3Upper bound	confirmed	T-119
2026-10-07 published	Exact rational ceiling refinements at $n = 68$	68	Rehwaldt after Couzo and earlier contributors	V3 C3Upper bound	confirmed superseded by T-174	T-118
2026-10-07 published	Exact rational ceiling refinements at $n = 105$ , 292	105, 292	Rehwaldt after Couzo and earlier contributors	V3 C3Upper bound	confirmed superseded by T-229 and others	T-117
2026-10-07 published	$s (n) \leq S_{n}$ at nine counts, from the second SQUISH update’s new rational packings	88, 108, 179, 180, 199, 207, 236, 263, 302	Chaoweeraprasit after Ellsworth, Couzo and SQUISH	V3 C3Upper bound	confirmed superseded by T-218 and others	T-116
2026-10-07 published	$s (n) \leq S_{n}$ at twelve counts, from the SQUISH update’s new and smaller rational packings	123, 126, 129, 154, 155, 179, 208, 237–239, 258, 263	Chaoweeraprasit after Couzo and Ellsworth	V3 C3Upper bound	confirmed superseded by T-222 and others	T-115
2026-10-07 published	$s (153) \leq 7250614903299225 / 562949953421312$ , from a SQUISH rational packing	153	Chaoweeraprasit after Ellsworth	V3 C3Upper bound	confirmed superseded by T-174	T-114
2026-10-07 published	$s (n) \leq S_{n}$ at ten counts, $n = 108$ to 303, from new SQUISH rational packings	108, 126, 129, 130, 154, 155, 180, 209, 238, 303	Chaoweeraprasit after Ellsworth	V3 C3Upper bound	confirmed superseded by T-259 and others	T-113
2026-10-06 established	Trump's packing is the only optimal packing of eleven squares, up to symmetry	11	Levy after Ahmed	V3 C2Uniqueness	confirmed	T-112
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 41$ , on a declared net	41	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-111
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 39$ , on a declared net	39	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-110
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 30$ , on a declared net	30	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-109
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 29$ , on a declared net	29	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-108
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 28$ , on a declared net	28	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-107
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 27$ , on a declared net	27	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-106
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 26$ , on a declared net	26	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-105
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 20$ , on a declared net	20	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-104
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 19$ , on the finest declared net yet	19	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-103
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 18$ , on the finest declared net yet	18	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-102
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 19$ , past the best 18-square packing	19	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-103	T-100
2026-10-06 published	Mixed rectangle-measure lower bound verified at $n = 18$ , on a finer declared net	18	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-102	T-099
2026-10-05 published	Exact certificates of 77 catalogue packings: `s(n) ≤ S'`, `1.2e-16` to `9.8e-15` above each side	28, 37, 39, 41, 50, 51, 53–55, 69–71, 83, 87, 88, 101, 104, 107–109, 122, 124, 125, 127–129, 145–151, 153, 170, 171, 173–176, 178, 179, 197, 198, 200–205, 226, 227, 229–235, 257, 258, 260–262, 264–267, 290, 291, 293–296, 298–300	Daniel after Couzo, de Winter, Ellsworth, Levy	V3 C3Upper bound	confirmed	T-101
2026-10-05 published	Exact optima of 48 known-best packings: `s(n) ≤ S'`, `3.5e-13` to `5.0e-11` below each printed side	68, 102, 103, 106, 110, 123, 126, 131, 132, 152, 154–156, 172, 177, 180–182, 199, 206–211, 228, 236–241, 259, 263, 268–273, 297, 301–307	Daniel after Couzo, de Winter, Ellsworth, Levy	V3 C3Upper bound	confirmed	T-098
2026-10-05 published	Mixed rectangle-measure lower bound verified at $n = 66$	66	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-097
2026-10-05 published	Mixed rectangle-measure lower bound replayed at $n = 18$ , on a net the certificate declares	18	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-102	T-096
2026-10-05 published	$s (12) \geq 7943 / 2000 = 3.9715$ , Daniel's points dilated and re-weighted	12	Ryu after Daniel, Levy	V3 C3Lower bound	confirmed	T-095
2026-10-05 published	Mixed rectangle-measure lower bounds verified at $n = 67$ and $84$	67, 84	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-094
2026-10-04 published	Mixed rectangle-measure lower bounds verified at 17 counts in $n = 53 \dots 95$	53, 54, 58, 70–73, 76, 87–95	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-091
2026-10-04 published	Mixed rectangle-measure lower bounds verified at 17 counts in $n = 42 \dots 96$	42–44, 51, 56, 57, 67, 69, 72, 75, 84, 86, 88, 93–96	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-090
2026-10-03 published	Smaller packings again at seven counts from $n = 208$ to $306$ , each certified two independent ways	208, 209, 228, 263, 272, 303, 306	Couzo	V3 C3Upper bound	confirmed superseded by T-240 and others	T-092
2026-10-03 published	Mixed rectangle-measure lower bounds verified at 22 counts in $n = 51 \dots 96$	51, 52, 55, 58, 69–71, 73–76, 86–96	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-082
2026-10-03 published	$s (k^{2} - 4) = k$ for every integer $k$ from 5 up; $k = 5 \dots 18$ are the cases held here	21, 32, 45, 60, 77, 96, 117, 140, 165, 192, 221, 252, 285, 320	Daniel after Burns, Massaccesi	V0 C1Optimality	reviewed	T-081
2026-10-02 published	Linear-measure lower bound replayed at $n = 101 \dots 105$	101–105	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-080
2026-10-02 established	$s (12) \geq 15680000 / 3949423 = 3.9702002 \dots$ , Daniel's points re-weighted	12	Levy after Daniel	V3 C3Lower bound	confirmed superseded by T-245 (reported) and others	T-079
2026-10-02 published	$s (12) \geq 31360 / 7901 = 3.9691178 \dots$ , Daniel's certificate rescaled by $7902 / 7901$	12	Ryu after Daniel	V3 C3Lower bound	confirmed superseded by T-245 (reported) and others	T-078
2026-10-02 published	Rectangle-density lower bounds replayed at $n = 20$ , 42 and 70	20, 42, 70	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-104 and others	T-077
2026-10-02 published	Linear-measure lower bound replayed at $n = 82$	82	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-076
2026-10-02 published	Mixed rectangle-measure lower bounds replayed at nine counts in $n = 83 \dots 96$	83, 85–88, 91–93, 96	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-075
2026-10-02 published	Linear-measure lower bounds replayed at $n = 83$ and $n = 101 \dots 105$	83, 101–105	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-073
2026-10-02 published	Mixed rectangle-measure lower bound replayed at $n = 76$	76	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-184	T-072
2026-10-02 published	Mixed rectangle-measure lower bounds replayed at $n = 84 \dots 87$	84–87	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-207 and others	T-071
2026-10-01 published	Rectangle-density lower bounds replayed at 31 counts in $n = 19 \dots 95$	19, 20, 26–31, 38–44, 53–58, 68–70, 74, 75, 88, 89, 93–95	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-074
2026-10-01 published	Mixed rectangle-measure lower bounds replayed at $n = 37, 65, 66, 90, 92$	37, 65, 66, 90, 92	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-069
2026-10-01 published	Rectangle-density lower bounds verified at 34 counts in $n = 19 \dots 95$	19, 20, 26–31, 38–44, 53–56, 66, 68–70, 74–76, 86–90, 93–95	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-068
2026-10-01 published	$s (77) = 9$ , by a mixed cover extended from Daniel's $s (60)$ cover	77, 78	Hosono after Daniel, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Optimality	confirmed	T-067
2026-10-01 published	$s (59) = 8$ , by a mixed cover of points and grid-line segments	59	Hosono after Daniel, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Optimality	confirmed	T-066
2026-09-30 published	$s (17) > 18641771 / 4000000 = 4.66044275$	17	Guzhou0806 after Overbeck, Mira-acc, Levy	V3 C3Lower bound	confirmed	T-093
2026-09-30 published	$s (k^{2} - 3) = k$ for every integer $k$ from 6 up; $k = 6 \dots 18$ are the cases held here	33, 46, 61, 78, 97, 118, 141, 166, 193, 222, 253, 286, 321	Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-064
2026-09-29 published	Hosono reports a hypothesis-free Lean proof that $s (21) = 5$ , by the point-only route	21	Hosono after Daniel, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V0 C0Formalization	recorded	T-234
2026-09-29 published	$s (k^{2} - 1) = k$ for every integer $k \geq 3$ ; $k = 3 \dots 18$ are the cases held here	8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323	Karakuş	V3 C3Optimality	confirmed	T-084
2026-09-29 published	$s (n) \geq 1 / 2 + \sqrt{n - ⌊ \sqrt{n} ⌋ + 1 / 4}$ for every nonsquare $8 \leq n \leq 324$	8, 10–15, 17–24, 26–35, 37–48, 50–63, 65–80, 82–99, 101–120, 122–143, 145–168, 170–195, 197–224, 226–255, 257–288, 290–323	Karakuş	V3 C3Lower bound	confirmed	T-083
2026-09-29 published	$s (11) > 3875000000 / 999999999 = 3.875000003875 \dots$ , 3.9e-9 above $31 / 8$	11	Wang, Li after Overbeck, Levy	V3 C3Lower bound	confirmed superseded by T-060	T-061
2026-09-29 published	Trump's eleven-square packing is globally optimal	11	Ahmed after Levy, Overbeck	V3 C3Optimality	confirmed	T-060
2026-09-29 published	Reported equality of 12028 n11 row minima reproduced by a complete bound replay	11	Hosono after Tokoharu, Daniel	V3 C3Audit	confirmed	T-059
2026-09-29 published	Rectangle-certificate ceiling `α·UB(n)` proved for $n = 1$ ..100; `B·UB(n)` on 64 grid rows	1–100	Hosono after Tokoharu, Daniel	V3 C3Method limit	confirmed	T-058
2026-09-28 published	Daniel reports a Lean kernel proof that $s (12) \geq 15680 / 3951$ , the bound T-049 holds	12	Daniel after Burns, Massaccesi	V0 C0Formalization	recorded	T-249
2026-09-28 published	Rectangle-density lower bounds replayed at 25 counts in $n = 29 \dots 95$	29, 38, 39, 41–44, 51–55, 57, 59, 60, 67–74, 86, 95	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-252 and others	T-070
2026-09-28 published	$s (61) = 8$ , by monotonicity from T-062	61	Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-063
2026-09-28 published	$s (60) = 8$ , by a mixed cover of points and grid-line segments	60	Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-062
2026-09-28 published	$s (21) = 5$ by a point-only route	21	Hosono after Daniel, Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Simplification	confirmed	T-055
2026-09-28 published	$s (45) = 7$ by a second, point-only route	45	Hosono after Daniel, Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Simplification	confirmed	T-054
2026-09-28 published	$s (50) \geq 37 / 5 = 7.4$	50, 51	Hosono after Daniel, Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed	T-048
2026-09-28 published	$s (17) > 116511 / 25000 = 4.66044$	17	Guzhou0806 after Overbeck, Mira-acc, Levy	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-043
2026-09-28 published	$s (17) > 233009 / 50000 = 4.66018$	17	Guzhou0806 after Overbeck, Mira-acc, Levy	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-042
2026-09-27 published	Smaller packings for 49 counts from $n = 68$ to $307$ , each certified two independent ways	68, 102, 103, 105, 106, 110, 123, 130–132, 152, 154–156, 172, 177, 180–182, 199, 206–210, 228, 236–241, 259, 263, 268–273, 292, 297, 301–307	Couzo	V3 C3Upper bound	confirmed superseded by T-259 and others	T-056
2026-09-27 published	$s (45) = 7$ , by a mixed cover of points and grid-line segments	45	Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-053
2026-09-27 published	$s (21) = 5$ , by a mixed cover of points and grid-line segments	21	Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-052
2026-09-27 published	Rectangle-density lower bounds verified at 48 counts in $n = 18 \dots 95$	18–20, 26–31, 37–44, 51–61, 66–78, 86, 88–91, 94, 95	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-252 and others	T-046
2026-09-27 published	Rectangle-density lower bounds replayed at 15 counts in $n = 18 \dots 78$	18–20, 26–28, 30–32, 40, 61, 75–78	Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-184 and others	T-045
2026-09-27 published	$s (17) > 466001 / 100000 = 4.66001$	17	Overbeck after Levy, Mira-acc, Guzhou0806	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-041
2026-09-26 published	$s (32) = 6$	32	Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-051
2026-09-26 published	$s (17) > 232001 / 50000 = 4.64002$	17	Overbeck after Levy, Mira-acc, Guzhou0806	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-040
2026-09-25 published	$s (17) > 231001 / 50000 = 4.62002$	17	Guzhou0806 after Overbeck, Mira-acc, Levy	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-039
2026-09-24 published	$s (83) \leq 9.63475764863195$ and $s (87) \leq 9.83881526994915$ , Chang's packings, certified exactly	83, 87	Chang, Ellsworth after Cantrell, Hajba, Stenlund, Bidwell; Chang after Ellsworth, Cantrell, Schadt, Hajba, DeVincentis	V3 C3Upper bound	confirmed superseded by T-155 and others	T-089
2026-09-24 published	$s (69) \leq 8.82719465572975$ , Ellsworth's degree-38 packing, certified exactly from its picture	69	Ellsworth after hmbelvedere, Cantrell, Schadt, Morandi	V3 C3Upper bound	confirmed superseded by T-155 and others	T-088
2026-09-24 established	Trump's pose is optimal among six-plus-five packings near its tilt, unique up to symmetry	11	Levy	V3 C2Restricted optimality	confirmed superseded in part by T-112 and others	T-036
2026-09-24 established	Six-plus-five packings near Trump's tilt with side $\leq U_{h i}$ lie within `rho` of his pose	11	Levy	V3 C3Case exclusion	confirmed	T-035
2026-09-23 published	$s (21) \geq 5000 / 1001 = 4.995004995 \dots$	21	Daniel after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-052	T-050
2026-09-23 established	$s (21) \geq 122 / 25 = 4.88$	21	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-052	T-034
2026-09-22 published	$s (11) \geq 381 / 100$ ; $s (n) \geq 1377 / 250$ for $n = 26 \dots 28$ ; $s (n) \geq 571 / 100$ for $n = 29 \dots 31$	11, 26–31	Tokoharu after Levy, Hosono, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-232 and others	T-047
2026-09-22 published	Weighted point lower bounds for ten counts in $n = 26 \dots 72$ , plus seven from the same files	26, 29, 39–41, 52–57, 68–73	Hosono after Levy, Stromquist, Nagamochi, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-205 and others	T-044
2026-09-22 published	$s (11) > 31 / 8 = 3.875$	11	Overbeck after Levy, Guzhou0806, Mira-acc	V3 C3Lower bound	confirmed superseded by T-060	T-037
2026-09-22 established	$s (11) \geq 955000 \sqrt{2073600042893309449} / 359341754646249 = 3.8269975 \dots$	11	Levy	V3 C3Lower bound	confirmed superseded by T-060	T-033
2026-09-21 published	$s (17) \leq 4.6755300936045509 \dots$ , Bidwell's packing certified exactly	17	Overbeck after Levy, Mira-acc, Guzhou0806	V3 C3Upper bound	confirmed	T-065
2026-09-21 published	$s (17) > 461300 / 99853 = 4.6197910929 \dots$	17	Overbeck after Levy, Mira-acc, Guzhou0806	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-038
2026-09-20 published	$s (17) \geq 461300 / 99999 = 4.61304613 \dots$ , and beneath it Mira's $s (17) \geq 4613 / 1000$	17	Guzhou0806, Mira-acc after Levy, Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-032
2026-09-20 established	The octagon corner class (threshold $1 / 2$ ) holds no eleven-square packing at side $96 / 25$	11	Levy	V3 C3Case exclusion	confirmed superseded by T-060	T-031
2026-09-19 established	$s (18) \geq 4679 / 1000 = 4.679$	18	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-102	T-030
2026-09-19 established	$s (18) \geq 1871 / 400 = 4.6775$	18	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-102	T-029
2026-09-19 established	$s (18) \geq 187 / 40 = 4.675$	18	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-102	T-028
2026-09-18 established	$s (18) \geq 467 / 100 = 4.67$	18	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-102	T-027
2026-09-16 published	$s (211) \leq 14.99796070496771500150 < 15$ , the first packing of 211 squares below the grid on record	211	de Winter	V3 C3Upper bound	confirmed superseded by T-188	T-057
2026-09-09 established	$s (11) \geq 955000 \sqrt{518400042893309449} / 179696714646249 = 3.8264474 \dots$	11	Levy	V3 C3Lower bound	confirmed superseded by T-060	T-026
2026-09-09 established	$s (11) \geq 191 / 50 = 3.82$ , by a threshold certificate	11	Levy	V3 C3Lower bound	confirmed superseded by T-060	T-025
2026-09-09 established	$s (11) \geq 3175000 \sqrt{518400042893309449} / 598960960743657 = 3.8166095 \dots$	11	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-060	T-024
2026-09-08 established	Conditional exclusion: no eleven-square packing in the four-owner branch at $q = 96 / 25$	11	Levy	V3 C3Case exclusion	confirmed superseded in part by T-060	T-023
2026-09-06 established	$s (11) \geq 38100 \sqrt{8100042893309449} / 899996306539 = 3.8100257 \dots$	11	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-060	T-022
2026-09-05 established	$s (n) \geq 97 / 20 = 4.85$ for $n = 20, 21$	20, 21	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-104 and others	T-021
2026-09-04 published	$s (k^{2} - 2) = k$ for every integer $k \geq 2$ ; $k = 3 \dots 18$ are the cases held here	7, 14, 23, 34, 47, 62, 79, 98, 119, 142, 167, 194, 223, 254, 287, 322	Vlasenko	V3 C3Optimality	confirmed	T-086
2026-09-04 published	Nagamochi 2005, Lemma 1 is false for every container with $a > 3$ and $b > 2$	10–324	Karakuş; Vlasenko	V3 C3Correction	confirmed	T-085
2026-09-04 established	$s (n) \geq 24 / 5 = 4.80$ for $n = 19, 20, 21$	19–21	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-104 and others	T-020
2026-09-04 established	$s (n) \geq 459 / 100 = 4.59$ for $n = 17, 18, 19$	17–19	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-019
2026-09-04 established	$s (11) \geq 381 / 100 = 3.81$	11	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-060	T-018
2026-09-04 established	$s (12) \geq 99 / 25 = 3.96$	12	Levy after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-245 (reported) and others	T-017
2026-09-03 established	Goebel's $n = 5$ optimum is rigid at fixed side: its pose is an isolated feasible point	5	Levy	V3 C3Rigidity	confirmed	T-014
2026-08-31 established	Bentz 2010, Lemma 10 is false as printed and true as corrected to $(1.74, 1)$	13	Levy after Bentz	V3 C3Correction	confirmed	T-005
2026-08-31 established	The sixteen-point set's unavoidability ceiling lies in $[4426213 / 1000000, 4427 / 1000)$	17, 18	Levy after Bentz	V3 C3Method limit	confirmed	T-003
2026-08-31 established	$s (18) \geq 4426213 / 1000000$ , by monotonicity from T-001	18	Levy after Bentz	V3 C3Lower bound	confirmed superseded by T-102	T-002
2026-08-31 established	$s (17) \geq 4426213 / 1000000 = 4.426213$ , from a sixteen-point unavoidable set	17	Levy after Bentz	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-001
2026-08-30 established	Goebel's $n = 40$ packing: seven verified first-order flexes, each refused at second order	40	Levy	V3 C3Rigidity	confirmed	T-013
2026-08-30 established	Goebel's $n = 5$ packing is second-order rigid at fixed side	5	Levy	V3 C3Rigidity	confirmed	T-012
2026-08-29 published	chelokot reports Lean proofs of $s (2), s (3), s (4) = 2$ , $s (5) = 2.707 \dots$ ; Daniel, rectangle theorems	2–5	Vlasenko; Daniel	V0 C0Formalization	recorded	T-238
2026-08-29 established	$s (29) \leq 5.93383346267692918974 \dots$ , by a Krawczyk interval certificate	29	Levy	V3 C3Upper bound	confirmed superseded by T-195	T-009
2026-08-25 published	$s (12) \geq 15680 / 3951 = 3.9686155 \dots$	12	Daniel after Burns, Massaccesi	V3 C3Lower bound	confirmed superseded by T-245 (reported) and others	T-049
2026-08-24 established	$s (11) \geq 2 + 4 / \sqrt{5}$ , by a repair of Stromquist 2003's Figure 14 point set	11	Levy after Stromquist	V3 C3Lower bound	confirmed superseded by T-060	T-010
2026-08-21 published	$s (n) \geq 22529 / 5000$ for $n = 18, 19$ , by monotonicity from T-015	18, 19	Massaccesi after Burns	V3 C3Lower bound	confirmed superseded by T-103 and others	T-016
2026-08-21 published	$s (17) \geq 22529 / 5000 = 4.5058$	17	Massaccesi after Burns	V3 C3Lower bound	confirmed superseded by T-153 (reported) and others	T-015
2018 published	$s (37) \geq 5 \sqrt{3} / 2 + 2 \sqrt{2} - 1$ and $s (61) \geq 7 \sqrt{3} / 2 + 2 \sqrt{2} - 1$ , by optimal piercing	37, 61	Bašić, Slivková	V3 C1Lower bound	reviewed superseded by T-178 and others	T-087
2010-09-13 published	$s (46) = 7$	46	Bentz	V3 C3Optimality	confirmed	T-008
2010-09-13 published	$s (13) = 4$	13	Bentz; Daniel after Burns, Massaccesi	V3 C3Optimality	confirmed	T-006
2010-09-13 published	Bentz 2010, Theorem 8 ( $s (46) \geq 7$ ) is correct as printed, machine-audited in full	46	Bentz	V3 C3Audit	confirmed	T-004
2005 published	$s (n) \geq min (⌈ \sqrt{n} ⌉, \sqrt{n - 2 ⌊ \sqrt{n} ⌋ + 1} + 1)$ for $4 \leq n \leq 324$	4–324	Nagamochi	V0 C1Lower bound	incomplete	T-007
1979 published	$s (2), s (3), s (4) = 2$ and $s (5) = 2 + 1 / \sqrt{2} = 2.70710678 \dots$ , the classical first cases	2–5	Göbel; Friedman	V3 C3Optimality	confirmed	T-237
1979 published	Trump's 1979 packing is exactly valid, so $s (11) \leq 3.877083590022814 \dots$	11	Trump	V3 C3Upper bound	confirmed	T-011

Visual Atlas Frontier Survey Verification