T-101: Exact certificates of 77 catalogue packings: s(n) ≤ S', 1.2e-16 to 9.8e-15 above each side

2005 published T-007 · 77 of these cases

s(n)≥min(⌈n​⌉,n−2⌊n​⌋+1​+1)$s(n)\ge min(\lceil \sqrt{n}\rceil ,\sqrt{n-2\lfloor \sqrt{n}\rfloor +1}+1)$ for $4\le n\le 324$$4\le n\le 324$

Lower bound incomplete on these cases, superseded by T-048, T-069, T-073, T-075, T-080, T-082, T-083, T-090, T-091, T-107, T-110, T-111, T-180 (reported) and T-216

Nagamochi · Nagamochi 2005 · source · register

2018 published T-087 · case 37

s(37)≥53​/2+22​−1$s(37)\ge 5\sqrt{3}/2+2\sqrt{2}-1$ and s(61)≥73​/2+22​−1$s(61)\ge 7\sqrt{3}/2+2\sqrt{2}-1$, by optimal piercing

Lower bound reviewed superseded by T-069

Bašić, Slivková · Basic-Slivkova 2018 · source · register

2026-09-04 published T-085 · 77 of these cases

Nagamochi 2005, Lemma 1 is false for every container with $a>3$$a>3$ and $b>2$$b>2$

Correction confirmed

Karakuş; Vlasenko · Karakuş 2026 · chelokot Nagamochi counterexample 2026 · packet · register

2026-09-22 published T-044 · 8 of these cases

Weighted point lower bounds for ten counts in $n=26\dots 72$$n=26\dots 72$, plus seven from the same files

Lower bound confirmed superseded by T-082, T-090, T-091, T-110 and T-111

Hosono after Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 point bounds 2026 · packet · source · review · register

2026-09-22 published T-047 · case 28

$s(11)\ge 381/100$$s(11)\ge 381/100$; $s(n)\ge 1377/250$$s(n)\ge 1377/250$ for $n=26\dots 28$$n=26\dots 28$; $s(n)\ge 571/100$$s(n)\ge 571/100$ for $n=29\dots 31$$n=29\dots 31$

Lower bound confirmed superseded by T-107

Tokoharu after Levy, Hosono, Stromquist, Nagamochi, Burns, Massaccesi · Tokoharu density 2026 · packet · source · review · register

2026-09-24 published T-088 · case 69

$s(69)\le 8.82719465572975$$s(69)\le 8.82719465572975$, Ellsworth's degree-38 packing, certified exactly from its picture

Upper bound confirmed superseded by T-101 and T-155

Ellsworth after hmbelvedere, Cantrell, Schadt, Morandi · Ellsworth n69 2026-09-24 · packet · packet · register

2026-09-24 published T-089 · cases 83, 87

$s(83)\le 9.63475764863195$$s(83)\le 9.63475764863195$ and $s(87)\le 9.83881526994915$$s(87)\le 9.83881526994915$, Chang's packings, certified exactly

Upper bound confirmed superseded by T-101 and T-155

Chang, Ellsworth after Cantrell, Hajba, Stenlund, Bidwell; Chang after Ellsworth, Cantrell, Schadt, Hajba, DeVincentis · Chang n83 2026-09-24 · Chang n87 2026-09-24 · packet · packet · register

2026-09-27 published T-045 · case 28

Rectangle-density lower bounds replayed at 15 counts in $n=18\dots 78$$n=18\dots 78$

Lower bound confirmed superseded by T-107

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026 · packet · packet · source · review · register

2026-09-27 published T-046 · 12 of these cases

Rectangle-density lower bounds reported for 48 counts in $n=18\dots 95$$n=18\dots 95$

Lower bound recorded superseded by T-069, T-082, T-090, T-091, T-107, T-110 and T-111

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026 · wand125 rectangle bounds 2026-09-28 · packet · packet · register

2026-09-28 published T-048 · cases 50, 51

$s(50)\ge 37/5=7.4$$s(50)\ge 37/5=7.4$

Lower bound confirmed

Hosono after Daniel, Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 point and mixed bounds 2026-09-28 · packet · source · review · register

2026-09-28 published T-070 · 9 of these cases

Rectangle-density lower bounds replayed at 25 counts in $n=29\dots 95$$n=29\dots 95$

Lower bound confirmed superseded by T-082, T-090, T-091, T-110 and T-111

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026-09-28 · packet · packet · source · review · register

2026-09-29 published T-058 · 15 of these cases

Rectangle-certificate ceiling α·UB(n) proved for $n=1$$n=1$..100; B·UB(n) on 64 grid rows

Method limit confirmed

Hosono after Tokoharu, Daniel · wand125 tools 2026 · packet · register

2026-09-29 published T-083 · 77 of these cases

s(n)≥1/2+n−⌊n​⌋+1/4​$s(n)\ge 1/2+\sqrt{n-\lfloor \sqrt{n}\rfloor +1/4}$ for every nonsquare $8\le n\le 324$$8\le n\le 324$

Lower bound confirmed

Karakuş · Karakuş 2026 · source · register

2026-10-01 published T-068 · 10 of these cases

Rectangle-density lower bounds verified at 34 counts in $n=19\dots 95$$n=19\dots 95$

Lower bound confirmed on these cases, superseded by T-082, T-090, T-091, T-107, T-110 and T-111

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026-10-01 · packet · source · review · register

2026-10-01 published T-069 · case 37

Mixed rectangle-measure lower bounds replayed at $n=37,65,66,90,92$$n=37,65,66,90,92$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds 2026-10-01 · packet · source · review · register

2026-10-01 published T-074 · 9 of these cases

Rectangle-density lower bounds replayed at 31 counts in $n=19\dots 95$$n=19\dots 95$

Lower bound confirmed on these cases, superseded by T-082, T-090, T-091, T-107, T-110 and T-111

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026-10-01 · packet · packet · source · review · register

2026-10-02 published T-071 · case 87

Mixed rectangle-measure lower bounds replayed at $n=84\dots 87$$n=84\dots 87$

Lower bound confirmed superseded by T-091

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds 2026-10-02 · packet · source · review · register

2026-10-02 published T-073 · cases 83, 101, 104

Linear-measure lower bounds replayed at $n=83$$n=83$ and $n=101\dots 105$$n=101\dots 105$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 linear certificates 2026-10-02 · packet · source · review · register

2026-10-02 published T-075 · cases 83, 87, 88

Mixed rectangle-measure lower bounds replayed at nine counts in $n=83\dots 96$$n=83\dots 96$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds afternoon 2026-10-02 · packet · source 1 · source 2 · review · register

2026-10-02 published T-077 · case 70

Rectangle-density lower bounds replayed at $n=20$$n=20$, 42 and 70

Lower bound confirmed superseded by T-091

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026-10-02 · packet · packet · source 1 · source 2 · review 1 · review 2 · register

2026-10-02 published T-080 · cases 101, 104

Linear-measure lower bound replayed at $n=101\dots 105$$n=101\dots 105$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 linear certificates 2026-10-02 · packet · source · review · register

2026-10-03 published T-082 · 7 of these cases

Mixed rectangle-measure lower bounds verified at 22 counts in $n=51\dots 96$$n=51\dots 96$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds 2026-10-03 · packet · packet · source · review · register

2026-10-04 published T-090 · cases 51, 69, 88

Mixed rectangle-measure lower bounds verified at 17 counts in $n=42\dots 96$$n=42\dots 96$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds 2026-10-04 · packet · source · review · register

2026-10-04 published T-091 · 6 of these cases

Mixed rectangle-measure lower bounds verified at 17 counts in $n=53\dots 95$$n=53\dots 95$

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds evening 2026-10-04 · packet · source · review · register

2026-10-05 published T-101 this result · 77 of these cases

Exact certificates of 77 catalogue packings: s(n) ≤ S', 1.2e-16 to 9.8e-15 above each side

Upper bound confirmed

Daniel after Couzo, de Winter, Ellsworth, Levy · evand exact optima 2026-10-05 · packet · register

2026-10-06 published T-107 · case 28

Mixed rectangle-measure lower bound verified at $n=28$$n=28$, on a declared net

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds check2 2026-10-06 · packet · source · review · register

2026-10-06 published T-110 · case 39

Mixed rectangle-measure lower bound verified at $n=39$$n=39$, on a declared net

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds check2 2026-10-06 · packet · source · review · register

2026-10-06 published T-111 · case 41

Mixed rectangle-measure lower bound verified at $n=41$$n=41$, on a declared net

Lower bound confirmed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds check2 2026-10-06 · packet · source · review · register

2026-10-07 published T-113 · cases 108, 129

s(n)≤Sn​$s(n)\le S_n$ at ten counts, $n=108$$n=108$ to 303, from new SQUISH rational packings

Upper bound confirmed superseded by T-174 and T-186

Chaoweeraprasit after Ellsworth · SQUISH ten packings 2026-10-07 · packet · register

2026-10-07 published T-114 · case 153

$s(153)\le 7250614903299225/562949953421312$, from a SQUISH rational packing

Upper bound confirmed superseded by T-173

Chaoweeraprasit after Ellsworth · SQUISH n153 2026-10-07 · packet · packet · register

2026-10-07 published T-115 · cases 129, 179, 258

s(n)≤Sn​$s(n)\le S_n$ at twelve counts, from the SQUISH update’s new and smaller rational packings

Upper bound confirmed superseded by T-146, T-174 and T-186

Chaoweeraprasit after Couzo and Ellsworth · SQUISH update 2026-10-07 · packet · register

2026-10-07 published T-116 · cases 88, 108, 179

s(n)≤Sn​$s(n)\le S_n$ at nine counts, from the second SQUISH update’s new rational packings

Upper bound confirmed superseded by T-127 and T-174

Chaoweeraprasit after Ellsworth, Couzo and SQUISH · SQUISH second update 2026-10-07 · packet · register

2026-10-07 published T-119 · case 266

Three exact feasible upper bounds at n=266,270,272 from new source arrangements

Upper bound confirmed

Daniel after Levy, Ellsworth, Couzo, Stead · Daniel new arrangements 2026-10-07 · packet · register

2026-10-07 published T-124 · case 28

Reported non-strict local minima for 178 source configurations

Restricted optimality recorded

Daniel after Couzo · Daniel exact and local reports 2026 · packet · register

2026-10-08 published T-125 · 14 of these cases

Complete rational construction reports at 25 counts

Upper bound confirmed superseded by T-126, T-127, T-134, T-146, T-173, T-174, T-186 and T-187

Xu · ry-xu square packing 2026 · packet · register

2026-10-08 published T-126 · case 51

Undilated n51 construction over Q(sqrt2)

Upper bound confirmed

Xu · ry-xu square packing 2026 · packet · register

2026-10-08 published T-127 · 5 of these cases

Fourteen rational refinements, seventeen complete source cases

Upper bound confirmed

Gupta after Chaoweeraprasit, Daniel · Gupta rational refinements 2026-10-08 · packet · register

2026-10-08 published T-128 · cases 108, 127

Eight complete rational refinements from Couzo

Upper bound confirmed superseded by T-174

Couzo after Xu, Chaoweeraprasit, Gupta, Ellsworth, Daniel, Levy · Couzo exact refinements 2026-10-08 · packet · register

2026-10-08 published T-130 · case 175

Five follow-up rational refinements from Couzo

Upper bound confirmed superseded by T-186

Couzo after Xu, Daniel, Ellsworth, Levy · Couzo follow-up refinements 2026-10-08 · packet · register

2026-10-09 published T-134 · case 267

Six exact rational certificates from Couzo

Upper bound confirmed

Couzo after Polkovskyi, Chaoweeraprasit, Gupta, Xu, Daniel, Ellsworth, Levy · Couzo exact certificates 2026-10-09 · packet · register

2026-10-09 published T-136 · cases 153, 232

Seventeen exact rational packings from SQUISH's third request

Upper bound confirmed on these cases, superseded by T-173 and T-186

Chaoweeraprasit after Couzo, Xu, Göbel, Schadt, Ellsworth, Hajba, Levy · SQUISH third request 2026-10-09 · packet · register

2026-10-09 published T-138 · 5 of these cases

Exact witnesses at Mishapolk's printed ceilings, the smallest known at 103 and 258 when registered

Upper bound confirmed superseded by T-134, T-146, T-174 and T-186

Polkovskyi after Stenlund, Friedman, Ellsworth, Chaoweeraprasit, Couzo, Xu, Levy · Mishapolk decimal poses 2026-10-09 · packet · register

2026-10-10 published T-137 · case 70

An exact rational refinement of Xu's packing of 70 squares

Upper bound confirmed superseded by T-146

Deleeuw after Xu, Levy · Deleeuw n70 refinement 2026-10-10 · packet · register

2026-10-10 published T-140 · case 175

Six more exact rational certificates from Couzo

Upper bound confirmed superseded by T-186

Couzo after Chaoweeraprasit, Polkovskyi, Xu, Daniel, Ellsworth, Levy · Couzo certificates 2026-10-10 · packet · register

2026-10-10 published T-142 · case 28

Mixed rectangle-measure lower bound $s(28)\ge 2297/400$$s(28)\ge 2297/400$ reported, on a 2,073-direction declared net

Lower bound recorded

Hosono after Tokoharu and Levy · wand125 fine-net n28 n30 2026-10-10 · packet · register

2026-10-10 published T-144 · cases 122, 124, 125

Linear-measure lower bound $s(n)\ge 563/50=11.26$$s(n)\ge 563/50=11.26$ for $n=122\dots 126$$n=122\dots 126$, reported

Lower bound recorded

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 linear n122 2026-10-10 · packet · register

2026-10-10 published T-146 · 6 of these cases

Exact rational certificates at fifteen counts from Daniel's regularized record lists

Upper bound confirmed

Daniel after Xu, Chaoweeraprasit, Polkovskyi, Levy · Daniel regularized lists 2026-10-10 · packet · register

2026-10-11 published T-148 · case 153

A packing of 153 squares built from Xu's packing of 70, its contacts reclosed at a new angle

Upper bound confirmed superseded by T-173

PingYou Ltd after Xu, Daniel, Levy · PingYou n153 certificate 2026-10-11 · packet · register

2026-10-11 published T-150 · cases 146, 261

Exact rational refinements of Xu's packings of 146 and 261 squares

Upper bound confirmed superseded by T-174 and T-187

Barnett after Xu, Daniel, Levy · Barnett refinements 2026-10-11 · packet · register

2026-10-11 published T-151 · case 176

Nine exact rational packings from SQUISH's fourth request

Upper bound confirmed superseded by T-186

Chaoweeraprasit after Couzo, Gupta, Ellsworth, Friedman, Levy · SQUISH fourth request 2026-10-11 · packet · register

2026-10-11 published T-185 · case 175

A tighter packing of 175 squares from Couzo, superseded by Ostashev's composition

Upper bound confirmed superseded by T-186

Couzo after Xu, Daniel, Ellsworth, Levy · Couzo n175 2026-10-11 · packet · register

2026-10-12 established T-155 · 58 of these cases

Exact regularized sides at 59 counts, 5.4e-20 to 9.9e-15 below the ceilings they replace

Upper bound confirmed

Levy after Daniel · register

2026-10-12 published T-158 · cases 175, 232, 264

New packings of 175, 232 and 264 squares built on a new 38-square rectangle, each certified exactly

Upper bound confirmed superseded by T-186

Ostashev after Nakajima, Ellsworth, Schadt, Friedman, de Winter, Daniel, Levy, Xu · Ostashev records 2026-10-12 · packet · register

2026-10-12 published T-161 · case 176

Exact rational certificates at 156, 176, 237 and 271 from Couzo

Upper bound confirmed superseded by T-186

Couzo after Ostashev, Chaoweeraprasit, Fang, Daniel, Ellsworth, Levy · Couzo certificates 2026-10-12 · packet · register

2026-10-12 published T-162 · cases 129, 204

New packings of 129, 204 and 303 squares, a cut-out and two compositions, each certified exactly

Upper bound confirmed superseded by T-186 and T-225

Ostashev after Nakajima, Chaoweeraprasit, Daniel, Xu, Levy · Ostashev compositions 2026-10-12 · packet · register

2026-10-12 published T-165 · case 176

A tighter certificate at 176 from Couzo, published with no issue

Upper bound confirmed superseded by T-186

Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy · Couzo certificates 2026-10-13 · packet · register

2026-10-12 published T-166 · case 153

A tighter rational realization of PingYou Ltd's packing of 153 squares

Upper bound confirmed superseded by T-173

PingYou Ltd after Xu, Daniel, Levy · PingYou n153 refinement 2026-10-12 · packet · register

2026-10-12 published T-168 · case 146

A further exact refinement of Xu's packing of 146 squares, after Barnett's

Upper bound confirmed superseded by T-187

PingYou Ltd after Xu, Barnett, Daniel, Levy · PingYou n146 refinement 2026-10-12 · packet · register

2026-10-12 published T-169 · case 261

A further exact refinement of Xu's packing of 261 squares, after Barnett's

Upper bound confirmed superseded by T-174

PingYou Ltd after Xu, Barnett, Daniel, Levy · PingYou n261 refinement 2026-10-12 · packet · register

2026-10-12 published T-173 · case 153

Polkovskyi's packings of 153 and 207 squares, each below the earlier refinements there

Upper bound confirmed

Polkovskyi after Xu, Chaoweeraprasit, Levy · Mishapolk exact certificates 2026-10-12 · packet · register

2026-10-13 established T-156 · case 290

$s(290)\le 17.5355339059327376\dots$$s(290)\le 17.5355339059327376\dots$, by monotonicity from T-155, with its own exact certificate

Upper bound confirmed

Levy after Daniel · register

2026-10-13 published T-174 · 18 of these cases

Tighter certificates at 68 counts from PingYou Ltd, of others' packings and its own

Upper bound confirmed

PingYou Ltd after Friedman, Ellsworth, Daniel, Xu, Barnett, Couzo, Ostashev, Chaoweeraprasit, Gupta, Fang, Polkovskyi, Levy · PingYou PR 574 certificates 2026-10-13 · packet · register

2026-10-13 published T-176 · case 39

Mixed rectangle-measure lower bound $s(39)\ge 533/80$$s(39)\ge 533/80$ reported, on a 2,073-direction declared net

Lower bound reviewed

Hosono after Tokoharu and Levy · wand125 fine-net n37 n39 n44 2026-10-13 · packet · register

2026-10-13 published T-178 · case 37

Mixed rectangle-measure lower bound $s(37)\ge 2599/400$$s(37)\ge 2599/400$ reported, on a 2,073-direction declared net

Lower bound reviewed

Hosono after Tokoharu and Levy · wand125 fine-net n37 n39 n44 2026-10-13 · packet · register

2026-10-13 published T-179 · 5 of these cases

Linear-measure lower bound $s(n)\ge 306/25=12.24$$s(n)\ge 306/25=12.24$ for $n=145\dots 149$$n=145\dots 149$, reported

Lower bound reviewed

Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 linear n145 2026-10-13 · packet · register

2026-10-13 published T-180 · 73 of these cases

Closed-form lower bound $s(N)\ge a(N)$$s(N)\ge a(N)$ for every non-square $N\ge 49$$N\ge 49$, reported

Lower bound reviewed

Hosono · wand125 closed form 2026-10-14 · packet · packet · register

2026-10-14 published T-186 · 6 of these cases

Exact certificates at twelve counts from Polkovskyi, tightening the smallest reported there

Upper bound confirmed

Polkovskyi after Ostashev, Couzo, PingYou Ltd, Levy · Mishapolk KKT refinements 2026-10-14 · packet · register

2026-10-14 published T-187 · case 146

A smaller packing of 146 squares from Daniel's chain search, started from Xu's packing

Upper bound confirmed

Daniel after Xu · Daniel n146 2026-10-14 · packet · register

2026-10-15 published T-192 · case 28

Continuous-pose lower bound $s(28)>1149/200$$s(28)>1149/200$ reported, by two of the source's programs

Lower bound recorded

Hosono after Guzhou0806, Tokoharu, Levy · wand125 continuous n28 2026-10-15 · packet · register

2026-10-16 published T-193 · 8 of these cases

Exact algebraic sides at sixteen counts from Daniel, of packings the record credits

Upper bound confirmed

Daniel after Xu, Chaoweeraprasit, Ostashev, Couzo, PingYou Ltd, Gupta, Polkovskyi, Levy · Daniel exact current records 2026-10-16 · packet · register

2026-10-16 published T-202 · case 41

Mixed rectangle-measure lower bound $s(41)\ge 2721/400$$s(41)\ge 2721/400$ reported, on a 2,073-direction declared net

Lower bound recorded

Hosono after Tokoharu and Levy · wand125 fine-net lower bounds 2026-10-16 · packet · register

2026-10-16 published T-204 · case 51

Mixed rectangle-measure lower bound $s(51)\ge 3011/400$$s(51)\ge 3011/400$ reported, on a 2,073-direction declared net

Lower bound recorded

Hosono after Tokoharu and Levy · wand125 fine-net lower bounds 2026-10-16 · packet · register

2026-10-16 published T-209 · case 88

Mixed rectangle-measure lower bound $s(88)\ge 3853/400$$s(88)\ge 3853/400$ reported, on the 201-direction net

Lower bound recorded

Hosono after Tokoharu and Levy · wand125 fine-net lower bounds 2026-10-16 · packet · register

2026-10-16 published T-215 · case 107

Mixed rectangle-measure lower bound $s(107)\ge 529/50$$s(107)\ge 529/50$ reported, on the 201-direction net

Lower bound recorded

Hosono after Tokoharu and Levy · wand125 fine-net lower bounds 2026-10-16 · packet · register

2026-10-16 published T-216 · case 108

Mixed rectangle-measure lower bound $s(108)\ge 531/50$$s(108)\ge 531/50$ verified, on the 201-direction net

Lower bound confirmed

Hosono after Tokoharu and Levy · wand125 fine-net lower bounds 2026-10-16 · packet · source · review · register

2026-10-17 published T-196 · cases 227, 229, 260

de Winter reports three smaller rational upper bounds at 227, 229 and 260

Upper bound confirmed superseded by T-225

de Winter after Levy · de Winter upper bounds 2026-10-17 · packet · register

2026-10-17 published T-198 · case 229

Daniel's opening n229 dilation certificate, after Couzo and de Winter

Upper bound confirmed superseded by T-225

Daniel after Couzo, de Winter, Levy · Daniel n229 dilation 2026-10-17 · packet · register

2026-10-17 published T-226 · case 204

Couzo's 204 of #670, below Polkovskyi's T-186, since superseded by his own #675 and #678

Upper bound recorded superseded by T-225

Couzo after Polkovskyi, Daniel, Levy · Couzo issue 670 2026-10-17 · packet · packet · register

2026-10-17 published T-227 · cases 227, 229

Couzo's refinements of de Winter's 227 and 229, below T-196 at both

Upper bound recorded superseded by T-225

Couzo after de Winter, Daniel, Levy · Couzo issue 672 2026-10-17 · packet · packet · register

2026-10-18 published T-199 · case 229

Daniel's smaller n229 update, replacing the opening certificate

Upper bound confirmed superseded by T-225

Daniel after Couzo, de Winter, Levy · Daniel n229 dilation update 2026-10-18 · packet · register

2026-10-18 published T-223 · cases 204, 260

Couzo's smaller packings at 204 and 260, the two in the corpus of issue 678's 85 bounds

Upper bound confirmed superseded by T-225

Couzo after de Winter, Polkovskyi, Daniel, Fang, PingYou Ltd, Levy · Couzo issue 678 2026-10-18 · packet · register

2026-10-18 published T-228 · case 204

Couzo's 204 of #675, below his #670, since superseded by his #678

Upper bound recorded superseded by T-225

Couzo after Polkovskyi, Daniel, Levy · Couzo issue 675 2026-10-18 · packet · packet · register

2026-10-20 published T-225 · cases 204, 227, 229, 260

Daniel's solved, regularized views at 204, 227, 229 and 260, each the smallest side reported there

Upper bound confirmed

Daniel after Couzo, de Winter, Polkovskyi, Levy · Daniel regularized lists 2026-10-20 · packet · register

2026-10-22 published T-229 · case 204

Polkovskyi's re-solves of the house packings at 105 and 204, below T-174 and T-225

Upper bound recorded

Polkovskyi after Couzo, Muglich, Daniel, Xu, PingYou Ltd, Levy · Mishapolk issue 719 2026-10-22 · packet · register