T-146: Exact rational certificates at fifteen counts from Daniel's regularized record lists

V3 C3 Upper bound confirmed

2026-10-10 published · Daniel after Xu, Chaoweeraprasit, Polkovskyi, Levy · 15 cases, $n = 70$ to 303

Fifteen complete rational certificates from Daniel's display-regularized record lists, which no issue reports, prove finite upper bounds at their exact sides: $s (70) \leq 8.880960371555579594785501178639$ , $s (102) \leq 10.605828696431578360490734944053$ , $s (103) \leq 10.679232047361306442680936279997$ , $s (123) \leq 11.591378145497698159550863183468$ , $s (129) \leq 11.872029849081179973752429831968$ , $s (146) \leq 12.583782277415076881948309755914$ , $s (153) \leq 12.872029849081179973762429831968$ , $s (236) \leq 15.863955747159267422617702706295$ , $s (258) \leq 16.563448002133789379765816191273$ , $s (263) \leq 16.733166007899378970679613144039$ , $s (269) \leq 16.901513582189132198548012552701$ , $s (292) \leq 17.591378145497698159610863183468$ , $s (295) \leq 17.704232790736030358056092972112$ , $s (302) \leq 17.872029849081179973812429831968$ and $s (303) \leq 17.913065462738532305839753791206$ .

Each certificate gives a rational side and, for each unit square, a rational centre and the tangent of its half-angle, in Daniel's format, retained as the original gzip the source publishes beside a JSON that prints the same side as S_cert. Each is below every value the record held or had pending at its count when read, by 2.21e-17 at 302 to 7.82e-10 at 295.

All 45 retained jobs, the fifteen positives with their duplicate-square and outside-container controls, were decided again here on 11 October 2026 by both maintained exact routes and equal their retained rows, and a third exact route, half-extent containment and exact intersection area, decided the fifteen with six controls each, decompressing each retained gzip itself, and held each retained file to its upstream bytes at the pin. No route here is the source's code, so the replay is independently re-implemented. The 11 October review found no blocking defect.

Each side was below the ceiling its case held. On 11 October 2026 the case records adopted all fifteen as the house, each packing credited to its finder as below.

The source presents each certificate as a display view and not a new bound. Its method log says every refreshed side is the exact optimum of the store's best packing at its count, below the posted side only by rounding, and classes each of the fifteen views as the same packing in a different arrangement, traversable without expansion, by a path test that samples angle paths in 0.01 degree steps and that it says is not a continuous proof; it reports all 324 certificates of the lists VALID under its two exact checkers and verified at 80 digits. Those statements are the author's: no source program ran here, and the solved point each view was made from is not published.

Measured pose by pose, every view differs from the certificate the record credits; at 123, 129 and 292 nearest centres match under no symmetry and only an optimal assignment pairs the squares, slid by up to 0.59, 0.83 and 0.59.

Credit the packings to their finders, as the source's provenance names them: Xu's (ry-xu, https://github.com/ry-xu/square_packing, issue 432) at 70, 102, 103, 123, 129, 146 and 295, at 103 as Mishapolk refined it (issue 470, T-138); Chaoweeraprasit's SQUISH packing of issue 401 at 258, as Mishapolk refined it; and his SQUISH packings of issue 481 (T-136) at 153, 236, 263, 269, 292, 302 and 303, composed from pieces of Couzo's, Xu's and earlier packings. At 70 Deleeuw's refinement of Xu's packing in place (issue 483, T-137) was the smallest side the record held.

Daniel (https://github.com/evand/square-packing) refreshed each packing from his store, solved it to the side he reports as its exact optimum, regularized it for display at that side, at 70, 129, 153, 236, 263, 269 and 292 also merging determined rotation groups by up to 2.96 degrees, and wrote the certificate.

His lists name the finders of the arrangements the packings descend from: DeVincentis at 70, Couzo at 102, 103, 123, 236, 263, 269, 292, 302 and 303, Ellsworth at 129 and 153 and Cantrell at 146, and no one at 258 and 295. The source claims no record, and its credits say the repository's work was produced by Claude (Anthropic) under human direction.

Significance, composition and next rung

Significance: Smaller finite construction sides at fifteen counts from 70 to 303, 2.21e-17 to 7.82e-10 below the least side the record held or had pending at each and 5.36e-12 to 9.28e-03 below the case ceilings, where the larger gaps are improvements SQUISH's issue 481 (T-136) already made: display-regularized arrangements at the sides the source reports as the exact optima of packings the record already credits, a citable detail of each case that moves no theorem, S2 as T-098 is; no lower bound, optimum or priority.
Next rung: V4 and C4 need a retained human oversight record: two accepted adversarial reviews by distinct AI reviewers are retained, the 11 October review and the 11 October final review (docs/project/reviews/review-2026-10-11-final-upper-bounds.md).
Regularizations: n = 70: a regularization of T-125’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 0.93°, 3 free angles moved; identity: the source’s claim; nearest centres one to one; 10 squares moved, at most 0.222; turns up to 22.5°).

n = 102: a regularization of T-125’s packing by Daniel (conservative; solved to its side; the regularizer changed no angle, as its source reports; identity: the source’s claim; nearest centres one to one; 18 squares moved, at most 0.169; turns up to 0.433°).

n = 103: a regularization of T-138’s packing by Daniel (conservative; solved to its side; the regularizer changed no angle, as its source reports; identity: the source’s claim; nearest centres one to one; 15 squares moved, at most 0.074; turns up to 0.411°).

n = 123: a regularization of T-125’s packing by Daniel (conservative; solved to its side; the regularizer changed no angle, as its source reports; identity: the source’s claim; nearest centres not one to one; 45 squares moved, at most 0.591; no square turned).

n = 129: a regularization of T-125’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 2.96°, 16 free squares straightened, 5 free angles moved; identity: the source’s claim; nearest centres not one to one; 43 squares moved, at most 0.834; turns up to 39.4°).

n = 146: a regularization of T-125’s packing by Daniel (conservative; solved to its side; the regularizer changed no angle, as its source reports; identity: the source’s claim; nearest centres one to one; 25 squares moved, at most 0.124; no square turned).

n = 153: a regularization of T-136’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 1.81°, 8 free angles moved; identity: the source’s claim; nearest centres one to one; 80 squares moved, at most 0.065; turns up to 2.43°).

n = 236: a regularization of T-136’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 0.67°, 5 free angles moved; identity: the source’s claim; nearest centres one to one; 53 squares moved, at most 0.068; turns up to 0.705°).

n = 258: a regularization of T-138’s packing by Daniel (conservative; solved to its side; the regularizer changed no angle, as its source reports; identity: the source’s claim; nearest centres one to one; 48 squares moved, at most 0.496; turns up to 1.13°).

n = 263: a regularization of T-136’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 1.06°, 14 free squares straightened, 18 free angles moved; identity: the source’s claim; nearest centres one to one; 132 squares moved, at most 0.049; turns up to 1.22°).

n = 269: a regularization of T-136’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 0.12°, 4 free squares straightened, 11 free angles moved; identity: the source’s claim; nearest centres one to one; 54 squares moved, at most 0.088; turns up to 1.16°).

n = 292: a regularization of T-136’s packing by Daniel (fewest; solved to its side; rotation groups merged by up to 0.03°, 9 free angles moved; identity: the source’s claim; nearest centres not one to one; 239 squares moved, at most 0.589; turns up to 4.6°).

n = 295: a regularization of T-125’s packing by Daniel (conservative; solved to its side; the regularizer changed no angle, as its source reports; identity: the source’s claim; nearest centres one to one; 122 squares moved, at most 0.138; no square turned).

n = 302: a regularization of T-136’s packing by Daniel (conservative; solved to its side; 56 free squares straightened, 26 free angles moved; identity: the source’s claim; nearest centres one to one; 198 squares moved, at most 0.102; turns up to 2.62°).

n = 303: a regularization of T-136’s packing by Daniel (conservative; solved to its side; 1 free square straightened; identity: the source’s claim; nearest centres one to one; 19 squares moved, at most 0.135; turns up to 1.21°).
Regularized drawings: n = 70: a regularization of T-146’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 0 squares moved, at most 7.51665e-20; no square turned).

n = 102: a regularization of T-146’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 1 square moved, at most 0.0218828; no square turned).

n = 123: a regularization of T-146’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 8 squares moved, at most 0.202407; no square turned).

n = 258: a regularization of T-146’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 0 squares moved, at most 1.35093e-19; no square turned).

n = 292: a regularization of T-146’s packing by Levy (regularize_grid_slack/1: Daniel's coincidence placement (evand/square-packing search/regularize reg.coincidences and reg.place, MIT), ported to start from the witness's exact frame and to keep its contacts, then the same-side exact re-solve, through devtools.regularize_grid_slack; the project’s modifications: port of his coincidence placement (regularize_grid_slack/1) rather than his code, same-side exact re-solve (devtools.regularize_same_side); at its own side; identity: measured here; nearest centres one to one; 59 squares moved, at most 0.164234; no square turned).

n = 295: a regularization of T-146’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 0 squares moved, at most 1.05119e-19; no square turned).
Novelty: previously-published Present in an identified source

The cases

This result concerns 15 cases, too many to draw one by one. Each is listed with the film’s bounds, the proved lower bound and the best known side, and links to its case record, where its packing and number line are drawn.

n	Proved lower	Best known	Gap	Status	Records
70	8.657500	8.880961	0.22346037…	open=	frontier n-070.md
102	10.280000	10.605829	0.32582869…		frontier n-102.md
103	10.280000	10.679233	0.39923204…		frontier n-103.md
123	11.094810	11.591379	0.49656809…		frontier n-123.md
129	11.374281	11.870014	0.49573226…		frontier n-129.md
146	12.086630	12.583783	0.49715196…		frontier n-146.md
153	12.384864	12.870014	0.48514952…		frontier n-153.md
236	15.374474	15.861935	0.48745960…		frontier n-236.md
258	16.064382	16.563449	0.49906558…		frontier n-258.md
263	16.224185	16.733167	0.50898081…		frontier n-263.md
269	16.413830	16.901514	0.48768311…		frontier n-269.md
292	17.090660	17.591379	0.50071812…		frontier n-292.md
295	17.180827	17.704233	0.52340547…		frontier n-295.md
302	17.389345	17.870014	0.48066809…		frontier n-302.md
303	17.418924	17.909959	0.49103397…		frontier n-303.md

Results on these cases

49 results in the register on these cases, oldest first

2005 published T-007 · 15 of these cases
$s (n) \geq min (⌈ \sqrt{n} ⌉, \sqrt{n - 2 ⌊ \sqrt{n} ⌋ + 1} + 1)$ for $4 \leq n \leq 324$
Lower bound incomplete on these cases, superseded by T-073, T-080, T-083, T-091 and T-180 (reported)
Nagamochi · Nagamochi 2005 · source · register
2026-09-04 published T-085 · 15 of these cases
Nagamochi 2005, Lemma 1 is false for every container with $a > 3$ and $b > 2$
Correction confirmed
Karakuş; Vlasenko · Karakuş 2026 · chelokot Nagamochi counterexample 2026 · packet · register
2026-09-22 published T-044 · case 70
Weighted point lower bounds for ten counts in $n = 26 \dots 72$ , plus seven from the same files
Lower bound confirmed superseded by T-091
Hosono after Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 point bounds 2026 · packet · source · review · register
2026-09-27 published T-046 · case 70
Rectangle-density lower bounds reported for 48 counts in $n = 18 \dots 95$
Lower bound recorded superseded by T-091
Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026 · wand125 rectangle bounds 2026-09-28 · packet · packet · register
2026-09-27 published T-056 · 9 of these cases
Smaller packings for 49 counts from $n = 68$ to $307$ , each certified two independent ways
Upper bound confirmed superseded by T-146, T-174, T-186 and T-218
Couzo · franciscouzo square-packing 2026-09-27 · packet · register
2026-09-28 published T-070 · case 70
Rectangle-density lower bounds replayed at 25 counts in $n = 29 \dots 95$
Lower bound confirmed superseded by T-091
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 · case 70
Rectangle-certificate ceiling α·UB(n) proved for $n = 1$ ..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 · 15 of these cases
$s (n) \geq 1 / 2 + \sqrt{n - ⌊ \sqrt{n} ⌋ + 1 / 4}$ for every nonsquare $8 \leq n \leq 324$
Lower bound confirmed
Karakuş · Karakuş 2026 · source · register
2026-10-01 published T-068 · case 70
Rectangle-density lower bounds verified at 34 counts in $n = 19 \dots 95$
Lower bound confirmed on these cases, superseded by T-091
Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026-10-01 · packet · source · review · register
2026-10-01 published T-074 · case 70
Rectangle-density lower bounds replayed at 31 counts in $n = 19 \dots 95$
Lower bound confirmed on these cases, superseded by T-091
Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 rectangle bounds 2026-10-01 · packet · packet · source · review · register
2026-10-02 published T-073 · cases 102, 103
Linear-measure lower bounds replayed at $n = 83$ and $n = 101 \dots 105$
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-077 · case 70
Rectangle-density lower bounds replayed at $n = 20$ , 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 102, 103
Linear-measure lower bound replayed at $n = 101 \dots 105$
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 · case 70
Mixed rectangle-measure lower bounds verified at 22 counts in $n = 51 \dots 96$
Lower bound confirmed on these cases, superseded by T-091
Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds 2026-10-03 · packet · packet · source · review · register
2026-10-03 published T-092 · cases 263, 303
Smaller packings again at seven counts from $n = 208$ to $306$ , each certified two independent ways
Upper bound confirmed superseded by T-174 and T-186
Couzo · franciscouzo square-packing 2026-10-03 · packet · register
2026-10-04 published T-091 · case 70
Mixed rectangle-measure lower bounds verified at 17 counts in $n = 53 \dots 95$
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-098 · 8 of these cases
Exact optima of 48 known-best packings: s(n) ≤ S', 3.5e-13 to 5.0e-11 below each printed side
Upper bound confirmed on these cases, superseded by T-146, T-174, T-186 and T-218
Daniel after Couzo, de Winter, Ellsworth, Levy · evand exact optima 2026-10-05 · packet · register
2026-10-05 published T-101 · 6 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 on these cases, superseded by T-146, T-173, T-186 and T-187
Daniel after Couzo, de Winter, Ellsworth, Levy · evand exact optima 2026-10-05 · packet · register
2026-10-07 published T-113 · cases 129, 303
$s (n) \leq S_{n}$ at ten counts, $n = 108$ to 303, from new SQUISH rational packings
Upper bound confirmed superseded by T-186
Chaoweeraprasit after Ellsworth · SQUISH ten packings 2026-10-07 · packet · register
2026-10-07 published T-114 · case 153
$s (153) \leq 7250614903299225 / 562949953421312$ , 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 123, 129, 258, 263
$s (n) \leq S_{n}$ 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 236, 263, 302
$s (n) \leq S_{n}$ at nine counts, from the second SQUISH update’s new rational packings
Upper bound confirmed superseded by T-174, T-186 and T-218
Chaoweeraprasit after Ellsworth, Couzo and SQUISH · SQUISH second update 2026-10-07 · packet · register
2026-10-07 published T-117 · case 292
Exact rational ceiling refinements at $n = 105$ , 292
Upper bound confirmed superseded by T-146
Rehwaldt after Couzo and earlier contributors · Rehwaldt Couzo refinements 2026-10-07 · packet · register
2026-10-07 published T-120 · case 102
Reported s(102) ≤ alpha_102 with a degree-8 exact side form
Upper bound recorded superseded by T-146
Daniel after Couzo · Daniel exact and local reports 2026 · packet · register
2026-10-07 published T-129 · case 292
Three dated Daniel certificate reports with historical source custody
Upper bound recorded superseded by T-146
Daniel after Couzo, Levy · Daniel dated certificates 105 and 130 2026-10-07 · Daniel dated certificate 292 2026-10-07 · packet · packet · packet · register
2026-10-08 published T-125 · 11 of these cases
Complete rational construction reports at 25 counts
Upper bound confirmed superseded by T-146, T-173, T-174, T-186, T-187 and T-218
Xu · ry-xu square packing 2026 · packet · register
2026-10-08 published T-127 · cases 123, 129, 153, 236
Fourteen rational refinements, seventeen complete source cases
Upper bound confirmed on these cases, superseded by T-146, T-173, T-186 and T-218
Gupta after Chaoweeraprasit, Daniel · Gupta rational refinements 2026-10-08 · packet · register
2026-10-09 published T-134 · cases 263, 303
Six exact rational certificates from Couzo
Upper bound confirmed on these cases, superseded by T-174 and T-186
Couzo after Polkovskyi, Chaoweeraprasit, Gupta, Xu, Daniel, Ellsworth, Levy · Couzo exact certificates 2026-10-09 · packet · register
2026-10-09 published T-136 · 7 of these cases
Seventeen exact rational packings from SQUISH's third request
Upper bound confirmed on these cases, superseded by T-146, T-173, T-174, T-186 and T-218
Chaoweeraprasit after Couzo, Xu, Göbel, Schadt, Ellsworth, Hajba, Levy · SQUISH third request 2026-10-09 · packet · register
2026-10-09 published T-138 · cases 103, 258, 302, 303
Exact witnesses at Mishapolk's printed ceilings, the smallest known at 103 and 258 when registered
Upper bound confirmed superseded by 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-144 · case 123
Linear-measure lower bound $s (n) \geq 563 / 50 = 11.26$ for $n = 122 \dots 126$ , 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 this result · 15 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 · case 146
Exact rational refinements of Xu's packings of 146 and 261 squares
Upper bound confirmed superseded by T-187
Barnett after Xu, Daniel, Levy · Barnett refinements 2026-10-11 · packet · register
2026-10-11 published T-159 · case 102
Another arrangement of Xu's design for 102 squares, certified exactly from its decimal layout
Upper bound confirmed superseded by T-146
Calle after Xu, Levy · Calle n102 2026-10-12 · packet · register
2026-10-12 published T-162 · cases 129, 303
New packings of 129, 204 and 303 squares, a cut-out and two compositions, each certified exactly
Upper bound confirmed superseded by T-186
Ostashev after Nakajima, Chaoweeraprasit, Daniel, Xu, Levy · Ostashev compositions 2026-10-12 · packet · register
2026-10-12 published T-164 · case 302
A packing of 302 squares from four boundary patches of Xu's packing of 70 and two upright banks
Upper bound confirmed superseded by T-186
PingYou Ltd after Xu, Daniel, Levy · PingYou n302 certificate 2026-10-12 · 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-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 published T-174 · 15 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-179 · case 146
Linear-measure lower bound $s (n) \geq 306 / 25 = 12.24$ for $n = 145 \dots 149$ , 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 · 15 of these cases
Closed-form lower bound $s (N) \geq a (N)$ for every non-square $N \geq 49$ , reported
Lower bound reviewed
Hosono · wand125 closed form 2026-10-14 · packet · packet · register
2026-10-13 published T-181 · case 302
Exact rational certificates at 211, 241 and 302 from Couzo
Upper bound confirmed superseded by T-186
Couzo after Daniel, Ostashev, Fang, Ellsworth, Levy; Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy · Couzo issue-583 certificates 2026-10-13 · Couzo certificates 2026-10-13 · packet · packet · register
2026-10-14 published T-186 · cases 129, 302, 303
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
2026-10-16 published T-193 · 6 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-218 · case 236
Daniel's smaller n236 packing, after Chaoweeraprasit's composition, certified exactly
Upper bound confirmed
Daniel after Chaoweeraprasit, Levy · Daniel n236 2026-10-16 · packet · register

Links

On this site: The frontier survey · T-146 in the results table

On GitHub, at main

Register: T-146 in results.yaml, line 16076
Evidence: E-evand-regularized-certificate-report · E-evand-regularized-exact-feasibility
Proofs and certificates: certificate certs
Sources: Daniel regularized lists 2026-10-10 (its own site, retained copy)
Source packet: resources/web/evand-regularized-2026-10-10/README.md
Artifacts: 24 artifacts and controls in 7 directories. Complete artifact list in the result entry. docs/project/reviews packing/devtools packing/resources/web/evand-regularized-2026-10-10 packing/resources/web/evand-regularized-2026-10-10/acquisition packing/resources/web/evand-regularized-2026-10-10/receipts packing/resources/web/evand-regularized-2026-10-10/source/search/regularize/lists/certs packing/tests
Case file: each case’s file is linked from its row above