T-186: Exact certificates at twelve counts from Mykhailo Polkovskyi, tightening the smallest reported there

V3 C3 Upper bound confirmed

2026-10-14 published · Polkovskyi after Ostashev, Couzo, PingYou Ltd, Levy · 12 cases, $n = 129$ to 304

Twelve complete rational source certificates report finite upper-bound improvements at the exact sides they state: $s (129) \leq 593500692520223217223007670039029699948354116213961 / 50000000000000000000000000000000000000000000000000$ , $s (154) \leq 646060328856631552497101463610355043240689434277149 / 50000000000000000000000000000000000000000000000000$ , $s (156) \leq 648958292691713822691804519015415761935309055406679 / 50000000000000000000000000000000000000000000000000$ , $s (175) \leq 6882087158743298314645090738433738429734596852921042192847398468605899002561978177069845581 / 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ , $s (176) \leq 137958723184364072631738953307277133712331066995515103744502117015291642972051776912348029686675350647263 / 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ , $s (204) \leq 740433161719347828316145172430104761481126338872178671530915993369069066972891707484286255665843382616078162213 / 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ , $s (232) \leq 1576417431748659662929018147686747685946919370584208438569479693721179800512385635413969116208071951422158405421 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ , $s (264) \leq 838736756619391642122125861799894632619976183429475268094914028891692156889593756790740302236975468449744536043 / 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ , $s (271) \leq 1694899235645120560305712851306208344982773066757282853717334516897079238059065607134656903415421834818577532691 / 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ , $s (302) \leq 893500692520223217223007670039029699948384116213961 / 50000000000000000000000000000000000000000000000000$ , $s (303) \leq 223874478638373849767708018731100462502930758319276667065271354307189968584331641646777792095999047220400719209 / 12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$ and $s (304) \leq 1792942775807517496548703186140836311278604266912137 / 100000000000000000000000000000000000000000000000000$ .

All 72 retained jobs, the packet's 24 certificates with their duplicate-square and outside-container controls, the twelve this entry cites among them, were decided again here on 16 October 2026 by both maintained exact routes and equal their retained rows, and the frozen comparison rebuilt equal. The review's third route read each of the twelve pinned .cert files with its own reader and found each derived fact to state its packing, side and every pose, and the pinned census to print each side. No route here is the source's code, so the replay is independently re-implemented. The 16 October review found no blocking defect.

The source's README, unchanged since the revision issue 593 reports, states that every certificate passes Daniel's exact checkers verify_cert.py and verify_cert2.py with zero tolerance and that every separating-axis margin and boundary clearance is strictly positive; census.json at the pin names the source of each count, 'Polkovskyi (ultra-precision KKT dual-verified optimum)' at the twelve counts registered here. The commit, 'Refine 14 contested certificates to ultra-precision KKT endpoints', states no further check. Those statements are the author's; no source program ran here.

Credit Polkovskyi (https://github.com/Mishapolk/square-packing-records), the name the author asks for on issue 593, with each certificate as a refinement of the packing it tightens, after that packing's finders as the entries it chains through credit them: Ostashev's packing at 129, 204 and 303 (T-162, issue 562), at 175, 232 and 264 (T-158, issue 528) and at 176 and 304 (issue 575; T-175 at 304); at 156 Ostashev's arrangement as Couzo continued it (T-161, issue 561); at 271 Chaoweeraprasit's SQUISH packing as Couzo refined it (T-161, after T-151); at 302 PingYou Ltd's issue-564 arrangement (T-164) as Couzo continued it (T-181, issues 583 and 586); and at 154 Couzo's arrangement after Daniel's issue-552 packing (T-182, issue 586).

At 129, 156, 175, 176, 204, 232, 264, 271 and 303 the certificates come by way of PingYou Ltd's refinement (T-174, PR 574).

Measured here, every certificate places every square centre within 1.1e-3 of the certificate it tightens, and within 1.3e-15 at 156, 175, 264, 271, 302, 303 and 304. The commit states no AI assistance; issue 593 discloses Gemini assistance with solver scripting, precision checks and formatting.

Significance, composition and next rung

Significance: Padding and exact re-solves of packings the record already credits, 1.25e-94 to 1.79e-19 below the nearest earlier report at each of twelve counts, as T-174's and T-170's are; no lower bound or optimum.
Next rung: V4 and C4 need a second accepted adversarial review by a distinct reviewer and a retained human oversight record; one AI review, of 16 October, is retained.
Regularizations: n = 129: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 0.0001414).

n = 154: a regularization of T-182’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 0.0006364).

n = 156: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 7.586e-16).

n = 175: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 9.237e-16).

n = 176: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 0.0001414).

n = 204: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 2 squares moved, at most 0.001019).

n = 232: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 0.0002828).

n = 264: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 1.206e-15).

n = 271: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 9.88e-16).

n = 302: a regularization of T-181’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 7.783e-16).

n = 303: a regularization of T-174’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 9.544e-16).

n = 304: a regularization of T-175’s packing by Polkovskyi (refinement to an ultra-precision KKT endpoint; solved to its side; identity: measured here; 0 squares moved, at most 9.377e-16).
Regularized drawings: n = 129: a regularization of T-186’s packing by Levy (Daniel's search/regularize (MIT), evand/square-packing@675a5ea, conservative, coincide, through devtools.regularize_evand; the project’s modifications: same-side exact re-solve (devtools.regularize_same_side); at its own side; 2 free angles moved; identity: measured here; nearest centres one to one; 28 squares moved, at most 0.111039; turns up to 4.72707°).

n = 156: a regularization of T-186’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; 21 squares moved, at most 0.201584; turns up to 0.0262316°).

n = 175: a regularization of T-186’s packing by Levy (Daniel's search/regularize (MIT), evand/square-packing@675a5ea, conservative, coincide, through devtools.regularize_evand; the project’s modifications: same-side exact re-solve (devtools.regularize_same_side); at its own side; 5 free squares straightened, 12 free angles moved; identity: measured here; nearest centres one to one; 26 squares moved, at most 0.107376; turns up to 3.54876°).

n = 176: a regularization of T-186’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 0.0340404; turns up to 0.00572958°).

n = 232: a regularization of T-186’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; 12 squares moved, at most 0.0605772; turns up to 0.0114592°).

n = 264: a regularization of T-186’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; 27 squares moved, at most 0.176199; no square turned).

n = 302: a regularization of T-186’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; 136 squares moved, at most 0.050554; turns up to 2.2217°).

n = 303: a regularization of T-186’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 4 squares moved, at most 0.0237571; no square turned).

n = 304: a regularization of T-186’s packing by Levy (regularize_axis_components/2; at its own side; identity: measured here; nearest centres one to one; 32 squares moved, at most 0.0503155; no square turned).
Novelty: previously-published Present in an identified source

The cases

This result concerns 12 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
129	11.374281	11.870014	0.49573226…	open=	frontier n-129.md
154	12.426860	12.921101	0.49424049…		frontier n-154.md
156	12.510412	12.979166	0.46875370…		frontier n-156.md
175	13.237739	13.764175	0.52643511…		frontier n-175.md
176	13.276932	13.795873	0.51893997…		frontier n-176.md
204	14.293114	14.808643	0.51552861…		frontier n-204.md
232	15.239402	15.764175	0.52477134…		frontier n-232.md
264	16.255951	16.774736	0.51878387…		frontier n-264.md
271	16.476545	16.948948	0.47240242…		frontier n-271.md
302	17.389345	17.870014	0.48066809…		frontier n-302.md
303	17.418924	17.909959	0.49103397…		frontier n-303.md
304	17.448451	17.929428	0.48097650…		frontier n-304.md

Results on these cases

44 results in the register on these cases, oldest first

2005 published T-007 · 12 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-083 and T-180 (reported)
Nagamochi · Nagamochi 2005 · source · register
2026-09-04 published T-085 · 12 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
2026-09-27 published T-056 · 6 of these cases
Smaller packings for 49 counts from $n = 68$ to $307$ , each certified two independent ways
Upper bound confirmed superseded by T-186, T-219 and T-222
Couzo · franciscouzo square-packing 2026-09-27 · packet · register
2026-09-29 published T-083 · 12 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
2026-10-03 published T-092 · case 303
Smaller packings again at seven counts from $n = 208$ to $306$ , each certified two independent ways
Upper bound confirmed superseded by T-186
Couzo · franciscouzo square-packing 2026-10-03 · packet · register
2026-10-05 published T-098 · 6 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-186, T-219 and T-222
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-186 and T-225
Daniel after Couzo, de Winter, Ellsworth, Levy · evand exact optima 2026-10-05 · packet · register
2026-10-07 published T-113 · cases 129, 154, 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 and T-222
Chaoweeraprasit after Ellsworth · SQUISH ten packings 2026-10-07 · packet · register
2026-10-07 published T-115 · cases 129, 154
$s (n) \leq S_{n}$ at twelve counts, from the SQUISH update’s new and smaller rational packings
Upper bound confirmed superseded by T-186 and T-222
Chaoweeraprasit after Couzo and Ellsworth · SQUISH update 2026-10-07 · packet · register
2026-10-07 published T-116 · case 302
$s (n) \leq S_{n}$ at nine counts, from the second SQUISH update’s new rational packings
Upper bound confirmed superseded by T-186
Chaoweeraprasit after Ellsworth, Couzo and SQUISH · SQUISH second update 2026-10-07 · packet · register
2026-10-08 published T-125 · cases 129, 175
Complete rational construction reports at 25 counts
Upper bound confirmed superseded by T-186
Xu · ry-xu square packing 2026 · packet · register
2026-10-08 published T-127 · cases 129, 154
Fourteen rational refinements, seventeen complete source cases
Upper bound confirmed on these cases, superseded by T-186 and T-222
Gupta after Chaoweeraprasit, Daniel · Gupta rational 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 303
Six exact rational certificates from Couzo
Upper bound confirmed on these cases, superseded by 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 · cases 154, 232, 302, 303
Seventeen exact rational packings from SQUISH's third request
Upper bound confirmed on these cases, superseded by T-186 and T-222
Chaoweeraprasit after Couzo, Xu, Göbel, Schadt, Ellsworth, Hajba, Levy · SQUISH third request 2026-10-09 · packet · register
2026-10-09 published T-138 · cases 175, 302, 303
Exact witnesses at Mishapolk's printed ceilings, the smallest known at 103 and 258 when registered
Upper bound confirmed superseded by T-186
Polkovskyi after Stenlund, Friedman, Ellsworth, Chaoweeraprasit, Couzo, Xu, Levy · Mishapolk decimal poses 2026-10-09 · 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-146 · cases 129, 302, 303
Exact rational certificates at fifteen counts from Daniel's regularized record lists
Upper bound confirmed on these cases, superseded by T-186
Daniel after Xu, Chaoweeraprasit, Polkovskyi, Levy · Daniel regularized lists 2026-10-10 · packet · register
2026-10-11 published T-149 · case 156
New packings of 155, 156 and 211 squares, each with an exact rational certificate
Upper bound confirmed superseded by T-186
Ostashev after Nakajima, Levy, Xu · Ostashev records 2026-10-11 · packet · register
2026-10-11 published T-151 · cases 176, 271, 304
Nine exact rational packings from SQUISH's fourth request
Upper bound confirmed superseded by T-186 and T-219
Chaoweeraprasit after Couzo, Gupta, Ellsworth, Friedman, Levy · SQUISH fourth request 2026-10-11 · packet · register
2026-10-11 published T-152 · case 304
Exact rational refinements of SQUISH's Mondrian packings of 304 and 305 squares
Upper bound confirmed superseded by T-186
Couzo after Chaoweeraprasit, Fang, Daniel, Ellsworth, Levy · Couzo certificates 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 · cases 204, 264
Exact regularized sides at 59 counts, 5.4e-20 to 9.9e-15 below the ceilings they replace
Upper bound confirmed on these cases, superseded by T-186 and T-225
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-160 · case 154
A smaller packing of 154 squares from Daniel's size-chaining explorer, certified exactly
Upper bound confirmed superseded by T-222
Daniel after Couzo, Levy · Daniel n154 2026-10-12 · packet · register
2026-10-12 published T-161 · cases 156, 176, 271
Exact rational certificates at 156, 176, 237 and 271 from Couzo
Upper bound confirmed superseded by T-186 and T-219
Couzo after Ostashev, Chaoweeraprasit, Fang, Daniel, Ellsworth, Levy · Couzo certificates 2026-10-12 · packet · register
2026-10-12 published T-162 · cases 129, 204, 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 and T-225
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-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-172 · case 154
A packing of 154 squares from Couzo, continuing Daniel's arrangement
Upper bound confirmed superseded by T-222
Couzo after Daniel, Ostashev, Fang, Ellsworth, Levy · Couzo issue-583 certificates 2026-10-13 · packet · register
2026-10-13 published T-174 · 11 of these cases
Tighter certificates at 68 counts from PingYou Ltd, of others' packings and its own
Upper bound confirmed on these cases, superseded by T-186, T-219 and T-225
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-175 · case 304
New packings of 211, 241 and 304 squares, two with merged tilted bands, each certified exactly
Upper bound confirmed superseded by T-186
Ostashev after Nakajima, Daniel, de Winter, Couzo, Levy, Xu · Ostashev merged bands 2026-10-13 · packet · register
2026-10-13 published T-180 · 12 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
2026-10-13 published T-182 · case 154
Exact rational certificates at 154, 211 and 241 from Couzo
Upper bound confirmed on these cases, superseded by T-222
Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy · Couzo certificates 2026-10-13 · packet · register
2026-10-14 published T-186 this result · 12 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
2026-10-16 published T-193 · cases 175, 204, 232, 302
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
2026-10-17 published T-219 · case 271
Daniel's smaller n271 packing, continuing Couzo's arrangement, certified exactly
Upper bound confirmed
Daniel after Couzo, Chaoweeraprasit, Levy · Daniel n271 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
2026-10-18 published T-223 · case 204
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-222 · case 154
Daniel's smaller n154 packing, continuing Couzo's #586 arrangement, certified exactly
Upper bound confirmed
Daniel after Couzo, Ostashev, Levy · Daniel n154 sweep 2026-10-20 · packet · packet · register
2026-10-20 published T-225 · case 204
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

Links

On this site: The frontier survey · T-186 in the results table

On GitHub, at main

Register: T-186 in results.yaml, line 25381
Evidence: E-mishapolk-70a033f-certificate-report · E-mishapolk-70a033f-exact-feasibility
Proofs and certificates: certificate facts
Sources: Mishapolk KKT refinements 2026-10-14 (its own site, retained copy)
Source packet: resources/web/mishapolk-kkt-refinements-2026-10-14/README.md
Artifacts: 17 artifacts and controls
resources/web/mishapolk-kkt-refinements-2026-10-14/README.md resources/web/mishapolk-kkt-refinements-2026-10-14/acquisition/claims.json resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-129.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-154.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-156.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-175.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-176.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-204.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-232.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-264.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-271.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-302.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-303.yaml.gz resources/web/mishapolk-kkt-refinements-2026-10-14/facts/n-304.yaml.gz devtools/upper_bound_reports.py docs/project/reviews/review-2026-10-16-upper-bound-imports-506-607.md tests/test_upper_bound_reports.py
Case file: each case’s file is linked from its row above