T-193: Exact algebraic sides at sixteen counts from Evan Daniel, of packings the record credits

V3 C3 Upper bound confirmed

2026-10-16 published · Daniel after Xu, Chaoweeraprasit, Ostashev, Couzo, PingYou Ltd, Gupta, Polkovskyi, Levy · 16 cases, $n = 88$ to 302

Daniel's issue 639 reports exact algebraic sides for the record's best-known packings at 23 counts. At the sixteen recorded here each side is the one root of an integer polynomial of degree 2 to 41 in a rational interval, realised by an exact configuration over a number field, every square's centre and angle parameter in the field. Each side, cut at 40 places:

$s (88) \leq 9.8824510304812468193284571556918969668693 \dots$ , $s (102) \leq 10.6058286964315783603846766570880096669418 \dots$ , $s (123) \leq 11.5913781454976981594349494020130208086995 \dots$ , $s (126) \leq 15 / 2$ + 3√2 = 11.7426406871192851464050661726290942357090…, $s (175) \leq 13.7641743174865966292901814768674768594691 \dots$ , $s (199) \leq 14.6175721735928068435558612724500328081986 \dots$ , $s (204) \leq 14.8086632343869565663229034486020952296225 \dots$ , $s (232) \leq 15.7641743174865966292901814768674768594691 \dots$ , $s (258) \leq 16.5634480021337893796001817112513963158640 \dots$ , $s (259) \leq 16.5913781454976981594349494020130208086995 \dots$ , $s (266) \leq 16.8230287507564759705405534237454448702252 \dots$ , $s (267) \leq 16.8388152699482622602660931895036575396753 \dots$ , $s (292) \leq 17.5913781454976981594349494020130208086995 \dots$ , $s (295) \leq 22$ (1 + √2)/3 = 17.7042327907360303578790506442044525761775…, $s (301) \leq 17.8466671928434897829433145909582979088797 \dots$ and $s (302) \leq 17.8700138504044643444601534007805939989658 \dots$ .

The source checks each configuration with its standard-library verify_exact.py, in exact rationals: every contact an identity in the field, every other pair separated and every corner inside the box by rational interval arithmetic at the field's root, and the side the polynomial's one root in its interval. It reports all 23 VALID, and a cross-check of its solver's 64-digit side against each polynomial's interval. It asserts each polynomial irreducible, which none of its programs checks.

Here verify_exact.py, read first and run unchanged from the retained copy, accepted all 23 files with the statements the source prints, and refused four mutated controls at each of the 19 forms the packet retains: a square moved 1e-6 through the wall it touches, the side raised by 1e-6 in the field, the side's interval moved below its root, and a duplicate square. That is a reproduction with the producer's code, on one route. SymPy factored each polynomial over the integers and found every one squarefree and a single factor of multiplicity 1, so irreducible, and each side algebraic of the degree stated.

The stage 4 review of 16 October read verify_exact.py line by line, stated the five hypotheses under which its VALID proves the packing, reproduced three of the replay's runs, and with a check of its own sharing no code with the checker decided all sixteen forms a packing at S* again; it found no blocking defect and accepted the claim at all sixteen counts, for finite feasibility only.

The 16 October report-order ledger records it at these sixteen counts, each below every earlier report, by 1.48e-99 (204) to 7.77e-35 (126): below PR 574's rational certificates (T-174) at twelve counts, by at least 7.77e-35 at 126, 1.18e-64 at 267, 1.66e-79 at 292 and 5.92e-95 to 4.48e-88 at the other nine, and below Polkovskyi's (T-186) at 175, 204, 232 and 302, by at least 1.48e-99 (204) to 1.79e-39 (302). At 51 the side is the (16 + 5√2)/3 both lanes hold, at 70, 153 and 207 it is T-174's algebraic side exactly, and at 172, 263 and 297 PR 574's rational certificates are smaller by about 1e-62, so those seven are not recorded.

Credit Daniel (https://github.com/evand/square-packing) with each exact form, a refinement of the packing it solves, after that packing's finder as the case records credit it: Chaoweeraprasit's at 88 and 199 (as Gupta improved them, T-127), 258 (as Polkovskyi improved it), 259 and 292; Xu's at 102, 123, 126, 267 (as Couzo improved it, T-134) and 295; Ostashev's at 175, 204 and 232; Couzo's at 301; PingYou Ltd's at 302, as Couzo improved it (T-181); and his own at 266 (T-119).

The regularizations items name PingYou Ltd's refinement (T-174) or Polkovskyi's (T-186) as the packing each form solves; the stage 4 review measured that route at 102, 123, 258, 259, 267, 295 and 302, and at the other nine counts found each form to be the case's own packing, to within 4.5e-4 at every centre (RE-1), so there the form refines the case's packing directly. The items are corrected in a later change (think-8ido).

The issue says the solver, checkers and batch were written and run with Claude (Anthropic) as a coding and research agent, directed and reviewed by the author.

Significance, composition and next rung

Significance: Exact algebraic forms of packings the record already credits, 1.5e-99 to 7.8e-35 below the nearest earlier report at each of sixteen counts: a citable detail of each case that changes no theorem, S2 as T-120 to T-123's exact forms are; the rational refinements they name (T-174, T-186) are S1, and at nine counts, by the review's RE-1, the forms tighten the case's own packing directly. No lower bound or optimum.
Next rung: V4 and C4 need, on top of V3 and C3, a second accepting adversarial AI review by a distinct reviewer of the checker's soundness and of this entry, and the owner's oversight record naming trust-boundary, certificate-meaning and ai-findings, which would disposition the stage 4 review's nine findings, none blocking. The review's own check, an independent decision of the same forms kept in the packet, would be an attribute beside the rung once registered (RE-9); a second route over number fields here, sqpack.witness.exact_verify, needs a converter of the source's format, a W7 slice with no bead.

The regularizations items at nine counts wait for the correction RE-1 asks, after the owner's Q2 (think-8ido). The house rule of 16 October 2026 makes the sixteen sides the houses at their counts, the smallest validated at each, and stages their adoption under think-ot5c (devtools.select_houses.PENDING_ADOPTION), until adopt_houses can write an algebraic side.

At 88, 126, 175, 199, 204, 232, 266, 292 and 301 the adoption also waits for RE-1's correction: the writer credits the packing a regularizations item names, so adopt_houses refuses T-193 there while the item names T-174 or T-186 (devtools.select_houses.CORRECTIONS_OWED, think-8ido).
Regularizations: n = 88: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 102: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 123: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 126: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 175: a regularization of T-186’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 199: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 204: a regularization of T-186’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 232: a regularization of T-186’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 258: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 259: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 266: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 267: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 292: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 295: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 301: a regularization of T-174’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).

n = 302: a regularization of T-186’s packing by Daniel (exact solve of the packing's contact system to its algebraic side (exactsolve.py, then minpoly.py), as for issue 419's exact forms; solved to its side; identity: the source’s claim).
Novelty: previously-published Present in an identified source

The cases

This result concerns 16 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
88	9.620000	9.882452	0.26245103…	open=	frontier n-088.md
102	10.280000	10.605829	0.32582869…		frontier n-102.md
123	11.094810	11.591379	0.49656809…		frontier n-123.md
126	11.235455	11.742641	0.50718541…		frontier n-126.md
175	13.237739	13.764175	0.52643511…		frontier n-175.md
199	14.110657	14.617573	0.50691458…		frontier n-199.md
204	14.293114	14.808643	0.51552861…		frontier n-204.md
232	15.239402	15.764175	0.52477134…		frontier n-232.md
258	16.064382	16.563449	0.49906558…		frontier n-258.md
259	16.096473	16.591379	0.49490418…		frontier n-259.md
266	16.319292	16.823029	0.50373673…		frontier n-266.md
267	16.350867	16.838816	0.48794778…		frontier n-267.md
292	17.090660	17.591379	0.50071812…		frontier n-292.md
295	17.180827	17.704233	0.52340547…		frontier n-295.md
301	17.359715	17.846668	0.48695189…	open≈	frontier n-301.md
302	17.389345	17.870014	0.48066809…	open=	frontier n-302.md

Results on these cases

50 results in the register on these cases, oldest first

2005 published T-007 · 16 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 · 16 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-046 · case 88
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 · 7 of these cases
Smaller packings for 49 counts from $n = 68$ to $307$ , each certified two independent ways
Upper bound confirmed superseded by T-098, T-127, T-136, T-146 and T-186
Couzo · franciscouzo square-packing 2026-09-27 · packet · register
2026-09-29 published T-058 · case 88
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 · 16 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 88
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 88
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 · case 102
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-075 · case 88
Mixed rectangle-measure lower bounds replayed at nine counts in $n = 83 \dots 96$
Lower bound confirmed on these cases, superseded by T-091
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-080 · case 102
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 88
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
2026-10-04 published T-090 · case 88
Mixed rectangle-measure lower bounds verified at 17 counts in $n = 42 \dots 96$
Lower bound confirmed on these cases, superseded by T-091
Hosono after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 mixed bounds 2026-10-04 · packet · source · review · register
2026-10-04 published T-091 · case 88
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 · 7 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
Daniel after Couzo, de Winter, Ellsworth, Levy · evand exact optima 2026-10-05 · packet · register
2026-10-05 published T-101 · 8 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-119, T-127, T-134, T-146, 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 · case 126
$s (n) \leq S_{n}$ at ten counts, $n = 108$ to 303, from new SQUISH rational packings
Upper bound confirmed superseded by T-139
Chaoweeraprasit after Ellsworth · SQUISH ten packings 2026-10-07 · packet · register
2026-10-07 published T-115 · cases 123, 126, 258
$s (n) \leq S_{n}$ at twelve counts, from the SQUISH update’s new and smaller rational packings
Upper bound confirmed superseded by T-139 and T-146
Chaoweeraprasit after Couzo and Ellsworth · SQUISH update 2026-10-07 · packet · register
2026-10-07 published T-116 · cases 88, 199, 302
$s (n) \leq S_{n}$ at nine counts, from the second SQUISH update’s new rational packings
Upper bound confirmed superseded by T-127 and T-186
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-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-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 · 8 of these cases
Complete rational construction reports at 25 counts
Upper bound confirmed superseded by T-127, T-134, T-139, T-146 and T-186
Xu · ry-xu square packing 2026 · packet · register
2026-10-08 published T-127 · cases 88, 123, 199
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-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 232, 259, 292, 302
Seventeen exact rational packings from SQUISH's third request
Upper bound confirmed
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, 258, 267, 302
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 and T-186
Polkovskyi after Stenlund, Friedman, Ellsworth, Chaoweeraprasit, Couzo, Xu, Levy · Mishapolk decimal poses 2026-10-09 · packet · register
2026-10-09 published T-139 · case 126
A more precise certificate of Xu's 126-square arrangement, from Daniel
Upper bound confirmed
Daniel after Xu, Chaoweeraprasit · Daniel trio126 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-144 · cases 123, 126
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 · 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-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
2026-10-11 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 · case 204
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-225
Levy after Daniel · register
2026-10-12 published T-158 · cases 175, 232
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-162 · case 204
New packings of 129, 204 and 303 squares, a cut-out and two compositions, each certified exactly
Upper bound confirmed superseded by 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
2026-10-13 published T-174 · 16 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-098, T-119, T-127, T-134, T-136, T-139, T-146, T-186 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-180 · 16 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 175, 204, 232, 302
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 this result · 16 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-209 · case 88
Mixed rectangle-measure lower bound $s (88) \geq 3853 / 400$ reported, on the 201-direction net
Lower bound recorded
Hosono after Tokoharu and Levy · wand125 fine-net lower bounds 2026-10-16 · packet · register
2026-10-17 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-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-193 in the results table

On GitHub, at main

Register: T-193 in results.yaml, line 26854
Evidence: E-evand-639-exact-sides-report · E-evand-639-verify-exact-replay
Proofs and certificates: certificate data
Sources: Daniel exact current records 2026-10-16
Source packet: resources/web/evand-exact-cur-2026-10-16/README.md
Artifacts: 9 artifacts and controls
resources/web/evand-exact-cur-2026-10-16/README.md resources/web/evand-exact-cur-2026-10-16/source/search/exact/cur/RESULTS.md resources/web/evand-exact-cur-2026-10-16/source/search/exact/cur/data/verify.txt campaign/issue-intake/upper-bounds-20261016/README.md campaign/issue-intake/upper-bounds-20261016/exact-sides.json campaign/issue-intake/upper-bounds-20261016/review/exact_sides.py resources/web/evand-exact-cur-2026-10-16/receipts/replay-verify-exact.json resources/web/evand-exact-cur-2026-10-16/review/replay_verify_exact.py tests/test_evand_exact_cur.py
Case file: each case’s file is linked from its row above