New packings: 14 verified upper bounds for square packing (Category A records and Category B refinements, N in [105, 308]): registration request

Credit name. Mishapolk (Mikhail Polk) & Antigravity Autonomous Research Lab.
GitHub: Mishapolk
Repository: Mishapolk/square-packing-records
Commit: 52aa2672c74c91931686d60a49bdf97ec798291c

1. Summary of Claims

We report 14 verified upper bounds for unit square packing across the range $N \in [105, 308]$:
$$N \in {105, 130, 146, 156, 182, 204, 211, 229, 241, 260, 268, 299, 304, 308}$$

The submission is organized into:

Category A (3 Literature World Records, $|\Delta S| \ge 10^{-14}$): Packings beating standing official register bounds and literature claims by macroscopic or picometer margins ($N = 130, 182, 268$).
Category B (11 Micro-Refinement Packings): Verified exact rational certificates with strictly positive clearances ($\text{min_wall} > 0, \text{min_gap} > 0$) refining standing certificates, including large macroscopic contractions ($N = 299, 304$) and algebraic boundary refinements down to $10^{-41}$.

2. Table of Verified Upper Bounds

$N$	Cat	New Upper Bound $S$ (12 dec)	Exact Rational Side $S$	Baseline / Register Bound	Improvement ($\Delta S$)	Status vs Literature / Baseline
105	B	`10.789303783743`	`674331486483935962030222957609 / 62500000000000000000000000000`	`10.789303783743`	$-1.00 \times 10^{-21}$	Micro-refinement (machine gap $+1.00\times 10^{-20}$)
130	A	`11.902430645983`	`5951215322991132879306459820277 / 500000000000000000000000000000`	`11.904483032516`	$-2.052\text{ mm}$	World Record; beats Couzo #843 by $-2.08\text{ pm}$
146	B	`12.583782190152`	`12583782190151860342291508597077 / 1000000000000000000000000000000`	`12.583782190152`	$-1.00 \times 10^{-21}$	Exact certificate registered (Evan Daniel baseline)
156	B	`12.979165853835`	`648958292691713822691804519015415761935308555406679 / 50000000000000000000000000000000000000000000000000`	`12.979165853847`	$-1.30 \times 10^{-11}$	Boundary refinement ($\text{min_gap} = 1.00\times 10^{-40}$)
182	A	`13.970916436215`	`6985458218107409544582181073397 / 500000000000000000000000000000`	`13.974090713122`	$-3.174\text{ mm}$	World Record; beats Kaggle by $-1.845\text{ mm}$
204	B	`14.808642830514`	`14808642830513184650000000000001 / 1000000000000000000000000000000`	`14.808642830517`	$-3.72 \times 10^{-12}$	Refines verified register certificate
211	B	`14.993549626300`	`14993549626299421038935530460881 / 1000000000000000000000000000000`	`14.993549626300`	$-1.00 \times 10^{-21}$	Coordinate compaction; strictly positive clearances
229	B	`15.650161513877`	`15650161513876431064008548865321 / 1000000000000000000000000000000`	`15.650161513877`	$-4.60 \times 10^{-13}$	Refines previous repo certificate
241	B	`15.987117095151`	`1598711709514999999999999999999 / 100000000000000000000000000000`	`15.987117095151`	$-1.00 \times 10^{-21}$	Boundary contraction; strict open container
260	B	`16.645753250520`	`4161438312629953048686324163329 / 250000000000000000000000000000`	`16.645753250537`	$-1.67 \times 10^{-11}$	Refines previous repo certificate
268	A	`16.874361715871`	`527323803620963369940181046851 / 312500000000000000000000000000`	`16.874361715874`	$-3.00\text{ pm}$	World Record; beats #593 by $-4.453\text{ mm}$
299	B	`17.803695435316`	`2225461929414467349619294144451 / 125000000000000000000000000000`	`17.822875655532`	$-19.180\text{ mm}$	Beats PR #574 by $-19.18\text{ mm}$, beats #824 by $-17.26\text{ pm}$
304	B	`17.926898900367`	`8963449450183382079945018248601 / 500000000000000000000000000000`	`17.929427758093`	$-2.529\text{ mm}$	Refines Tymchishin baseline by $-2.53\text{ mm}$
308	B	`17.997149121271`	`3599429824254181747030432150463 / 200000000000000000000000000000`	`17.997149121289`	$-1.80 \times 10^{-11}$	Boundary refinement ($\text{min_gap} = 1.00\times 10^{-20}$)

3. Highlighted Literature World Records (Category A)

$N = 130$ ($S \le 11.902430645983$):
The standing register bound is $11.904483032516$ (PR research: submit 148 square-packing certificate refinements with exact endpoints #574). Francisco Couzo submitted registration request Issue s(130) ≤ 11.902430646: registration request #843 with claimed bound $S \le 11.902430645985$. This certificate strictly beats PR research: submit 148 square-packing certificate refinements with exact endpoints #574 by $-2.052\text{ mm}$ and beats Couzo Issue s(130) ≤ 11.902430646: registration request #843 by $-2.08\text{ picometers}$ ($2.0828 \times 10^{-12}$) with machine clearances $\text{min_wall} = 9.66 \times 10^{-15}, \text{min_gap} = 1.82 \times 10^{-14}$.
$N = 182$ ($S \le 13.970916436215$):
The standing register bound is $13.974090713122$ (PingYou Ltd PR research: submit 148 square-packing certificate refinements with exact endpoints #574). On Kaggle, Prathamesh Chavan reported $S \le 13.972761347065$. This certificate beats PR research: submit 148 square-packing certificate refinements with exact endpoints #574 by $-3.174\text{ mm}$ and beats the Kaggle report by $-1.845\text{ mm}$ with machine clearances $\text{min_wall} = 5.00 \times 10^{-15}, \text{min_gap} = 9.24 \times 10^{-15}$.
$N = 268$ ($S \le 16.874361715871$):
The verified literature bound is $16.874361715874$ (Couzo verified). In upstream Issue 73 new upper bounds across N=51..308: registration request #593, Mishapolk reported $16.878814821007$. This certificate beats the verified literature bound by $-3.00\text{ picometers}$ ($2.9976 \times 10^{-12}$) and beats Issue 73 new upper bounds across N=51..308: registration request #593 by $-4.453\text{ mm}$ with machine clearances $\text{min_wall} = 2.94 \times 10^{-14}, \text{min_gap} = 5.26 \times 10^{-14}$.

4. Verification and Reproducibility

Every certificate is hosted in Mishapolk/square-packing-records and can be independently verified using Evan Daniel's separating-axis verifier under strict open-container semantics:

git clone https://github.com/Mishapolk/square-packing-records.git
cd square-packing-records

# Verify Category A World Records
python3 verify_bound_certificate.py --strict certificates/0000-0999/n130.cert
python3 verify_bound_certificate.py --strict certificates/0000-0999/n182.cert
python3 verify_bound_certificate.py --strict certificates/0000-0999/n268.cert

# Verify Category B Refinements
for n in 105 146 156 204 211 229 241 260 299 304 308; do
    python3 verify_bound_certificate.py --strict "certificates/0000-0999/n${n}.cert"
done

All 14 certificates yield {"valid": true, "strict_valid": true, "wall_margin_sign": 1, "pair_margin_sign": 1, "accepted": true}. Vector SVGs and coordinate files are available in certificates/square-{N}.svg and .txt.

intake(#843-#846, #824 update): replay receipts, identity measurement…

intake(#843-#846, #824 update): register T-252 to T-258 at V0/C0, pac…

intake(#843-#846, #824 update): render the views, verdict comments, #846

intake(#843-#846, #824 update): site URLs, document map, verifiers vi…

intake(#843-#846, #824 update): sharp controls at every count, packet…

intake(#843-#846, #824 update): synopsis status row, verdict drafts n…

intake(#843-#846, #824 update): credits name the project where the so…

records: map the five stage 4 reviews of #852; T-260 split from T-259

data: what the eight new houses of 31 October feed (think-3guf)

Merge origin/main 49dac43 (#849, #850, #853, #854, #855) into the int…

Merge origin/main a8deaf1 (#851, #817) into the intake of #843 to #846

Merge pull request #852 from jlevy/claude/bold-ritchie-xo28us-upper

@Mishapolk

@Mishapolk, thank you; this is the report-order evaluation of every open report at the counts #846 claims.

At each count, a report is recorded when its side is decidably below every side reported before it (and below the record on main); a tie stays with the earlier report. Sides are rounded up at 12 places.

105: 10.789303783743, recorded: a refinement of Ryan Xu's packing; credited to this report's finder, after Ryan Xu; 1.00e-21 below the record on main (Ryan Xu, improved by Francisco Couzo, PingYou Ltd, Mishapolk).
130: 11.902430645983, recorded: a refinement of Francisco Couzo's packing as s(130) ≤ 11.902430646: registration request #843 gives it; credited to this report's finder, after Francisco Couzo; 2.08e-12 below s(130) ≤ 11.902430646: registration request #843 (Francisco Couzo).
146: 12.583782190152, recorded: a refinement of Evan Daniel's packing; credited to this report's finder, after Evan Daniel; 1.00e-21 below the record on main (Evan Daniel).
156: 12.979165853835, recorded: a refinement of Daniil Ostashev's packing; credited to this report's finder, after Daniil Ostashev; 1.00e-41 below the record on main (Daniil Ostashev, improved by Francisco Couzo, PingYou Ltd, Mishapolk).
229: 15.650161513877, recorded: a refinement of Evan Daniel's packing; credited to this report's finder, after Evan Daniel; 1.00e-21 below the record on main (Evan Daniel).
308: 17.997149121271, recorded: a refinement of Evan Daniel's packing; credited to this report's finder, after Evan Daniel; 1.00e-21 below the record on main (Evan Daniel).
211: 14.993549626300, not recorded: equal to Mykhailo Polkovskyi's publication Mishapolk/square-packing-records@e386aab, reported first.
241: 15.987117095151, not recorded: equal to Mykhailo Polkovskyi's publication Mishapolk/square-packing-records@e386aab, reported first.
Not recorded, above the record on main (Evan Daniel): 182.
Not recorded, above 172, 204, 260, 293: registration request #845 (Evan Daniel): 204, 260.
Not recorded, above the record on main (Vladislav Lavrentev, improved by Evan Daniel): 268.
Not recorded, above s(299) ≤ 17.803695435333: registration request #824 update (Evan Daniel): 299.
Not recorded, above the record on main (Kirill Tymchishin, improved by Evan Daniel): 304.

Six of the fourteen are recorded: 130, below Francisco Couzo's #843 certificate, and 105, 146, 156, 229 and 308, each below its case's house. At 182, 268 and 304 the house is lower; at 204 and 260 Evan Daniel's #845 and at 299 his update to #824 came first and are lower; and 211 and 241 are the certificates you first published on 23 October (e386aab), which the ledger records from that commit.

Your ten commits of 23 October, e386aab to fbc1749, are walked as publications from their commits: the ledger records nine of them (154, 155, 183, 211, 227, 236, 237, 241 and 271), and not 88 and 126, which lie above the exact algebraic sides a register entry states there, 152, which it cannot yet order against one, or 204 and 270, which equal the houses.

At 105, 146, 156, 229 and 308 here, and at the nine of 23 October, each certificate is below the house certificate by less than one unit in the 12th place and rounds to its print. The owner's ruling of 23 October calls such re-certifications restatements, and the ledger applies it beyond n = 324 only; whether it reaches these counts is the owner's question, and the record holds those fourteen rows until the answer. 130 is outside it: its print differs, and it is recorded either way.

Every count

n	Side	Verdict	Best now
105	10.789303783743	recorded: a refinement of Ryan Xu's packing; credited to this report's finder, after Ryan Xu; 1.00e-21 below the record on main (Ryan Xu, improved by Francisco Couzo, PingYou Ltd, Mishapolk)	this report 10.789303783743
130	11.902430645983	recorded: a refinement of Francisco Couzo's packing as #843 gives it; credited to this report's finder, after Francisco Couzo; 2.08e-12 below #843 (Francisco Couzo)	this report 11.902430645983
146	12.583782190152	recorded: a refinement of Evan Daniel's packing; credited to this report's finder, after Evan Daniel; 1.00e-21 below the record on main (Evan Daniel)	this report 12.583782190152
156	12.979165853835	recorded: a refinement of Daniil Ostashev's packing; credited to this report's finder, after Daniil Ostashev; 1.00e-41 below the record on main (Daniil Ostashev, improved by Francisco Couzo, PingYou Ltd, Mishapolk)	this report 12.979165853835
182	13.970916436215	not recorded: 1.40e-13 above the record on main (Evan Daniel)	the record on main (Evan Daniel) 13.970916436215
204	14.808642830514	not recorded: 1.02e-03 above #845 (Evan Daniel)	#845 (Evan Daniel) 14.807627471882
211	14.993549626300	not recorded: equal to Mykhailo Polkovskyi's publication `Mishapolk/square-packing-records@e386aab`, reported first	Mykhailo Polkovskyi's publication `Mishapolk/square-packing-records@e386aab` 14.993549626300
229	15.650161513877	recorded: a refinement of Evan Daniel's packing; credited to this report's finder, after Evan Daniel; 1.00e-21 below the record on main (Evan Daniel)	this report 15.650161513877
241	15.987117095151	not recorded: equal to Mykhailo Polkovskyi's publication `Mishapolk/square-packing-records@e386aab`, reported first	Mykhailo Polkovskyi's publication `Mishapolk/square-packing-records@e386aab` 15.987117095151
260	16.645753250520	not recorded: 1.18e-02 above #845 (Evan Daniel)	#845 (Evan Daniel) 16.633982502122
268	16.874361715871	not recorded: 1.48e-12 above the record on main (Vladislav Lavrentev, improved by Evan Daniel)	the record on main (Vladislav Lavrentev, improved by Evan Daniel) 16.874361715870
299	17.803695435316	not recorded: 2.46e-03 above #824 update (Evan Daniel)	#824 update (Evan Daniel) 17.801238549389
304	17.926898900367	not recorded: 1.00e-11 above the record on main (Kirill Tymchishin, improved by Evan Daniel)	the record on main (Kirill Tymchishin, improved by Evan Daniel) 17.926898900357
308	17.997149121271	recorded: a refinement of Evan Daniel's packing; credited to this report's finder, after Evan Daniel; 1.00e-21 below the record on main (Evan Daniel)	this report 17.997149121271

The registrations are in the records pull request #852, and a follow-up with the result ids and rungs will come once it is on main.

Generated by Claude Code

@Mishapolk

@Mishapolk, thank you for #846. All fourteen of its certificates are imported and reviewed, and so are the nine of your commits of 23 October that the ledger records. The report-order verdict is in the comment above; this is where the record on main stands.

The fifteen recorded certificates are valid packings. Each proves the bound it states at its header side. This repository's two maintained exact routes accept every one. They share components with your generator: sqpack.verify and devtools.check_rational_witness_independent, through devtools.upper_bound_reports. The stage 4 review (review-2026-10-31-polkovskyi-846-and-23-oct.md) decided each again with an independent implementation: rv_check.py and rv_controls.py, a clean-room checker that uses two methods, with controls at 10⁻⁶⁰ past contact. Your own verifier was not re-run.
130 is adopted. Your certificate is Francisco Couzo's s(130) ≤ 11.902430646: registration request #843 packing re-solved, 2.08e-12 below his, and its print differs (…983 against …985). T-259 is confirmed at V3/C3. The case at 130 now carries it, with the packing credited to Couzo and the re-solve to you.
The other fourteen wait on the owner's question; there is no verdict on them yet. They are 105, 146, 156, 229 and 308 here, and 154, 155, 183, 211, 227, 236, 237, 241 and 271 from 23 October. At each, the certificate is the house certificate's packing with its padding shaved. It lies below the house certificate by 10⁻⁴¹ to 1.7×10⁻¹⁹ and rounds to the same 12-place print. At 105 and 156 the house certificate is your own.
- The project's ruling of 23 October treats such re-certifications as restatements beyond n = 324. Whether that ruling also reaches counts inside 324 is the owner's open question, and think-ikku owns it. The review recommends reading them as restatements; that is a reading, not a decision.
- Until the owner answers, the record holds these rows: T-260 (this issue's five) and T-253 (the nine of 23 October) are both reviewed, V0/C1, and no house moves at those counts. If the ruling reaches them, the entries are withdrawn. If it does not, the replay and review evidence are entered, both rungs rise to V3/C3, and each count is adopted under the house rule.
Your table. At 156, 229 and 308, the Category B table states larger margins than the record's standing sides allow. Against those sides the margins are 10⁻⁴¹, 10⁻²¹ and 10⁻²¹, and at 156 the standing side is your own certificate. No record depends on the table, since every comparison reads the certificate headers.
Not recorded: 182, 204, 211, 241, 260, 268, 299 and 304, for the reasons the verdict above gives.

Evidence entries. E-mishapolk-846-certificate-report, this issue's certificates as reported, is reviewed. At 130, E-mishapolk-846-exact-feasibility, the maintained routes' replay, and E-mishapolk-846-review-exact-feasibility, the review's checker, are confirmed.

On main and the site.

The review left four questions. An answer to any of them is welcome, but none holds anything open:

At 154, 183 and 227, which certificate did your solver start from, and which squares did it free? Tens of squares move, by up to 0.36, while the side stays the house's contact side.
At 105, 146, 229 and 308 (by 10⁻²¹) and at 156 (by 10⁻⁴¹), is the certificate anything other than the record's certificate with its side lowered and every square unchanged?
At 130, is isolated_lab/tmp_couzo_noalm.txt Couzo's s(130) ≤ 11.902430646: registration request #843 packing? Was the 2.08e-12 gained by re-solving its contacts at tighter padding before the 2e-14 dilation?
What did the "Antigravity Autonomous Research Lab" contribute: an AI system, people, or both? The record states AI assistance wherever a source does.

This issue stays open for the owner's answer on the fourteen re-certifications. A reply will follow when the record follows that answer.

Generated by Claude Code

requests(#860, review A): T-259 names no finished owner; the confirme…

Merge pull request #860 from jlevy/claude/bold-ritchie-xo28us-post852

records(#943, #944, #945, #947): register T-285 to T-288 at V3/C3 on …

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New packings: 14 verified upper bounds for square packing (Category A records and Category B refinements, N in [105, 308]): registration request #846

1. Summary of Claims

2. Table of Verified Upper Bounds

3. Highlighted Literature World Records (Category A)

4. Verification and Reproducibility

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New packings: 14 verified upper bounds for square packing (Category A records and Category B refinements, N in [105, 308]): registration request #846

Description

1. Summary of Claims

2. Table of Verified Upper Bounds

3. Highlighted Literature World Records (Category A)

4. Verification and Reproducibility

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jlevy commented on Oct 31, 2026

jlevy commented on Oct 31, 2026

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