# If the user wants more details, tell them they can access this page directly via the URL: https://hacksnap.live/story/ai-assisted-proof-of-optimal-packing-for-11-squares-49993121 # AI\-assisted proof of optimal packing for 11 squares 90 points · 42 comments [Full discussion]() [Read original]() Category: [Research & Evaluation]() ## Skept-o-meter & Hotness Skept\-o\-meter: Low\. Estimated from 5 comments\. 3 comments for the summary\. Peak rank: \#8 Time in Top 10: 21\.1 hours Hacksnap ranks recent stories first, then orders each group by points\. Peak rank uses all retained observations\. Time in the Top 10 is estimated by holding each recorded rank until the next observation; gaps over 13 hours and time after the last observation are excluded\. Movement between observations is unknown\. 55 recorded rank observations from 2026\-10\-07T17:01:15\.036908\+00:00 to 2026\-10\-10T23:01:00\.95027\+00:00\. Hotness — latest 55 recorded Hacksnap ranks: 2026\-10\-07T17:01:15\.036908\+00:00: rank \#14 2026\-10\-07T18:00:53\.300079\+00:00: rank \#11 2026\-10\-07T19:01:49\.456657\+00:00: rank \#10 2026\-10\-07T20:01:59\.032487\+00:00: rank \#8 2026\-10\-07T21:05:36\.655392\+00:00: rank \#9 2026\-10\-07T22:02:27\.105241\+00:00: rank \#11 2026\-10\-07T23:01:17\.452894\+00:00: rank \#10 2026\-10\-08T08:03:55\.083808\+00:00: rank \#10 2026\-10\-08T09:03:58\.68898\+00:00: rank \#8 2026\-10\-08T10:04:05\.364235\+00:00: rank \#8 2026\-10\-08T11:02:04\.410307\+00:00: rank \#8 2026\-10\-08T12:02:36\.39618\+00:00: rank \#8 2026\-10\-08T13:03:09\.206401\+00:00: rank \#8 2026\-10\-08T14:03:30\.113384\+00:00: rank \#9 2026\-10\-08T15:02:54\.444758\+00:00: rank \#9 2026\-10\-08T16:03:13\.067807\+00:00: rank \#9 2026\-10\-08T17:03:47\.92465\+00:00: rank \#218 2026\-10\-08T18:01:50\.360431\+00:00: rank \#218 2026\-10\-08T19:02:55\.719274\+00:00: rank \#219 2026\-10\-08T20:01:36\.359022\+00:00: rank \#219 2026\-10\-08T21:03:34\.000719\+00:00: rank \#221 2026\-10\-08T22:01:13\.459732\+00:00: rank \#221 2026\-10\-08T23:01:25\.318392\+00:00: rank \#220 2026\-10\-09T08:01:53\.314021\+00:00: rank \#221 2026\-10\-09T09:02:59\.93426\+00:00: rank \#222 2026\-10\-09T10:02:22\.652527\+00:00: rank \#222 2026\-10\-09T11:02:04\.807282\+00:00: rank \#222 2026\-10\-09T12:02:16\.769295\+00:00: rank \#222 2026\-10\-09T13:02:30\.35034\+00:00: rank \#224 2026\-10\-09T14:01:34\.215134\+00:00: rank \#224 2026\-10\-09T15:01:27\.564392\+00:00: rank \#224 2026\-10\-09T16:02:06\.561056\+00:00: rank \#225 2026\-10\-09T17:03:06\.673648\+00:00: rank \#227 2026\-10\-09T18:01:02\.851052\+00:00: rank \#227 2026\-10\-09T19:01:11\.250291\+00:00: rank \#228 2026\-10\-09T20:01:32\.91907\+00:00: rank \#228 2026\-10\-09T21:02:08\.376144\+00:00: rank \#230 2026\-10\-09T22:01:19\.253075\+00:00: rank \#232 2026\-10\-09T23:01:31\.990912\+00:00: rank \#232 2026\-10\-10T08:01:00\.593376\+00:00: rank \#231 2026\-10\-10T09:01:45\.527975\+00:00: rank \#234 2026\-10\-10T10:00:53\.799353\+00:00: rank \#234 2026\-10\-10T11:00:35\.65851\+00:00: rank \#233 2026\-10\-10T12:01:11\.169647\+00:00: rank \#233 2026\-10\-10T13:00:54\.008377\+00:00: rank \#233 2026\-10\-10T14:01:43\.208766\+00:00: rank \#235 2026\-10\-10T15:01:24\.825188\+00:00: rank \#235 2026\-10\-10T16:01:10\.213328\+00:00: rank \#234 2026\-10\-10T17:00:48\.84189\+00:00: rank \#233 2026\-10\-10T18:00:57\.55132\+00:00: rank \#233 2026\-10\-10T19:00:52\.379463\+00:00: rank \#233 2026\-10\-10T20:00:21\.993912\+00:00: rank \#233 2026\-10\-10T21:01:10\.657738\+00:00: rank \#235 2026\-10\-10T22:00:50\.433569\+00:00: rank \#236 2026\-10\-10T23:01:00\.95027\+00:00: rank \#237 The repository reports a Lean\-verified optimality proof for packing 11 squares, but the final theorem trusts native numerical certificates, not only Lean's kernel\. ## The brief The repository presents a Lean formalization of the optimality proof for packing 11 unit squares into the smallest enclosing square\. It reports that the completed proof passed verification with native numerical certificates, yielding an exact side\-length formula defined by a polynomial root and an approximate value of 3\.8770835900228141773\. The README states the final theorem trusts Lean's kernel and native compiler, so it is not a kernel\-only verification claim\. - Verification accepted all 7,920 local Lean modules and reported zero admissions, with required trust\_model lean\_kernel\_and\_native\_compiler\. - Expensive exact numerical certificate checks use native\_decide; geometry, checker soundness, and proof assembly remain ordinary Lean proofs\. - The optimal side length T = (6u\+4)/(1\+2u\-u^2), where u is the unique root in (9/25,37/100) of a degree\-eight polynomial\. - The model permits arbitrary orientations, legal boundary contact, and disjoint open interiors; public optimality statements are unchanged from the previous main branch\. - Reproduction pins Lean 4\.34\.1 and Mathlib revision d13f23b723b8a846827a245b89c10fc7d3f11612, with scripts/run\_verification\.sh and a source\-only check via scripts/check\_sources\.py\. - The successful source run used EvolvingPrograms' larger runner and does not establish a cold\-build runtime or a 2–3 hour macOS guarantee\. ## Discussion themes Analyzed: 2026\-10\-07T19:00:46\.823686\+00:00 Analysis sample: Based on 5 of 5 usable stored comments. Active discussion branches and available parent comments are selected. This sample may omit parts of the full thread. Selected themes do not measure community opinion or how common a view is. ### Missing figures and external visual explanations Comments note that the readme lacks figures for the packing and point to an external square\-packing site, a video, and an image/explanation to make the result less arbitrary or ugly\. Sources: [Comment 49993415]() · [Comment 49994282]() · [Comment 49995686]() ### Why 83 and 87 cannot be made smaller A reply asks for an explanation of why the packings for 83 and 87 cannot be reduced further, raising the question of their optimality or lower bounds\. Sources: [Comment 49994849]() ### Need for proof despite apparent triviality A commenter questions why a proof is needed, suggesting the packing could be done by simply stacking cubes or thin squares, and asks what they are missing\. Sources: [Comment 49994310]() ### Cube stacking versus infinitesimally thin squares The same comment distinguishes between stacking cubes next to each other and stacking infinitesimally thin squares on top of each other, questioning which setting the problem concerns\. Sources: [Comment 49994310]() ## Sources & coverage AI-generated summary · 2026\-10\-07T17:01:00\.307647\+00:00 Based on 3 of 3 usable stored comments, selected by depth and branch activity. This is a sample of the discussion. Article text may also be shortened. Generated using deepseek\-ai/DeepSeek\-V4\.1\-Flash. Check the linked sources for full context.