Square Packing Fan

math @yale

[natcha @thatennine]

built SQUISH to tackle square-packing problems; 23 are now verified as upper bounds by The Squares Project (ids T-113 to T-116)

posting before it immediately becomes out of date :)

ty to @ojoshe and crew for verification and running the site - https://t.co/YFS04uWFUd

[Square Packing Fan @_ManaA2006]

@CyXie0604 @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis in this case you can just look at it, i'm not sure if there's a better way tbh

[Square Packing Fan @_ManaA2006]

The optimality of the packing for 11 squares has been formalized in lean thanks to Astra and Claude! Huge thanks to @ojoshe, @kleddamag, @wand_125, @guzhou0806, and @ctjlewis for aiding in the process.

Image credit: https://t.co/2oUaPKe2Hz
1/n

[Square Packing Fan @_ManaA2006]

@ctjlewis @CrashdAstronaut @ojoshe @kleddamag @wand_125 @guzhou0806 lowkey a win for humanity that this packing ended up being optimal

[Square Packing Fan @_ManaA2006]

@CandideIII @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis Small errors as in different lean files used slightly different names for certain lemmas, this stemmed from having multiple ppl working in different branches

[Square Packing Fan @_ManaA2006]

@SuperSodium holy ball knowledge

[Square Packing Fan @_ManaA2006]

@jfonsecarivera just wait until we prove it for 17

[Square Packing Fan @_ManaA2006]

@ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis @evanbd it's been a crazy ride

[Evan Daniel @evanbd]

@GillibertLuc @ManassehA06 @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis 83 squares is my new favorite ugly packing. Not simply because the packing itself is ugly (it's an extension of 17, with minor adjustments), but because of the side length:

It's a root of an irreducible polynomial of degree 672, with coefficients up to 724 digits.

[Square Packing Fan @_ManaA2006]

@tmosselboss @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis oh no thats just a rendering artifact, the two intended colors are green and pink

[Square Packing Fan @_ManaA2006]

@tmosselboss @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis Squares of the same color are tilted at the same angle

[Square Packing Fan @_ManaA2006]

@AlexanderRKlotz @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis It’s proven to be global

[Square Packing Fan @_ManaA2006]

@GillibertLuc @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis Also no hope for an even uglier packing

[Square Packing Fan @_ManaA2006]

@mmaaz_98 @evanbd @ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis The packing was proven optimal and along the way we also formalized the induced side length(which was surprisingly hard to find online!)

[Square Packing Fan @_ManaA2006]

@ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis Now, what remains is the most important part of the process: human digestion. We’ve started working on a human readable and human written paper providing high quality exposition on this crazy proof. 4/n

[Square Packing Fan @_ManaA2006]

@ojoshe @kleddamag @wand_125 @guzhou0806 @ctjlewis Additionally, with each run, small errors in the code would pop up which we’d need to remedy. In the end our repo is approximately 400k lines of lean and took roughly 20 hours to compile. 3/n

[anish lakkapragada @_anishlk]

We extend @cognition’s SWE-2 reward function to steer the Pareto frontier, not just improve it.

SWE-2 uses S − λₑC, where λₑ is cleverly the frontier’s derivative at that effort.

We show that adapting λₑ can target a desired score/cost improvement balance. See below!

[Square Packing Fan @_ManaA2006]

Should cleaning up slop results be a community effort or should it be a responsibility of the author? I’m struggling to decide