Bounded-distortion L_1 embeddings of planar and bounded-treewidth graphs at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

A
D
V
E
R
T

I
S
E
M
E
N
T

Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

thinking... about 3 hours remaining

If this game doesn't work on your computer, go here for help. (Lean version available!)

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	shapes, measuring stuff	Levels:	2
Category:	Convex and metric geometry	Lean version:	YES! ✔
Rate this game! 4.2 out of 5 (7,736 votes)

>>> How to Play <<<

Bounded-distortion L₁ embeddings of planar and bounded-treewidth graphs. Resolves the planar and bounded-treewidth cases of the Gupta–Newman–Rabinovich–Sinclair conjecture. Shortest-path metrics of finite connected graphs with arbitrary positive edge lengths embed into real L₁ with universal distortion for planar graphs, and distortion depending only on treewidth for bounded-treewidth graphs. The corresponding multicommodity flow–cut gaps are uniformly bounded.

>>> Level Select <<<

LEVEL 1 Planar Graph Metrics Embed into L1 with Constant Distortion

released 2026-09-23 | 2 theorems · 27 lemmas · 35 proofs · 22,657 words | PLAY LEVEL 1 » (pdf)

We prove that every finite connected planar graph with arbitrary positive real edge lengths embeds into real L₁ with a universal distortion bound. This resolves the planar embedding conjecture positively.

LEVEL 2 L1 Embeddings of Graphs of Bounded Treewidth

released 2026-09-23 | 3 theorems · 16 lemmas · 21 proofs · 13,816 words | PLAY LEVEL 2 » (pdf)

For every fixed treewidth bound, the shortest-path metrics of finite connected graphs with arbitrary positive real edge lengths embed into real L₁ with uniformly bounded distortion. This resolves the bounded-treewidth case of the Gupta–Newman–Rabinovich–Sinclair conjecture positively.

More Convex and metric geometry Games!
Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures	Subpolynomial dimension reduction in $L_p$	Hyperbolicity cones without semidefinite lifts	The Gaussian propeller conjecture
The Euclidean Steinitz–Bergström conjecture	A negative answer to the Lang–Plaut problem	The sharp distortion of edit distance into $\ell_1$	A counterexample to Bang's cylinder-covering bound

COOLMAITH GAMES SPONSORS: (not real)
Big Al's USED GPUs	Epsilon & Delta LLP attorneys at limit	QED Bail Bonds	Hilbert's Hotel always a vacancy!

Cool Links: openai/math Lean Mathlib arXiv the real Coolmath Games

You are visitor number 000719

Thanks for visiting CoolmAIth Games
© 1997-2026 CoolmAIth Games. A parody. Not affiliated with Coolmath.com LLC or OpenAI.
Every proof here was written by an internal OpenAI model and lives at github.com/openai/math.
Best viewed in Netscape Navigator 4.0 at 800x600