Global uniqueness in smooth isotropic elasticity 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

Global uniqueness in smooth isotropic elasticity

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:	fluids, heat, waves	Levels:	1
Category:	Partial differential equations	Lean version:	YES! ✔
Rate this game! 4.8 out of 5 (8,818 votes)

>>> How to Play <<<

Global uniqueness in smooth isotropic elasticity. Proves that full static boundary displacement-to-traction data determine both smooth real Lamé moduli on every bounded connected smooth domain in ℝ³, provided μ > 0 and $3\lambda+2\mu\gt 0$ on the closure. Neither analyticity, proximity to constant coefficients nor prior knowledge near the boundary is required.

>>> Level Select <<<

LEVEL 1 Global Uniqueness for the Smooth Isotropic Elasticity Inverse Problem

released 2026-09-24 | 1 theorem · 8 lemmas · 15 proofs · 9,963 words | PLAY LEVEL 1 » (pdf)

We prove that the full static displacement-to-traction map uniquely determines both real smooth Lamé moduli on every bounded connected smooth domain in ℝ³, provided μ > 0 and $3\lambda+2\mu\gt 0$ on the closure. This resolves the smooth three-dimensional isotropic elastic Calderón uniqueness problem under these positivity assumptions.

More Partial differential equations Games!
Kinetic limits and fluctuations over the Boltzmann lifespan	Joint metric and connection recovery from one boundary patch	The planar Mumford–Shah regularity conjecture	The critical dimension for the one-phase Bernoulli problem
The three-dimensional Ball–Evans approximation problem	The hot spots conjecture for simply connected planar domains PLAYABLE!	The subcritical Lane–Emden and Hénon–Lane–Emden conjectures	Stable blowup for a defocusing Schrödinger equation

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