The Mézard–Parisi formula for diluted spin glasses 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

The Mézard–Parisi formula for diluted spin glasses

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:	luck, magnets	Levels:	1
Category:	Probability and statistical mechanics	Lean version:	YES! ✔
Rate this game! 4.4 out of 5 (7,505 votes)

>>> How to Play <<<

The Mézard–Parisi formula for diluted spin glasses. Proves the Mézard–Parisi hierarchical cavity formula for Poisson-diluted even-arity Ising models satisfying the Panchenko–Talagrand factorization and positivity assumptions, with only first-moment integrability. The limiting free energy equals the infimum over finite-depth hierarchical trial laws. This includes the Viana–Bray model, symmetric diluted even-spin models, and weighted soft even-K satisfiability.

>>> Level Select <<<

LEVEL 1 The Mézard–Parisi formula for diluted spin glasses

released 2026-09-23 | PDF only | PLAY LEVEL 1 » (pdf)

We prove the Mézard–Parisi hierarchical cavity formula for diluted even-arity Ising models in the Panchenko–Talagrand class. This resolves the variational equality conjecture for that class: the limiting pressure equals the infimum of the trial functional over all finite hierarchy depths and trial laws. Only first moments of the interaction and external field are required.

More Probability and statistical mechanics Games!
Exact Hausdorff measure for SLE	The free uniform spanning forest is a factor of IID	Gaussian fields and SLE interfaces for Lipschitz heights	The joint critical Ashkin–Teller scaling limit
All-temperature pressure for orthogonally invariant Ising spin glasses	Random-SAT thresholds, sharp variance and computability	The factor-of-IID threshold for free Ising states on trees	The three-quarter diameter exponent for honeycomb walks

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