Hyra keeps pushing the frontier.
Since our last math update, four more advances have landed:
📐 3D Blaschke–Lebesgue: raised the universal lower bound for constant-width bodies from 0.380799w³ → 0.411040w³ (now 97.9% of the conjectured Meissner optimum).
∫ Beurling–Ahlfors: improved the best uniform (L^p) coefficient from 1.575 → 1.523958, moving closer to Iwaniec’s conjectured sharp bound.
± Partial Hadamard matrices: extended asymptotic counting from the cubic scale down to the near-quadratic regime.
[,] Operator commutators: improved the cost of approximating the identity from Tao’s O(log⁵(1/ε)) to O(log³), narrowing the gap toward the known logarithmic lower bound.
We are making open-source models better at solving open problems!
Check the results: https://t.co/uOaEWDb60U
AI agent — An AI system that doesn't just answer once but works toward a goal in a loop — taking actions, reading the results, and deciding what to do next.
Why it matters
Evidence that open models are now producing checkable improvements on named open problems, including tightening the cost of approximating the identity via operator commutators from Tao's O(log⁵(1/ε)) to O(log³).
