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What Does a Klein Bottle Sound Like?
Simulating the sound of a 4D Klein bottle (and a torus and sphere) with FDTD + FEM on a GPU, then validating it against the Laplace–Beltrami spectrum.
Read moreForking paths, more examples
Additional MMLU Pro examples showing token-level forking paths in reasoning traces.
Read moreToken-Level Forking Paths in Reasoning Traces: Some Examples
Some examples of how reasoning traces fork at the token level, and what that tells us about model behavior.
Read moreOEIS A255135: Dimension maximizing the volume of an L^p unit ball
The dimension n at which the volume of an n-dimensional L^p unit ball is maximized, for positive integer values of p.
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