805 research outputs found
LLMSTEP: LLM proofstep suggestions in Lean
We present LLMSTEP, a tool for integrating a language model into the Lean
proof assistant. LLMSTEP is a Lean 4 tactic that sends a user's proof state to
a server hosting a language model. The language model generates suggestions,
which are checked in Lean and displayed to a user in their development
environment. We provide a baseline language model, along with code for
fine-tuning and evaluation to support further development. We provide server
implementations that run on CPU, a CUDA GPU, or a Google Colab notebook, as a
step towards fast, effective language model suggestions for any user
Frame-dragging and the kinematics of Galactic-Center stars
We calculate the effects of frame dragging on the Galactic-Center stars.
Assuming the stars are only slightly relativistic, we derive an approximation
to the Kerr metric, which turns out to be a weak field Schwarzschild metric
plus a frame dragging term. By numerically integrating the resulting geodesic
equations, we compute the effect on keplerian elements and the kinematics. We
find that the kinematic effect at pericenter passage is proportional to
(a(1-e^2))^{-2}. For known Galactic-center stars it is of order 10 m/s. If
observed this would provide a measurement of the spin of the black hole.Comment: To appear in Ap
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