Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
Loop Equation and Area Law in Turbulence
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abstract
This is the extended version of the preprint \ct{Loop}, based on the lectures given in Cargese Summer School and Chernogolovka Summer School in 93. The incompressible fluid dynamics is reformulated as dynamics of closed loops $C$ in coordinate space. We derive explicit functional equation for the pdf of the circulation $P_C(\Gamma)$ which allows the scaling solutions in inertial range of spatial scales. The pdf decays as exponential of some power of $ \Gamma^3/A^2 $ where $A$ is the minimal area inside the loop.
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Odd-N Euler ensemble polygons are locally Lyapunov-stable attractors of decaying NS turbulence, with universal defect spectrum λ_m=−sec²(πm/N) and leading angular Laplacian.
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Fine-Tuning Small Reasoning Models for Quantum Field Theory
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
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Euler Ensemble as Decaying Turbulence Attractor: Universality, Stability and Parity Classes
Odd-N Euler ensemble polygons are locally Lyapunov-stable attractors of decaying NS turbulence, with universal defect spectrum λ_m=−sec²(πm/N) and leading angular Laplacian.