This paper, submitted to arXiv on August 15, 2026, investigates the G-equation in cellular flows, specifically disproving the expectation of an effective burning velocity. The research demonstrates that for certain conditions in two-dimensional cellular flows, periodic corrections develop oscillations, and solutions decrease at a significant rate. The findings suggest that even with physical scaling, a gap persists between points, preventing locally uniformly convergent subsequences. The proof utilizes a Hamiltonian sandwich approach, and the paper includes Lean 4 appendices formalizing parts of the proof. The authors also discuss implications for statistics and machine learning, noting that time-consistent local uncertainty does not necessarily imply forgetting initial states in sequential decision-making. AI
IMPACT Discusses implications for statistics and machine learning, particularly in robust sequential decision making.
RANK_REASON Academic paper published on arXiv detailing mathematical research. [lever_c_demoted from research: ic=1 ai=0.4]
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