Gao Lezhe

A finite-color partition relation for $\omega_1^2$ under $\mathrm{MA}_{\aleph_1}$

We prove that, assuming $\mathrm{MA}_{\aleph_1}$, for every finite $k\ge 1$,\[\omega_1^2 \to (\omega_1\omega, \underbrace{3,\ldots,3}_{k})^2_{k+1}.\]This gives a conditional affirmative answer to Erd\H{o}s Problem \#1171.The main ingredient is a general color-reduction lemma: if...

Precision, Round-off, and the Illusion of Local Predictability in Chaotic Hamiltonian Systems: A Million-Window Benchmark

I perform a large-scale benchmark of whether local geometric features can predict the oscillation-amplitude variation of the energy error in conservative chaotic systems. Over 1.25 million sliding windows from 22,380 double-pendulum trajectories are computed at three precision le...