Haibo Lu

An $n^2\log_2 n-O(n^2)$ lower bound for Hilbert numbers via two-source renewal

We construct real planar polynomial vector fields establishing H_hyp(n) ≥ n² log₂ n − Cn² for every sufficiently large integer n, where C is an absolute constant and H_hyp(n) denotes the supremum of the number of hyperbolic limit cycles among fields of total degree at most n. The...

Finite cyclicity of the quadratic graphic $I_{6b}^1$ in its full five-parameter quadratic unfolding

Version 3.0.0 is a single self-contained 113-page preprint. This revision replaces the former multi-range four-passage argument with a direct estimate on the full positive product leaf and clarifies the first-hit partition, center-ideal division, complementary returns, and zero-r...

Local Maximal-Canard Threshold Shifts under Runge–Kutta Discretization: An Observable-Specific Order Condition

This research compendium contains the complete 106-page extended preprint and its compilable LaTeX source, together with exact symbolic checks, numerical programs, machine-readable data, vector figures, environment specification, manifests, and SHA-256 checksums. The preprint pro...