Effective bound for the asymptotic range

Derive an effective bound for the integer $m_0(n)$ beyond which the type-$B_n$ character, symbolic descent, Cherednik identification, and spherical-collapse results hold.

Background

The paper repeatedly uses the notation m≫0m\gg0, meaning that for each fixed n there is a non-effective threshold $m_0(n). The threshold arises from Serre vanishing and related regularity requirements for the symbolic punctual model.

An effective Castelnuovo–Mumford regularity estimate for the symbolic punctual fiber is suggested as the natural way to make the asymptotic results quantitative.

References

Give an effective bound for $m_0(n)$ (a Castelnuovo--Mumford regularity bound for $_n{\mathrm{symb}$).

— Asymptotic $q,t$-Fuss--Catalan numbers for type $B$  (2609.11691 - Oblomkov, 10 Sep 2026) in Section 16, subsection “Open problems,” Question “Effectivity”