The coefficient-bound conjecture for the critical-slope regulator form

Let $b_n$ be the coefficient of the $n$-th basis vector in the Kolberg-basis expansion of $h=\iota^*(\Theta_1^{-1}\mathcal{F}^{[\mathfrak{p}_1]})$. Coefficient-bound conjecture. One has

$$v_3(b_n)\geqslant 10$$

for every $n>55$. This bound is introduced as an assumption needed because precise bounds on the coefficients are unavailable; the supplied source gives no resolution evidence.