Nagi

Resonant Gap Certificates and Rooted Dyadic Ancestry in Finite Collatz Record Ladders

We study first passages between consecutive dyadic record thresholds for the shortcut Collatz map, using shifted coordinates in which the two branches are \(\A(x)=3x/2\) on even states and \(\B(x)=(x+1)/2\) on odd states. A record endpoint carries a terminal layer of suffixes who...

An Oscillatory Christoffel--Darboux Transfer from Finite-Height RH Verification to Local Toeplitz--Hankel Positivity

Let $\xi(s)=\frac12s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s),\qquad$ $F(x)=\frac{\xi'}{\xi}\!\left(\frac1{1-x}\right)=\sum_{m\ge0}f_mx^m,$ and define the symmetric Toeplitz--Hankel coefficients $g_{ij}=f_{|i-j|}-f_{i+j+1}+\delta_{ij}f_0.$ The adjacent matrices $M_n=\begin{pmatrix}g_{nn...

Directional Jet Packets, Euclidean Resolution Forests, and Sharp Low-Cost Root Returns for Primitive Binary Quadratic Germs

Let $R=\kk[[x,y]]$ over an algebraically closed field of characteristic zero, and let $q=a u^2+2buv+c v^2\in R\otimes_\kk\Sym^2(V^*)$ be a primitive binary quadratic germ with nonzero discriminant $\Delta(q)=b^2-ac$. Iterated point blowups of the coefficient ideal $(a,b,c)$ produ...

Resonant Gap Certificates and Rooted Dyadic Ancestry in Finite Collatz Record Ladders

We study first passages between consecutive dyadic record thresholds for the shortcut Collatz map, using shifted coordinates in which the two branches are \(\A(x)=3x/2\) on even states and \(\B(x)=(x+1)/2\) on odd states. A record endpoint carries a terminal layer of suffixes who...