Huynh Hai Dang Vo

PRIMES AT THE LEGENDRE SCALE: UNIVERSAL SIDON RIGIDITY, THE 2D MAIER MATRIX, AND ALGEBRAIC PIVOTS

We present a rigorous structural theory of primes at the critical short-interval exponent $\theta=1/2$ (the Legendre scale), strictly delineating unconditional geometric rigidity from conditional topological transfers. First, we embed the classical $X^{1/2}$ intervals into a two-...

PRIMES AT THE LEGENDRE SCALE: UNIVERSAL SIDON RIGIDITY, THE 2D MAIER MATRIX, AND ALGEBRAIC PIVOTS

We present a rigorous structural theory of primes at the critical short-interval exponent $\theta=1/2$ (the Legendre scale), strictly delineating unconditional geometric rigidity from conditional topological transfers. First, we embed the classical $X^{1/2}$ intervals into a two-...

Conditional Resolution of the Oppermann, Andrica, and Legrende Conjectures via the Non-Linear Maier Matrix Topology

We introduce a two-parameter array of polygonal gnomon numbers $A_{m,j}, W_{m,j}$ ($m,j \ge 1$) and study the family of generalized explicit intervals $I^{(\lambda)}_{m,j}$ it generates under a Continuous Amplitude Scaling Factor $\lambda \in (0, 1]$. In Part I we show that this...