Security Framework: The Perez Hourglass, Theorem 7, and the Future of Post-Quantum Information Architecture

Security Framework: The Perez Hourglass, Theorem 7, and the Future of
Post-Quantum Information Architecture
1. The Mathematical Genesis: The Perez Hourglass and Theorem 7
The Perez Hourglass represents a landmark discovery in fractal geometry and number theory,
emerging from a recursive parity filtering of the centered Pascal triangle. This bidirectional
structure acts as a bridge between two mathematical realms: the Northern Hemisphere, which
reproduces the Sierpiński triangle (Matter), and the Southern Hemisphere, a "Digital Antimatter"
counterpart. This southern hemisphere is constructed through recursive signed differences or
absolute-value folding, creating a self-similar lattice governed by the golden ratio ( $\phi$ ). The
southern interior counts resolve a 256-year-old conjecture by geometrically generating the
Lichtenberg Sequence (OEIS A000975) .