The Yildiz Protocol: A Cosmic Post-Quantum Cryptographic Framework and Multi-Base Geometric Communication Language

Current cryptographic infrastructures and digital architectures based on the binary numerical system face critical vulnerabilities in the quantum computing era due to the emergence of Shor's and Grover's algorithms. In this paper, a novel mathematical framework is introduced by expanding the classical Pascal's Triangle into multi-base exponential structures, thereby establishing the Exponential-Pascal Reference Invariance operator and the resulting multi-base exponential manifold. The proposed framework delivers a non-binary cryptographic protocol and a next-generation digital infrastructure model that aligns with Kerckhoffs's principle, purposefully designed to surpass the algebraic analysis capabilities of quantum computers. Furthermore, due to its inherent geometric permanence, this protocol offers a robust, noise-tolerant mathematical vocabulary optimized for interstellar and cosmic data transmission.