Jacobsthal Function Bounds

**Title:** Jacobsthal Function Bounds – Analytical Framework and Resolution **Description:** This paper presents a comprehensive resolution to the Jacobsthal function bounding problem. By modeling coprime sequences on modular lattice grids and applying number-theoretic sieve theory, we establish a provable upper bound for the Jacobsthal function in terms of Euler’s totient function. Our method applies compactified logarithmic filtering to yield scalable, efficient predictions. The result advances both theoretical insight and practical implications for prime-based number systems, cryptography, and modular arithmetic. **Tags:** Number Theory, Coprime Sequences, Euler's Totient Function, Jacobsthal Function, Modular Lattice, Prime Gaps, Cryptography