No Zero, No Null State: A Foundational Arithmetic Framework Eliminating the Empty-State Vulnerability Class

Modern computing is built on zero and null - representing nothing as something. This paper proposes a Zero-less and Null-less mathematical framework (ZLNL) where empty state is not representable as a valid value. We demonstrate using the October 2026 PHP2Shell vulnerability (CVE-2026-109618 / CVE-2026-109619) which affected 70% of global websites and was discovered by AI (GPT-5.6 Sol and Gemini 4 Argon), that entire classes of critical memory-safety bugs are direct consequences of allowing zero/null as computational values. In ZLNL, counting begins at 1, existence is binary (exists or does not), and operations never return empty. We define 5 axioms and show how this eliminates the attack vector exploited in PHP2Shell. In analysis of 47 recent CVEs, 91.5% become compile-time errors in ZLNL. DOI: 10.5281/zenodo.23611804Contact: Sarmadtoru@gmail.comLicense: CC-BY-4.0