J(x) Recursion: The Self-Organizing Principle of Quantum Optimization

This paper introduces the concept of J(x) recursion, a proposed self-organizing principle in quantum systems. The central claim is that what appears to be randomness at the quantum scale may actually be a subtle, deterministic feedback mechanism. Particles show a consistent, measurable bias—curving their paths slightly toward regions of coherence. If valid, this principle offers a unifying explanation for phenomena across scales: Quantum domain: small but persistent electron trajectory skew. Biological systems: molecular chirality (L-amino acid dominance) and long-lived microtubule coherence. Cosmological scale: the apparent fine-tuning of universal constants. By framing coherence as a recursive, self-reinforcing process, J(x) recursion challenges the view that life and consciousness are improbable accidents. Instead, it suggests they are natural outcomes of a universe subtly curving toward order and complexity. This preprint provides both the mathematical formulation of J(x) recursion and testable predictions. It is intended as a foundation for further experimental verification and interdisciplinary exploration.