Quantization as an Emergent Property of Recursive Ordering

This work presents a minimal structural framework for interpreting quantum discreteness and coherence as emergent properties of recursive ordering, rather than as primitive features of microscopic degrees of freedom. Motivated by recent experimental results demonstrating enhanced coherence under quasiperiodic (e.g., Fibonacci) driving, the paper explores how stability can arise from structured, non-repeating dynamical constraints imposed on system evolution. We introduce a conservative formalization in which discrete quantum states correspond to states that remain stable under recursive domain cycling (up to global phase), while incompatible modes fail to accumulate coherently and are naturally expelled toward boundaries. This perspective is expressed through three complementary layers: a minimal conceptual statement, an extended dynamical formulation compatible with standard quantum mechanics, and a purely algorithmic pseudocode representation suitable for simulation and toy-model exploration. The framework does not propose new physical primitives, nor does it replace existing quantum formalisms. Instead, it provides an interpretive and organizational lens through which familiar features—such as half-factors, coherence plateaus, boundary effects, and quasiperiodic stabilization—may be understood as signatures of relational and recursive structure. The presentation intentionally emphasizes clarity, restraint, and reproducibility, leaving room for independent rediscovery, reinterpretation, and future extension by others. This work builds on a year-long exploration of structured recursive geometry, toy models, and quasiperiodic dynamics, and is intended as a conceptual bridge between abstract stability principles and concrete quantum behavior.