Computational Constraints on Quantum State Transitions in a Finite-Resource Substrate: A Reinterpretation of the Uncertainty Principle and the Derivation of the Operational Density Zquant

Within the framework of the Computational Resource Finiteness Hypothesis (CRFH), this work presents a computational reinterpretation of the quantum mechanical uncertainty principle as a constraint arising from finite operational resources on a Universal Substrate. Uncertainty is shown to emerge from unavoidable competition between information writing and state-transition buffering, rather than from intrinsic randomness or measurement disturbance. By imposing resource conservation expressed through $L^2$-norm preservation and minimizing operational dissipation, we derive an effective operational density that converges to a stable rated point,\[Z_{\mathrm{quant}} = \frac{1}{\sqrt{2}} \approx 0.707 .\]This value is interpreted not as an exact instantaneous bound, but as an engineering-rated operating point ensuring long-term stability under finite computational capacity. The result suggests that probabilistic structures in quantum mechanics may reflect an underlying optimization principle governing resource allocation on the Universal Substrate. This formulation provides a scale-consistent bridge between microscopic uncertainty relations and macroscopic operational density limits observed in larger physical systems.