The Quantized Harmonic Sieve: Overcoming the Decimal Metric — An Addendum to The Theory of Harmonic Quantization

This addendum to The Theory of Harmonic Quantization (THQ) addresses the "epistemological trap" of the decimal metric—an anthropocentric reliance on base-10 arithmetic that generates artificial infinities and the 122-order-of-magnitude discrepancy known as the Vacuum Catastrophe. We propose the Quantized Harmonic Sieve, a base-agnostic geometric operator that replaces linear, continuous integration with a discrete summation of resonant modes. By defining the vacuum as a High-Q Resonator governed by pure geometric proportion (π and Φ), we demonstrate how geometric impedance suppresses non-resonant "noise" and stabilizes the spacetime metric. This framework provides a unified mechanical explanation for structural emergence across scales, bridging cosmological constant determination with recent empirical observations of biological cosmogenesis and affective resonance.