Spectral Representation of Finite Decimals

This entry is Day 5 xpost lecture series and sets foundational concepts crucial to Spectral Number Theory (SNT). In particular we show how decimal valued numbers are converted into fractions by spectral decompositon This is the continuation of the groundwork for the broader SNT framework, which treats integers as waveforms, primes as basis modes, and arithmetic as resonance. This document is intended as both a mathematical reference and an accessible companion to the daily Xpost lectures, https://x.com/LoiseauZeta