Definition: Truncated Spectral Vector Representation

This entry is Day 6 xpost lecture series and sets foundational concepts crucial to Spectral Number Theory (SNT). In particular we introduce: The definition expressing sparse spectral vectors in "shorthand" form. 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