D2 — Hankel Spectral Gap as an Observable Indicator of Rank Structure (Observable Layer) (v1.03)

This document defines observable quantities derived from data within the COS45 framework. It belongs to the OBSERVABLE layer and introduces measurable indicators of structural rank using Hankel matrices. No decision rule is defined. No inference claim is made. The main quantity of interest is the spectral gap (e. g. , σ₃ or σ₍+₁), which serves as an observable proxy for deviations from a lower-rank structure. These observables are subject to noise and sampling constraints. They do not establish admissibility and do not imply the existence of underlying components. Their role is to construct δ (observable structure) used later in the DECISION layer, where admissibility is evaluated through η = δ − τ. This document separates clearly: exact spectral structure (handled in D1), observable proxies (this document), decision rules (handled in the COS45 DECISION layer). Version (v1. 1) clarifies the separation between observable quantities and inference. No change to the underlying definitions.