Hankel Spectral Gap as a Local Indicator of Rank-2 Structure in Laplace Signals

We introduce the Hankel spectral channel as an observable indicator of structural rank in Laplace mixture signals. The exact result σ₃(H)=0 ⇔ F ∈ V₂ (bi-exponential family) is classical. We establish a local equivalence σ₃(H_W) ≍ dist(F,V₂) under explicit non-degeneracy conditions (transversality, spectral gap, positive weights). We define a unified detectability scale:SNR_spec = σ₃(H_W) / (σ√h) Structural deviations are observable only above a calibrated noise floor. Below this threshold, NON-CONCLUSIVE is the correct outcome. No global coercivity is claimed. No global equivalence between σ₃, Δ, and dist(F,V₂) is claimed. A structural null space (span{F, tF}) is identified as invisible at first order. This document provides an observable structural indicator, not a global proof. This framework does not impose a result. It measures when a result is justified.