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 (HW) ≍ dist (F, V₂) under explicit non-degeneracy conditions (transversality, spectral gap, positive weights). We define a unified detectability scale: SNRₛpec = σ₃ (HW) / (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 (spanF, 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.
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louis morissette
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louis morissette (Thu,) studied this question.
www.synapsesocial.com/papers/69d0af52659487ece0fa549e — DOI: https://doi.org/10.5281/zenodo.19389585