What question did this study set out to answer?

The aim is to explore the Hankel spectral channel as an indicator of structural rank in Laplace mixture signals.

April 4, 2026Open Access

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

Key Points

The aim is to explore the Hankel spectral channel as an indicator of structural rank in Laplace mixture signals.
Introduced the concept of Hankel spectral channel to measure structural rank.
Established local equivalence under specific conditions like transversality and spectral gap.
Defined a detectability scale relating the spectral gap to noise levels.
Identified conditions under which structural deviations in signals become observable.
Proved that non-conclusive results occur below a determined noise threshold.
Pointed out an invisible structural null space at the first order.

Abstract

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.

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

Key Points

Abstract

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