COS 45 A Detectability and Abstention Framework for Multi-Exponential Signals

We present COS45, a falsifiable detection framework combining spectral dynamics and Hankel structure to assess rank-2 behavior in Laplace signals. Detection is governed by a single calibrated quantity:SNR_spec = σ₃(H_W) / (σ√h) Three regimes are defined:<1: UNDETECTABLE (NON-CONCLUSIVE),1–3: BORDERLINE,≥3: DETECTABLE. The framework integrates two complementary channels:(i) spectral deviation Δ(t),(ii) structural deviation σ₃(H). A five-verdict system is introduced, where NON-CONCLUSIVE is a first-class outcome reflecting intrinsic detectability limits. No global coercivity is claimed. No global equivalence between σ₃, Δ, and dist(F,V₂) is claimed. No pole reconstruction from (r, v) is claimed. COS45 does not perform inversion. It measures when inversion is justified. This framework does not impose a result. It measures when a result is justified.