Cos45 A Geometric Detectability Boundary for Noise-Constrained Inference

COS45 defines a geometric separability condition between observable structure and noise. It establishes a detectability boundary that determines when a conclusion is admissible based on data and noise level. The framework is built on a strict separation of layers: Exact (mathematical structure), Observable (data and noise), and Decision (admissibility rule). The core quantities are derived from the third singular value of a Hankel matrix constructed from observed data and a noise-scaled resolution threshold. COS45 does not assert the existence, nature, or cause of any underlying phenomenon. It defines only whether the available data supports a decision or requires abstention. The decision rule is based on the margin: η = δ − τ, with δ = σ₃ (HW) and τ = σ√h. If η > 0, the decision is ADMISSIBLE. If η ≤ 0, the result is NON-CONCLUSIVE. NON-CONCLUSIVE is a valid and informative output, not a failure. This version includes conceptual applications to MRI (T2 mapping) and hydraulic signals, illustrating how the framework operates on observable data without model inversion. All results are structural simulations. Field validation is required.