COS45 — A Geometric Boundary for Admissible Inference under Observable Indistinguishability

COS45 is a geometric decision framework that determines when inference is admissible under observable indistinguishability. Observable data are embedded into a Hankel matrix HWHW. The distance to the rank-nn manifold is defined as δn:=σn+1(HW).δn:=σn+1(HW). An operational indistinguishability scale τWτW is extracted from the tail singular spectrum as an observable proxy. The decision variable is ηn:=δn−τW.ηn:=δn−τW. The rule is binary: ηn>0⇒ADMISSIBLE,ηn≤0⇒NON-CONCLUSIVE.ηn>0⇒ADMISSIBLE,ηn≤0⇒NON-CONCLUSIVE. COS45 does not identify structure, estimate parameters, or select models. It evaluates whether observable separation exceeds an indistinguishability threshold sufficient to justify inference. If no measurement is available, HWHW is undefined and COS45 does not apply. The framework is organized into strictly separated layers (EXACT → STRUCTURAL → OBSERVABLE → DECISION), with no direct transfer of information across non-adjacent layers. All results are local to the window WWand embedding conditions. The case n=1n=1 admits a controlled local bridge; extensions for n≥2n≥2 remain partial, and n≥3n≥3 is open. COS45 defines a necessary condition for admissible inference. NON-CONCLUSIVE is a valid scientific outcome This version is a corrected update of the previous release. The changes address presentation errors only, including layout inconsistencies and figure alignment issues. No definitions, equations, or decision rules have been modified.The mathematical content and the logical structure of COS45 remain unchanged. This update ensures consistency between text, figures, and notation.