COS45 — D7 — Bridge Consistency and Calibration Coherence Local Consistency Between Observable and Exact Layers

This document establishes the consistency conditions between the OBSERVABLE and EXACT layers of COS45. The DECISION layer is closed: ηₙ (W) = δₙ (W) − τW requires no reference to the EXACT layer. The EXACT layer provides a local bridge for n=1 only. No global identifiability is claimed. Calibration is defined via admissible transformations: Tₐdm = T: ||HW − T (HW) ||₂ ≤ α · δₙ (W) The indistinguishability threshold τW is defined as a quantile over singular values beyond rank n: τW = Qq (σₖ (HW) ₊>₍) NON-CONCLUSIVE is a geometric state: δₙ (W) ≤ τW. All results are local and protocol-dependent (W, n, q, K, Tₐdm).