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) − τ_W 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:T_adm = { T : ||H_W − T(H_W)||₂ ≤ α · δₙ(W) } The indistinguishability threshold τ_W is defined as a quantile over singular values beyond rank n:τ_W = Q_q({σ_k(H_W)}_{k>n}) NON-CONCLUSIVE is a geometric state: δₙ(W) ≤ τ_W. All results are local and protocol-dependent (W, n, q, K, T_adm).