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The paper investigates the consistency conditions between observable and exact layers in COS45, focusing on local calibration.

April 17, 2026Open Access

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

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Key Points

The paper investigates the consistency conditions between observable and exact layers in COS45, focusing on local calibration.
Defines consistency conditions using mathematical formulations.
Establishes a calibration method via admissible transformations.
Describes the indistinguishability threshold based on singular values.
Explains geometric states concerning local identifiability.
Confirms that decision layer does not depend on exact layer for local conditions.
Establishes that results are protocol-dependent and context-specific.
Suggests that non-conclusive states occur when local conditions are met.

Abstract

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).

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Louis Morissette

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

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