What question did this study set out to answer?

To develop a geometric framework for identifying admissibility in observable decision boundaries based on scalar decision variables.

April 15, 2026Open Access

COS45A Geometric Admissibility Framework for Observable Decision Boundaries with Empirical Boundary Crossing (v2.3)

Key Points

To develop a geometric framework for identifying admissibility in observable decision boundaries based on scalar decision variables.
Defined ηₙ as a scalar derived from spectral quantities of a data matrix H_W.
Enforced strict separation between different layers of analysis, from exact to observable.
Performed empirical observations to assess the conditions under which the non-conclusive regime occurs.
Identified configurations are admissible when ηₙ > 0, and non-conclusive when ηₙ ≤ 0.
Non-conclusive outcomes are related to choice of quantile level in null-calibrated thresholding.
Crossings of ηₙ = 0 were noted under structured signal degradation.

Abstract

COS45 is a geometric admissibility framework operating at the observable decision layer. It defines a scalar decision variable ηₙ derived from spectral quantities of a data matrix HW. If ηₙ > 0, the configuration is declared ADMISSIBLE; if ηₙ ≤ 0, the result is NON-CONCLUSIVE. No claim is made beyond admissibility. All components are observable. The framework performs no structure detection, classification, or causal inference. Strict layer separation is enforced: EXACT → STRUCTURAL → LOCAL BRIDGE → OBSERVABLE → DECISION. Under null-calibrated thresholding, the NON-CONCLUSIVE regime is empirically observed as a consequence of the chosen quantile level. Under structured signal degradation, a crossing of ηₙ = 0 is

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Cite This Study

Louis Morissette (Mon,) studied this question.

synapsesocial.com/papers/69df2b2ce4eeef8a2a6b0174 https://doi.org/https://doi.org/10.5281/zenodo.19555415

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