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The Correspondence Equation: A Falsifiable Framework for Measuring Representation–Reality Drift

Year: 2026
Type: preprint
Abstract: The Correspondence Equation (CE) is a quantitative framework for measuring how well an operational representation corresponds to the true, relevant state of a system, across weighted dimensions with variable observability. Version 1.1 resolves two failure modes found by adversarial stress-testing of v1.0: the equation was undefined with zero evidence, and a fully unobserved catastrophic dimension could be reported as near-perfect correspondence. Both are fixed here by blending unobserved dimensions toward a disclosed conservative prior rather than excluding them, verified to reduce the hidden-catastrophe gap from 0.99/0.0012 to 0.55/0.0012 on the same test case. This version also formalizes an exact decomposition separating a genuine change in the underlying state from a change caused by improved observability of an already-existing problem — the same identifiability question addressed in epidemiological surveillance (true vs. detected incidence), applied here to representational correspondence. A serious vulnerability found during testing is disclosed and left unresolved: reducing the declared weight of a known-failing dimension can neutralize the model's bottleneck sensitivity nearly as effectively as hiding it. This is stated explicitly as a condition of publishing v1.1 at all. CE is presented as a falsifiable hypothesis, not a validated instrument. No claim is made about performance on any real historical system. A tested, executable Python reference implementation is included, reproducing every numeric result in the paper. Builds on and cites: Situation Awareness theory (Endsley), organizational sensemaking (Weick), epidemiological ascertainment bias, and intelligence indications-and-warning analysis (Wohlstetter, Grabo).
DOI: 10.5281/zenodo.22543571
Language: English
Open Access status: green
OpenAlex ID: W7210285051
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