Representational Divergence: A Method for Measuring the Gap Between Assertion and Realization in Contested Domains

I take up a situation that recurs across the humanities and social sciences: one party asserts the state of a contested domain while an independent source documents what that domain was, and we lack a general, reproducible way to measure the gap between the two without sliding into treating the gap itself as proof of motive. I define that gap as a formal object, representational divergence, and I use the term in a specific sense, distinct from its looser appearances elsewhere. Given an assertion surface and an independently constructed realization surface, registered over a shared domain and time index and coerced to a common comparison space, representational divergence is their signed, directional difference, reported not as a raw quantity but as the excess over a pre-specified baseline of non-motivated processes (error, inaccessibility, recording effort). I demonstrate the construct across three domains that share nothing but the logic of the object itself: colonial cartography, public-health service coverage, and corporate financial reporting. I state the method's defining property as a formal limit: excess divergence is necessary but never sufficient evidence of intent, which has to be established from an evidence stream independent of the measure. To show the instrument fixed end to end, I rehearse a pre-registered confirmatory application to Dutch colonial cartography of the Darien, 1609 to 1714, in which the instrument, baseline, inference plan, and falsification conditions are locked before any data are seen.