Identifiability of Neologism Dynamics from Aggregate Corpus Counts

Abstract

Aggregate lexical frequencies reflect both what speakers do and how a corpus records it. We develop a stochastic framework for lexical adoption, abandonment and reactivation on a temporal multilayer network, together with a count observation model separating speaker prevalence, use intensity and detectability, and ask what such data identify. We give a necessary and sufficient condition for the never-active and dormant states to be merged exactly, collapsing the three-state chain to two, and show that the condition constrains the exposures a given network can deliver, not the response function as a whole. No count design can distinguish use intensity from detectability, an exact invariance distinct from the merely practical loss of information in sparse series. And we prove that in a low-prevalence community approximation the rates enter only through the net growth $β-μ$ and the coupling product $βκ$, so that a one-parameter family of triples has identical trajectories, the only separating information lying in a term quadratic in prevalence whose size depends on the emission scale. Simulations characterise recovery, prediction and sensitivity to misspecification. An exploratory analysis of 144 candidate forms in CREA and CORPES XXI press subcorpora illustrates the consequences: under the chosen emission scale and a symmetric contact graph, very different rate triples give nearly identical fitted trajectories, and in leave-one-country-out comparison with training-only proxies and seeds on a retrospectively selected cohort, a constant-rate count baseline beats the evaluated dynamic specifications on 84 to 94% of forms. These findings neither establish nor refute contact-driven diffusion. They delimit what this model and panel can support, and name the calibration, geographical contrast and repeated speaker observations that would make the question answerable.