Most research on human–LLM interaction examines discrete task performance at single time points. How sustained collaboration with an LLM evolves over months - and whether it leaves measurable cognitive traces - remains empirically uncharacterised. We present an open-source computational pipeline for quantifying longitudinal cognitive dynamics, demonstrated on a naturalistic corpus of 20,449 messages spanning eight months of ChatGPT interaction (64 conversation threads, single participant). The pipeline applies lexical cognitive profiling, topic modelling, dyadic alignment measurement, and vocabulary analysis at monthly resolution, validating all trends against permutation null distributions. Applied to the demonstration corpus, the framework detected coherent longitudinal structure across five measures: progressive growth in structural reasoning language, a non-monotonic epistemic uncertainty arc, an eightfold increase in exchange density, vocabulary narrowing, and stable conversation linearity, consistent with progressive domain specialisation. These findings demonstrate the pipeline's sensitivity to meaningful longitudinal dynamics. The full pipeline is openly available for application to any ChatGPT/Claude export.