Persona Without Substrate: Regime-Dependence and the LLM Individuation Problem

Beckmann & Butlin's (2026) ontological framework for the LLM individuation problem inherits an unargued cross-regime co-reference assumption from the persona-vectors literature: that the same direction picks out the same content under prompt-conditioning, gradient-descent fine-tuning, and inference-time steering. We present four empirical wedges from persona-topology experiments on Qwen3-4B-Instruct and Mistral-7B-Instruct-v0.2 - non-collinearity of prompt-extracted vectors and fine-tune basins; fictional personas displacing the model along real-anchor directions more strongly than real anchors do; contradictory-valenced mixtures biased toward a training-history-determined attractor; and asymmetric compositional algebra under inference-time arithmetic versus fine-tune-time chimera training - that jointly undermine the assumption. We propose regime-indexed individuation: the identity unit for representational content is a (vehicle, regime) pair, not a vehicle alone. Under this framework, Beckmann & Butlin's three candidate positions describe three different regime-internal objects rather than competing for the same referent; the same diagnosis applies to Mollo & Milli\`ere, Chalmers, and Cerullo.