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

Beckmann & Butlin (2026) elevate the LLM individuation problem to an ontological question with falsifiable candidate positions, drawing empirical support from recent mechanistic-interpretability work, Anthropic's persona vectors, the Persona Selection Model, and the emergent-misalignment literature. We argue that this framework inherits an unargued cross-context co-reference assumption: the persona-vectors literature tacitly assumes that "v_t" picks out the same content-bearing object under different elicitation regimes. This is the structure Field (1973) identifies as partial reference in pre-relativistic mechanics. Through four paired measurements in our persona-topology experiments on Qwen3-4B-Instruct and Mistral-7B-Instruct-v0.2, we present empirical wedges that, jointly, undermine the cross-regime collinearity prediction the assumption requires. Prompt-extracted vectors are not collinear with fine-tune basin directions across base models. Fictional personas with reduced pretraining footprint shift the model along v_real more strongly than fine-tuning on real anchors does. Contradictorily-valenced mixed fine-tunes deviate from the linear-interpolation prediction toward a training-history-determined attractor (the Anthropic Assistant Axis). And, most decisively, inference-time activation arithmetic and fine-tune-time chimera training carry distinct compositional algebras over the same persona vectors—an algebraic asymmetry that no shared-substrate reading can absorb. We propose regime-indexed individuation: the identity unit for representational content is a (vehicle, regime) pair, not a single vehicle, and cross-regime family resemblance is an empirically measured probe-equivalence relation rather than substrate identity. Under this framework, Beckmann & Butlin's three candidate positions (virtual instance, instance-persona, model-persona) cease to compete and instead describe three distinct objects, each valid within its respective regime; the original "which is the LLM mind?" question receives an empirically grounded negative answer rather than being avoided. The same diagnosis and (vehicle, regime) reading apply to Mollo & Millière's vector grounding, Chalmers' propositional interpretability, and Cerullo's modular-dynamic-composition critique of PSM.