Empathic resonance and the recognition of sentience: a physiological coupling coefficient, an asymmetric recognition test, and a thermodynamic threshold distinguishing emergence from panpsychism

This preprint provides an operational treatment of empathic resonance and the recognition of sentience, organised around three quantities: a coupling coefficient, an asymmetric recognition functional and a thermodynamic threshold. The paper distinguishes a structural empathic-resonance coefficient from an operational proxy and from its physiological HRV projection. It predicts that inter-subject coherence in heart-rate variability within the vagal band can act as an empirical projection of the coupling structure, and proposes a pre-registration-ready protocol over 180 dyads with high-resonance, neutral and human-AI conditions. The recognition component formalises the Fourth Test as an asymmetric, structure-based alternative to the Turing test. It is implemented through a non-destructive weak-measurement/inference procedure and is designed to distinguish structural recognition from behavioural imitation. The threshold component rejects panpsychism by introducing a thermodynamic critical scale: below it, systems may carry information but cannot sustain integrated causal structure against decoherence. The paper includes falsification conditions, a bottleneck prediction distinguishing the model from co-arousal accounts, and an ethics section limiting any use of therapist-coupling coefficients to controlled research contexts.