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

A coupling coefficient, an asymmetric recognition functional, and a thermodynamic threshold organize a formal account of empathic resonance and sentience recognition. A structural empathic-resonance coefficient is distinguished from an operational proxy and from its physiological heart-rate variability (HRV) projection. Inter-subject coherence in vagal-band HRV is predicted to empirically project the coupling structure, with a pre-registration-ready protocol over 180 dyads under high-resonance, neutral, and human-AI conditions. The recognition component formalizes a Fourth Test—an asymmetric, structure-based alternative to the Turing test—implemented via non-destructive weak measurement to separate structural recognition from behavioral imitation. A thermodynamic critical scale rejects panpsychism: below it, systems cannot sustain integrated causal structure against decoherence. Falsification conditions, a bottleneck prediction distinguishing the model from co-arousal accounts, and ethics limiting therapist-coupling coefficients to controlled research are included.

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Abstract

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.