Spikes as perturbations of resonant neural circuits: an RLC framework with testable predictions.

Computational neuron models commonly reduce subthreshold membrane dynamics to a leaky RC integrator, confining computation to the spike and treating the inter-spike trajectory as passive decay. Yet impedance measurements and channel-specific analyses show that many excitable membranes have band-pass, inductance-like impedance profiles with a tuneable resonant peak - dynamics a first-order RC model cannot represent. This paper develops a spike-as-perturbation framework in which spikes act as impulse perturbations that launch regime-dependent transient trajectories in an equivalent parallel RLC membrane. We define the biological grounding and domain of validity of the reduction, show that post-perturbation RLC ringdowns carry circuit-identity and perturbation-timing state variables not available to a single matched first-order RC element without added delays, recurrence, or extra state variables, and demonstrate a concrete primitive - phase-based temporal discrimination - together with a spike-timing readout that makes it network-visible. A closed-form comparison (