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 (Q = 2, τRC = 25 ms, f₀ = 10 Hz) gives an RLC sensitivity half-life of 44 ms versus 17 ms for a matched RC decay. We identify the quality factor Q - strongly shaped by I_h and related slow conductances - as a candidate neuromodulatory control variable that fixes the membrane pole radius and hence its transient (short-term) memory horizon, the biological analogue of selectivity in machine state-space models. We do not claim a universal in vivo phase code: a simulation under high-conductance bombardment shows that the readout is reliable in quiescent, high input-resistance states and is suppressed as conductance loading drives the effective Q below the underdamped threshold. We derive four falsifiable predictions spanning cellular, network, decoding, and population levels, and present the argument in three tiers of decreasing evidential support.