A Causal Formulation of Spike-Wave Duality

Understanding the relationship between brain activity and behavior is a central goal of neuroscience. Despite significant advances, a fundamental dichotomy persists: neural activity manifests as both discrete spikes of individual neurons and collective waves of populations. Both neural codes correlate with behavior, yet correlation alone cannot determine whether waves exert a causal influence or merely reflect spiking dynamics without causal efficacy. According to the Causal Hierarchy Theorem, no amount of observational data--however extensive--can settle this question; causal conclusions require explicit structural assumptions or careful experiment designs that directly correspond to the causal effect of interest. We develop a formal framework that makes this limitation precise and constructive. Formalizing epiphenomenality via the invariance of interventional distributions in Structural Causal Models (SCMs), we derive a certificate of sufficiency from Pearl's do-calculus that specifies when variables can be removed from the model without loss of causal explainability and clarifies how interventions should be interpreted under different causal structures of spike-wave duality. The purpose of this work is not to resolve the spike-wave debate, but to reformulate it. We shift the problem from asking which signal matters most to asking under what conditions any signal can be shown to matter at all. This reframing distinguishes prediction from explanation and offers neuroscience a principled route for deciding when waves belong to mechanism and when they constitute a byproduct of underlying coordination