Joint Embedding Predictive Architectures (JEPA) offer a promising path toward self-supervised learning, but their application to SNNs is hindered by significant challenges. Training heuristics like stop-gradient and Exponential Moving Averages (EMA) are often unstable and provide no mathematical guarantee against representation collapse. This problem is amplified by the training unstability of SNNs. Some JEPA models like VICReg and LeJEPA use statistical regularizers to prevent collapse and optimize the representation distribution for downstream tasks but those methods are designed for continuous representations and are not directly applicable to the discrete, event-based nature of SNNs. To address this, we introduce a novel framework for a bio-plausible spiking JEPA. We derive the theoretically optimal target distribution for latent representations up to the second-order moment, and enforce it using only locally available statistics. Using a binary latent space over a single timestep, our model achieves performance on-par with comparable continuous models on the ImageNette benchmark. Future work will focus on scaling up experiments to larger datasets and more complex architectures.