ψ-Neuro: Retentive Topology of Epileptic Dynamics with ψ-Invariants (RCI, b₁, SPI) and a Reproducible Lagrangian Framework

We introduce ψ-Neuro, a retentive-topological framework for epileptic dynamics. Seizures are modeled not as uncontrolled electrical bursts, but as transient collapses of retention (Ξ) and fragmentation of difference (Δψ). The framework is mathematically formalized by the ψ-Lagrangian: \mathcal{L}\psi = \tfrac{1}{2}(\partial\tau Δψ)^2 - \big(αΔψ^2 - βΞΔψ + γΞ^2\big) + \Lambda(Ξ)\cdot\nabla Δψ - μ||\nabla Δψ||^2 This formulation defines predictive ψ-invariants — the Retentive Capacity Index (RCI), persistent homology cycles b₁, and the Seizure Predictive Index (SPI). Validation on synthetic EEG demonstrates reproducibility, predictive power, and opens therapeutic outlooks (retention-oriented stimulation, Ξ-support pharmacology).