Borderline Personality Disorder as Dynamic Ground State Instability: Emotional Dysregulation as Shallow Basin, Identity Diffusion as S⁰ Ambiguity, and the Return Path of Dialectical Behavior Therapy

We apply the Displacement Framework to Borderline Personality Disorder (BPD), formalizing the condition as dynamic ground state instability rather than wrong-attractor capture. The core geometry: shallow emotional basins (small perturbations drive large displacement), S0_self ambiguity (identity diffusion as borrowed ground state), and splitting as oscillation between two wrong attractors with no stable intermediate.

Seven formal propositions are derived covering shallow basin definition, identity diffusion, splitting, abandonment fear as ontological displacement anticipation, self-harm as dysregulated return mechanism (pain spike forcing endorphin return signal), developmental landscape deformation via early trauma, and DBT as basin deepening. The BPD-PTSD contrast is formalized: PTSD = stable displaced ground state (wrong attractor); BPD = unstable ground state (shallow basins everywhere).

DBT modules are analyzed as displacement-geometric interventions.