Neuroplasticity as Ground State Migration: Learning as Intentional S⁰ Displacement, LTP/LTD as Return Mechanisms, and the Formal Geometry of Forgetting

We apply the Displacement Framework to neuroplasticity, formalizing the brain's capacity for plasticity as the ability to migrate its own ground state S0_neural. The synaptic weight matrix W is identified as the landscape generator: LTP (long-term potentiation) deepens attractor basins (Proposition 1), LTD (long-term depression) shallows them (Proposition 2). Learning proceeds in three phases: acquisition as high-displacement departure from current S0, consolidation as S0 migration completion (dependent on sleep), and retrieval as basin re-entry.

Eight formal propositions are derived covering Hebbian use-driven deepening, sleep as consolidation engineering, the pruning paradox (forgetting is necessary for learning), trauma as unauthorized S0 migration, and critical periods as landscape fluidity windows. The framework unifies plasticity mechanisms including BDNF, CaMKII, perineuronal nets, and synaptic homeostasis under a single geometric description.