Depression as Stuck Displacement: Gradient Collapse, the Rumination Loop, and the Emotional Ground State

Depression is typically characterized by depressed mood, anhedonia, and cognitive dysfunction. We apply the displacement framework to depression, identifying the emotional ground state () and tracing three compounding mechanisms that produce stuck displacement: (1) gradient collapse --- the cost function loses its gradient, making the return path invisible; (2) the rumination loop --- displacement path cost accumulates without reducing, a closed trajectory in affective space; and (3) HPA dysregulation --- the hypothalamic-pituitary-adrenal axis maintains autonomous displacement forcing, independent of external stressors.

A fourth structural layer, BDNF depletion and dendritic atrophy, constitutes accumulated displacement at the neural architecture level. We propose that depression is the wrong-attractor case for the emotional system: the system has found a stable state that is not. DC5 (irreversibility) applies: the return path from entrenched depression costs more than early intervention. The framework provides a unified account of anhedonia, rumination, and treatment resistance, and identifies distinct targets for each displacement mechanism.