Collapse as Loss of Restoring Mode: Two Structural Routes to Persistence Failure

Collapse in complex adaptive systems is commonly attributed to a single cause: the system is overwhelmed. This paper establishes that collapse, properly defined as the loss of an admissible restoring mode, can arise through two structurally independent mechanisms. The first route is strength-loss collapse: the persistence mass m₀ weakens until retained constraint can no longer counterbalance forcing. This is the classical resilience narrative, detectable via rising variance, rising autocorrelation, and lengthening recovery time. The second route is depth-dominated collapse: persistence mass remains present but the kernel acts at delays too long to stabilise the trajectory within the recovery horizon. This route is invisible to standard early-warning indicators and requires full kernel geometry to detect. Its observable precursor is the emergence of oscillatory recovery - damped overshoot appearing while the scalar stability parameter remains stable.