The universal shapes underneath every life. Invested or neglected.
$\omega_t$ transitions as $\omega_{t+1} = \omega_t \cdot (1 - \mu(h_t, r_t, p_t, t))$. It is not a fixed discount — it is a state variable shaped by the policy you run. An invested policy keeps $\omega_t$ higher for longer. A neglected policy accelerates the decay. In the canonical model, future joy is discounted by $\omega_t$ — it represents your odds of being alive to experience it. A unit of joy at 70 is worth less than the same unit at 40, not because joy matters less, but because the probability of reaching 70 is lower. That probability is not fixed. It is shaped by the policy you run.
Health, wealth, relationships, and purpose. Each shaped by the policy you run. Invested or neglected.
Both curves share a peak in the late 20s. Neglect compresses the peak and steepens the decline. The neglected curve hits the floor about a decade earlier.
Sigmoid accumulation in either case. Neglect cuts the ceiling roughly in half and accelerates draw-down after retirement.
The widest gap in the system. Neglect compounds the same way investment does, just in the wrong direction.
The mid-30s dip is real. Recovery is possible but not automatic. Drifted purpose flattens at low and stays there.
Set the dimensional weights $\lambda_i$. The chart shows total contribution $C(S_t, X_t^\pi) = \omega_t \cdot J(S_t)$ summed over a lifetime under an invested and a neglected policy. The difference between the curves is what your policy choice is worth.