Chrono-debt spectrum

What the plate operates. Definition 1.1 defines the chrono-debt spectrum as the difference between the pre-closure baseline survival function and the closed-loop one, evaluated at every scale. As the policy ${\theta }_t$ converges to the fixed point ${\theta }^{\ast }$, the bars climb across the scales the closure forecloses first.

The scale-differentiated structure.Per the proposition's property (b), the spectrum varies across $\tau$:

• At short scales ($\tau \sim {\delta }_{\min }$), both survival functions are near unity and the debt is small.
• At intermediate scales (${\delta }_{\min }\ll \tau \lesssim {\theta }_{\mathrm{ref}}$), the closed loop has driven the current survival down sharply while the baseline retains substantial mass. The debt is maximal here.
• At long scales ($\tau \gg {\theta }_{\mathrm{ref}}$), both survival functions are small and the debt asymptotes.

Weighted view.Toggle “weighted by scale” to multiply each bar by $\tau$(the framework's default weighting). The weighting encodes the substantive claim: a foreclosed adolescence weighs more than a foreclosed second by the relevant timescale ratio. Unweighted shows where the foreclosure first concentrates; weighted shows what carries the political weight.

The aggregate readout. ${\int }_0^{\infty }D(t,\tau )d\tau$ is the unweighted aggregate chrono-debt; under the framework the integral grows as ${\theta }_t\to {\theta }^{\ast }$ and the spectrum widens. The number in the readout is the instantaneous integrated debt — the chronopolitical magnitude of the foreclosure at the current ${\theta }_t$.