Rank current and actual earlier label

22 Rank current and actual earlier label

Appendices C and D provide the quantitative inputs for this step. Use the new wave's own radial conditional CDF given the live pair $(S,Z)$. Its material derivative has clock and pointer contributions; the radial current cancels pointwise in the conditional-rank identity. The hidden-coordinate absolute values precede all integrations. The hybrid comparison yields

The rank collar is optimized once on this sum, giving $2C\sqrt{2NI_{\rm post}}$. Independently optimized component costs are not silently substituted for that expression.

The common good-clock event requires $|S_h-0.102|\leq0.000839\,\mathrm m$ and whole-path clock deviation at most $10^{-5}\,\mathrm m$ through $0.09\,\mathrm s$. On that event $S_t<S_{\rm on}$ for every prewitness time, with a strict $1\,\mu\mathrm m$ margin at $t_a$. Hence $G_*=\psi_{\rm old}g_0$ there. The same event places the witness conditional age in $[355/300,377/300]$, completes the writer by $0.038389\,\mathrm s$, and keeps the clock beyond the pulse throughout the hold.

The earlier-label composition retains the new preparation event, both distinct exact-CDF bridges, the original conditional age-union and outer-ray events, the common good-clock complement, the actual radial exit event, and the unchanged conditional-reference endpoint comparison. The new absolute barrier estimate gives radial-exit probability below $9.127218\times10^{-8}$ through readout. These terms prove (9) on the original reference coupling. Conditional rank uniformity is used only under its own wave law, then transferred with the same cap $C$; no conditional Born law is assigned to actual states.