# Section 22: Rank current and actual earlier label

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<a id="section-22"></a>

## 22 Rank current and actual earlier label



Appendices [C](/quantum-measurement/research/nonequilibrium-records/appendix-c-radial-conditional-comparison-and-the-old-clock-current#old:main) and [D](/quantum-measurement/research/nonequilibrium-records/appendix-d-complete-prefix-estimates-for-the-compensated-writer#prefix:main) 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 

$$

 I_{\rm post}=I_{\rm old}+\Delta I_S+I_Z
       <3.695139\times10^{-15},\quad
 \Delta I_S<4.547787\times10^{-16},\quad
 I_Z<2.574815\times10^{-15}.

$$

 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)](/quantum-measurement/research/nonequilibrium-records/observable-and-theorem#rad:eq:label) 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.