= Common-clock contribution to a maximum receiver horizon
A <common-clock contribution to a maximum receiver horizon> is a residual timing error that survives in every channel's inferred input-time horizon. Write $H_j=h_j+C+\varepsilon_j$, with common error $C$ independent of the remaining channel errors. Then the identity
$$
\max_j H_j=C+\max_j(h_j+\varepsilon_j)
$$
shows that selecting the latest channel does not average away the common term. With finite <variances>,
$$
\operatorname{Var}(\max_jH_j)=\operatorname{Var}(C)+
\operatorname{Var}\!\left(\max_j(h_j+\varepsilon_j)\right).
$$
Here $C$ means a component remaining after each channel's subtraction $T_j-d_j$. A clock contribution that already cancels inside that subtraction must not be added again; see <receiver-latency uncertainty in the inferred input-time horizon>.
For two equal nominal horizons $h_j=\mu$, take independent channel errors $\varepsilon_j\sim N(0,s^2)$ and $EC=0$. The independent maximum moments derived in <channel switching under uncertainty in a combined receiver horizon> give
$$
EH=\mu+\frac{s}{\sqrt\pi},\qquad
\operatorname{Var}(H)=\sigma_C^2+s^2\left(1-\frac1\pi\right).
$$
If the common error is also normal, each channel has <variance> $\sigma_C^2+s^2$ and their correlation is $\sigma_C^2/(\sigma_C^2+s^2)$, recovering the equal-channel model in <distribution of the maximum of correlated receiver horizons>.
For an original example, choose $\sigma_C=0.8\,\mathrm{ns}$ and $s=0.3\,\mathrm{ns}$. The combined <mean> is about $0.1693\,\mathrm{ns}$ above $\mu$, and its <standard deviation> is about $0.8375\,\mathrm{ns}$. Yet the difference between channel horizons has <standard deviation> only $\sqrt2s\approx0.4243\,\mathrm{ns}$, because $C$ cancels there. Good agreement between channels therefore need not establish a precise absolute horizon.
A timing experiment needs an independently justified reference for the common component, in addition to channel-to-channel alignment observations. Shared-input <covariance> is explicitly retained in NIST's uncertainty law.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[Appendix A, equation A-3]{ref} Repeated reads sharing the same clock realization cannot estimate away its absolute displacement simply by choosing the largest result.
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