 Receiver-latency uncertainty in the inferred input-time horizon

Receiver-latency uncertainty in the inferred input-time horizon propagates uncertainty in timing calibration into the latest input time that could have influenced a stored output record. For one channel, the horizon in input-time horizon of a delayed optical receiver record is $H=T-d$, with last output time $T$ and effective input-to-output timing offset $d$. HenceThis linear variance identity retains shared timing influences.^[ref]

A common calibration offset can cancel when it enters both quantities. In an original model, let errors be $\delta T=c+e_T$ and $\delta d=c+e_d$, with independent components of standard deviations $0.8$, $0.2$ and $0.6\mathrm{ns}$. Then $\delta H=e_T-e_d$ and $u(H)=\sqrt{0.2^2+0.6^2}\approx 0.6325\mathrm{ns}$. Discarding their common-offset covariance would instead give $\sqrt{0.8^2+0.2^2+0.8^2+0.6^2}\approx 1.296\mathrm{ns}$.

The shared component must come from the actual calibration model. Here $d$ is the effective timing offset relating the input and output coordinates, so an output-clock alignment error can enter both $T$ and $d$. A physical transport-delay error is not automatically correlated with the last-sample timestamp.

For hard timing limits, propagate validated bounds rather than reinterpret standard uncertainty as a guarantee. If $T=150\mathrm{ns}$ is known and $8\le d\le 12\mathrm{ns}$, then $138\le H\le 142\mathrm{ns}$. Claiming the optimistic endpoint as though it held for every allowed delay would overstate the input-time reach.

With several channels, $H={\max }_j(T_j-d_j)$. Channel switching under uncertainty in a combined receiver horizon makes this a nonsmooth function when the maximizing channel is uncertain. Propagate the justified joint timing set or distribution; a derivative of only one nominally best channel can miss such switching.

NIST's primary pulse calibration measured the detector, cable and oscilloscope together using a short known optical input.^[ref] The numerical timing errors above are chosen examples, not values from that apparatus. A timing horizon remains a necessary information limit; it does not guarantee invertibility of the receiver or bound future optical illumination.