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Causal indistinguishability of delayed optical inputs on a finite record means that an observation ending at a fixed time cannot discriminate inputs whose differences have not yet reached its receivers. The unobserved delayed-pulse counterexample to a fitted tail bound proves this for one calibrated convolution channel. The same information limit holds for any finite set of causal linear channels.

Let channel $j$ have response $h_j$ with $h_j(t)=0$ for $t<0$, and record $y_j=P\ast h_j$ only for $t\le T$. Every perturbation $q$ supported strictly after $T$ satisfiesfor every channel. Thus the finite-record observation operator has a whole family of invisible input directions. This is compatible with nonnegative optical power: choose any nonnegative delayed pulse and compare $P$ with $P+q$. No cancellation between unphysical negative powers is required.

Known propagation or detector latency can hide part of the input even before the record ends. If $h_j(t)=0$ for $t<d_j$, an input starting at $S$ produces no response before $S+d_j$. The input-time horizon of a delayed optical receiver record therefore depends on the channel's time reference, not just the last stored sample time.

For an original example, suppose two ideal delay channels measure $y_1(t)=P(t-2\mathrm{ns})$ and $y_2(t)=P(t-7\mathrm{ns})$, both recorded through $T=100\mathrm{ns}$. A pulse starting at input time $99\mathrm{ns}$ first appears at output times $101$ and $106\mathrm{ns}$. Both stored records are unchanged by that pulse, even though it began before the nominal record endpoint. Additional causal channels with smaller delays can extend the input horizon; none can observe an input that begins after their recording ends.

Offline processing of identical stored records still gives identical results, even if the processing filter itself uses samples on both sides of each stored time. To distinguish the inputs, obtain additional observations or supply independently justified restrictions on later illumination. Exact knowledge of the receiver response alone supplies neither.

NIST's pulse calibration characterized the detector, cable and oscilloscope as a combined response chain using a short optical input.^[ref] Such characterization is important for aligning the physical input and recorded output times. The two pure delays above are chosen models, not measured delays of that apparatus. A future-valid optical envelope or documented source cutoff remains additional information needed for an all-future missed-energy bound.

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.