Twin State Reconciliation Under Disordered Telemetry

#Abstract

Observations reaching an industrial digital twin arrive late, duplicated and out of order, at rates that make disorder the normal case rather than an exception. This report gives a reconciliation construction based on event-time folding with a per-channel reorder window derived from measured lateness, argues that staleness must be represented as a value rather than an absence, and states the conditions under which interpolation across a gap is a defect rather than a convenience. The lateness measurements the window is derived from are not reproduced here, which is the report's main evidential gap.

#Motivation

A digital twin is a virtual counterpart of a physical object maintained by a data connection between the two [7]. Classifying implementations by the direction and automation of that connection separates digital models, digital shadows and digital twins proper [6], and in every category the state of the virtual object must be derived from observations that the physical world delivers on its own schedule.

Field measurements from operating sites show four distinct sources of disorder:

1. Buffered flush. An edge gateway loses connectivity and later delivers hours of observations at once, internally ordered and collectively very late.
2. Redundant collection. Two collectors attached to one source produce byte-identical duplicates.
3. Clock skew. Field devices stamp observations slightly in the future.
4. Bulk backfill. Historical import arrives at a rate and volume unlike the live stream.

On an operating site, late data is a double-digit percentage of the total. A design that treats it as an exception will spend its life in the exception.

#State as an event-time fold

State is defined as a fold over observations keyed on the time each observation describes rather than the time it arrived. This is the event-time and processing-time separation that stream processing settled some time ago [1] [4].

Because the fold is keyed on the event time τ(o), replaying observations in any order converges on the same state. That property is what makes a derived store recoverable and what makes historical questions answerable.

#A per-channel reorder window

Sorting requires a window, and the window must close or nothing is emitted. The contribution here is that the window is derived per channel from that channel's own observed lateness rather than fixed globally.

Observations arriving within ω sort into place before state is recomputed. Observations arriving outside it are accepted and stored as corrections, which re-project their window and propagate forward. Nothing is discarded for lateness.

The justification for making this per channel is empirical: a satellite-linked site and a wired unit differ in lateness by orders of magnitude. A constant chosen for one makes the other either unnecessarily laggy or permanently in correction, which matches the conclusion the out-of-order stream processing literature reaches on punctuation and slack [2] [3].

#Duplicate absorption

Observation identity is derived from channel, event time and value. A redelivered observation therefore collapses onto the original with no lookup before insert and no constraint violation to catch, making ingestion idempotent under replay.

#Staleness as a value

Each channel declares an expected interval. When the elapsed time since the last observation exceeds a multiple of it, the value's state becomes stale.

Stale is returned as the last known value together with its observation time and an explicit flag. No read path returns the value alone. Industrial protocols already carry this information as a status code [5], and a pipeline that discards it is discarding a signal the field devices provided deliberately.

#What the construction rules out

• Last value carried forward as a state semantic. It is a rendering choice and must be labelled.
• Interpolation across an absent interval without an explicit model the consumer opted into.
• Any read interface that cannot distinguish a measured zero from no observation.

The safety argument for the second is direct. A twin that closes the loop on physical equipment is part of a system with assurance requirements [9], and a value that was inferred rather than observed must be distinguishable from one that was measured.

#Limitations

Window adaptation lag. ω is estimated from history, so a channel whose lateness distribution changes spends a period with an incorrect window. No adaptation policy is given here.

Correction storms. A large backfill produces corrections across many windows simultaneously. The re-projection is correct and the downstream delta volume is not rate limited in the implementation described.

Derived values across channels. Two channels feeding one computed value may sit at different points in their respective windows, and the computed value has no principled staleness state. This is unresolved and is the most consequential gap, because derived values are what operators actually read.

No published lateness distributions. The per-channel argument rests on measurements not reproduced here. Publishing anonymised distributions would be the most useful contribution a follow-up could make, and would allow others to test the quantile choice [8].