Coupling and a Delayed Observer
In this parameterized example, a chosen observer can cross its detection threshold after the simulated lattices cross a synchronization threshold.
A model companion to Timing Inaccessibility and the Projection Bound. No universal ordering of Tsync and Tdetect is assumed.
Structure
This authored integration rate, feature count, and the two thresholds jointly determine whether a verification lag appears.
Coupling Channel
Under the selected Kuramoto dynamics and one-way coupling, the two lattices can develop high phase similarity. The canvas reports a chosen cross-coherence statistic.
Measurement Channel
The observer compares a selectable number of Fourier magnitudes, exponentially smooths that score at an adjustable rate, and applies a fixed threshold. It is one estimator, not an optimal decoder or a general channel-capacity bound.
The Model Lag
When the synchronization statistic crosses 0.7 before the smoothed observer score crosses 0.5, the display marks a lag. Faster response, richer features, other thresholds, or a better estimator can shrink or remove it.
Why This Matters
The simulation is an existence example: a process criterion and a verification criterion can be crossed at different times. Whether that occurs in neurons, cells, or immune systems depends on the physical coupling, measured variables, estimator, sampling rate, and error target.
Change observer bandwidth and response speed to see that the lag is parameter-dependent. Disable coupling to test whether the chosen statistic still crosses threshold.