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Local Coherence Probe

Local coherence monitor — instantiates Decentralized Phase Locking

Measures whether each unit's own neighbourhood is actually in lock, so a healthy global average can't mask a locally incoherent patch.

The order parameter that tells you a population is 90% locked is computed over the whole population — and that is exactly its blind spot. Local Coherence Probe computes the same measure at neighbourhood scale: each unit evaluates the coherence of just the peers it can see, producing a field of local coherence values instead of one global scalar. Its defining property is locality — it reports "is my corner in lock?", not "is the population on average in lock?" — because a single incoherent patch that would seed a failure can hide comfortably inside a healthy global average. It is the coherence meter of the family, deliberately pointed at the small scale, and it is what a global panel is assembled from.

Example

A patch of coupled pacemaker cells (modelled on a sensor lattice) drives a rhythm that must stay coordinated to be useful. The global order parameter across the whole patch reads ≈0.9 — reassuringly high. But each cell also runs a local probe, evaluating coherence over just its immediate neighbours, and in one small region the local value has fallen to ≈0.4: a knot of cells that has quietly lost lock with its surroundings while the global average, dominated by the healthy majority, barely moved. That local dropout is precisely the kind of seed a re-entrant disturbance grows from, and the probe surfaces it while it is still a local patch — long before it is large enough to move the global number. The fix (retune, recouple, or isolate the patch) can be aimed exactly where the probe points, not sprayed across a population the average says is fine.

How it works

The distinguishing move is scope: the same coherence mathematics, computed locally and continuously:

  • Neighbourhood order parameter. Each unit computes coherence — a local order parameter and mean phase — over only the peers within its neighbourhood, yielding a spatial field of coherence rather than a single figure.
  • Per-unit and continuous. The measurement lives at each unit and runs constantly, so a patch losing lock shows up as a local dip the moment it starts, not when it finally shifts the global average.
  • A field, not a number. Its output is the distribution of local coherence across the population — the raw material a global panel or a structural scan is built on.

Tuning parameters

  • Neighbourhood radius — how many peers count as "local." Too small and the reading is noisy; too large and it converges on the global average, losing the locality that is the whole point.
  • Averaging window — instantaneous coherence versus time-smoothed. Instantaneous catches fast dropouts but jitters; smoothed is stable but lags.
  • Alarm threshold — the local coherence below which a patch is flagged. Set by how much local incoherence the system can tolerate before it matters.
  • Metric choice — order-parameter magnitude versus phase variance or lock duration; different metrics expose different kinds of local failure.

When it helps, and when it misleads

Its strength is surfacing the patch a global average hides, cheaply and early, because the measurement lives at every unit[1]. It is the difference between learning a region is failing while it is still a region and learning it only once it has grown enough to drag the whole population's number down.

Its failure modes come from scope and from what coherence does not tell you. Too small a neighbourhood makes the reading noise; too large quietly reproduces the global blindness it was meant to cure. And a high local coherence is not the same as correctness: a patch can be tightly locked to the wrong phase — coherent but out of step with the rest — and the probe, which measures agreement not target-matching, will happily call it healthy. The classic misuse is to trust the single global order parameter and never look at the local field at all. The discipline is to size the neighbourhood to the real coupling range and to read local coherence alongside the target, not as a proxy for it.

How it implements the components

  • coherence_and_order_parameter_panel — it computes the order parameter itself, at neighbourhood scope, producing the field of local coherence values a global panel is assembled from.
  • phase_observation_channel — it samples each unit's neighbourhood phase readings as its raw input, binding every coherence figure to the specific local sample it came from.

It does not classify the population into clusters or chimeras (cluster_chimera_and_outlier_monitor — Cluster and Chimera Scan), set the coupling law that produces the coherence (reciprocal_coupling_law — Adaptive Pulse-Coupled Update), or act on a low reading (desynchronization_escape_and_learning_record — Anti-Herd Coupling Breaker).

Notes

Local coherence answers agreement, never target: a neighbourhood can score a perfect local lock while sitting at the wrong phase relative to the rest of the population. Read on its own the probe will bless such a patch; it must be paired with the functional target (and, at population scale, with the Cluster and Chimera Scan) to tell a good lock from a confidently wrong one.

References

[1] The order parameter is the standard summary of how phase-aligned a population of oscillators is — near one when they move together, near zero when scattered. Computing it over a neighbourhood rather than the whole population yields a local order parameter, the accepted way to expose spatial structure that the global value averages out. ↩