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Cluster and Chimera Scan

Coherence-structure monitor — instantiates Decentralized Phase Locking

Watches for the population fracturing into rival phase clusters or a chimera — part locked, part incoherent — that a single global average would hide.

A single global coherence number is a comforting liar. A population can report "80% synchronised" while it is really two tight clusters locked a quarter-cycle apart, or a chimera — one region marching in perfect lock while an adjacent region, built from identical units, churns incoherently. Cluster and Chimera Scan is the monitor whose entire job is to surface that hidden structure. It does not produce a coherence value; it produces a classification — how many locked groups exist, at what phases, whether a coherent and an incoherent domain coexist, and which units are persistent outliers. Where a scalar order parameter answers "how synchronised, on average?", this answers "synchronised into what shape?" — the question the average is built to obscure.

Example

A 500-drone light show is choreographed to blink as one. The global order parameter reads ≈0.8 — high enough that an operator glancing at a single gauge would call it healthy. The scan resolves what the gauge cannot: the ≈300-drone main body is locked tightly, but a ≈200-drone wing has settled into its own lock roughly a quarter-cycle behind, and along the seam between them ≈30 drones are neither — flickering incoherently, a chimera edge. To the crowd this would read as a smeared, doubled pulse rather than a crisp flash. Because the scan reports the structure (two clusters at ≈90° apart, plus an incoherent boundary) rather than a single number, the operators know precisely what to fix — the wing needs a bridge or a retune — instead of trusting an average that certified a fractured show as fine.

How it works

The distinguishing move is that it looks for structure the global average erases:

  • Resolve phases into groups. It clusters the population on the phase circle to detect multiple locked sub-populations, reporting their sizes and phase separations rather than collapsing them to one mean.
  • Detect chimeras. It flags the coexistence of a coherent domain and an incoherent one among like units — the signature a global order parameter cannot show because the two partly cancel in the average.
  • Track persistent outliers. It separates units that are transiently off from those chronically failing to lock, since only the latter signal a real fault.

Tuning parameters

  • Grouping resolution — how finely (spatially or by neighbourhood) the population is partitioned before scanning. Fine resolution catches small clusters but risks inventing them from noise; coarse resolution can miss a real split.
  • Cluster-separation threshold — the minimum phase gap that counts as two clusters rather than one broad one. Set it tight and you over-report; loose and you merge genuine clusters.
  • Chimera persistence window — how long a domain must stay incoherent to be called a chimera rather than a transient. Longer windows suppress false alarms but delay detection.
  • Outlier threshold — how far and how long a unit must deviate to be flagged as chronic rather than momentary.

When it helps, and when it misleads

Its strength is catching failure states that a global metric actively certifies as healthy: a two-cluster split, a chimera, a drifting sub-group. It turns "80% coherent" into "two clusters 90° apart plus an incoherent seam," which is the difference between a number and a diagnosis[1].

Its failure modes are the twin errors of any classifier. Over-segmentation invents clusters out of noise and raises false alarms; under-resolution smooths a real chimera into an apparently-uniform average and misses it. The classic misuse is upstream of the scan entirely: reporting only the global order parameter and declaring the population healthy — exactly the blindness this monitor exists to remove. The discipline is to match grouping resolution to the real neighbourhood structure and to require persistence before crying chimera.

How it implements the components

  • cluster_chimera_and_outlier_monitor — it is this monitor: it classifies the population into locked clusters, chimera domains, and chronic outliers that a scalar coherence figure conceals.

It does not compute the plain local order parameter it builds on (coherence_and_order_parameter_panel — Local Coherence Probe), repair a detected split by bridging the clusters (multiscale_phase_bridge — Bridge Oscillator Link), or break coupling when a cluster hardens into a dangerous herd (harmful_lockstep_and_herd_guardrail — Anti-Herd Coupling Breaker).

Notes

This scan and the Local Coherence Probe are complementary, not redundant: the probe measures how coherent a single neighbourhood is (a value), while this scan reads what overall shape those neighbourhoods form (a classification — one lock, two clusters, or a chimera). The probe feeds the scan; the scan is what turns a field of local values into a diagnosis of the population.

References

[1] A chimera state is the coexistence of synchronised and desynchronised groups within a population of identical, symmetrically-coupled oscillators — coherence and incoherence side by side where uniformity would be expected. Named in the coupled-oscillator literature, it is the canonical example of a structured state a global order parameter averages away. ↩