3D Sighting-Report Spacetime Clustering

Spacetime Case Cloud

Noise-report rate 220

Cluster count 3

Cluster tightness 0.5

Detector sensitivity 1.00

Reports total

–

3D R statistic

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Detected clusters

–

False-positive rate

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How it works

Each point is one filed sighting report placed in a spacetime volume: x/y is where it was reported, height (z) is when — older reports sit low, recent ones high. Independent noise reports (hoaxes, misidentifications, duplicates) scatter uniformly through the whole volume. A genuinely correlated event produces many reports that are close together in both location and time, so they form a visibly tight point-cluster rather than spreading through the cloud.

For a Poisson process in 3D with report density λ (reports per unit volume), the expected mean nearest-neighbor distance is:

r_expected = Γ(4/3) / λ^(1/3) ≈ 0.55396 · λ^(-1/3)
R = r_observed_mean / r_expected

As in the 2D case-database view, R ≈ 1 means the spacetime pattern looks like pure noise; R < 1 means points are packed tighter than random chance predicts. Reports whose own nearest-neighbor distance falls well under r_expected are flagged red and grouped into candidate clusters (≥3 members) — the diffuse cyan cloud is noise, the flagged red knots are candidate real events.

Noise-report rate — independent random reports filling the spacetime volume.
Cluster count — genuinely correlated events seeded into the volume.
Cluster tightness — spatial and temporal spread of a real event's reports; tighter events are easier to pick out from the noise field.
Detector sensitivity — how far below r_expected a report must fall to be flagged.

Real-world relevance: adding the time axis is what turns a flat spatial cluster check into genuine event detection — a real event clusters in space and arrives in a short burst, while independent hoaxes and misidentifications land at unrelated times even if a few coincidentally share a location.

Unflagged (noise field) Flagged (detected cluster) Ground truth: real event (wireframe box)

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