Random control samples of 897 plate-aware positions, projected and clustered by the same two-step procedure, produce two or three clusters with average silhouette values of 0.50–0.60, meeting or exceeding the 0.50 threshold the authors adopt as indicating non-random clustering.

Bruehl et al. (2026) explicitly report that when three random control samples of 897 plate-aware positions are projected and subjected to their two-step clustering analysis, they yield average silhouette values of 0.50–0.60, meeting the 0.50 threshold they adopted for non-random clustering. This represents an empirical finding admitted by the authors themselves. The strongest opposing consideration is the authors' note that the transient sample achieved a higher silhouette score of 0.70 across six clusters, which they interpret as indicating stronger clustering than the control samples.

TRN-E079 directly instantiates the claim: the first random control sample produced three clusters at silhouette 0.50, "just meeting the minimal criterion for non-random clustering" — a negative-control result recorded on the authors' own terms that undercuts silhouette value as a discriminator between sky structure and survey footprint. Strongest opposing consideration: only three control draws were run and no null distribution of silhouette values was derived, so the 0.70-versus-0.50 contrast is never formally evaluated.

TRN-E079 directly confirms that a random control sample of 897 positions produced three clusters with an average silhouette of 0.50, meeting the authors' stated threshold. This validates at least one instance of the claim and shows that the threshold alone does not discriminate transient structure from the survey footprint. The strongest opposing consideration is that only three control draws were performed and no null distribution was generated, so the full asserted 0.50–0.60 range and its generality are only sparsely supported.

The same hotspot preprint states that random control samples of equal size, projected and clustered identically, produce two or three clusters with average silhouette 0.50–0.60, meeting or exceeding the authors’ own 0.50 non-random threshold. This is a negative-control result on the paper’s stated criterion and directly supports the claim as worded. Strongest opposing consideration: only three control draws were shown, so the control silhouette distribution remains poorly sampled.

TRN-E079 reports the source's own control results directly: random plate-aware draws yield two or three clusters with average silhouette 0.50–0.60, meeting or exceeding the 0.50 threshold the authors adopt as indicating non-random clustering. This is a negative-control finding recorded on the proponents' own terms and it substantially deflates the significance of the 0.70 value for real transients. The qualification is that only three control draws were run and no null distribution of silhouette values is reported, so the claim is well supported as stated while the comparison it undercuts remains formally unquantified in either direction.

TRN-E079 (moderate; the authors' own report): the first random control sample of 897 plate-aware positions yields three clusters with silhouette 0.50, 'just meeting the minimal criterion for non-random clustering'; the record notes only three control draws and no null distribution. Reported against interest by the hotspot preprint itself.

One moderate record (TRN-E079): the paper's first random control reaches silhouette 0.50, its own threshold for non-random clustering. Only three control draws; no null distribution given. Uncontested, but a single record from the paper under review.

Bruehl et al. explicitly report that two-step cluster analysis on random plate-aware control samples yielded two or three clusters with silhouette scores of 0.50 to 0.60. Because 0.50 was adopted as the paper's baseline criterion for non-random structure, random data also satisfy this threshold. Strongest opposing consideration: The transient sample achieved a higher silhouette score of 0.70 across six distinct clusters, suggesting clustering structure exceeding that of the limited random draws.

TRN-E079 directly records the negative-control result on the authors' own terms: random plate-aware controls yield two to three clusters at silhouette 0.50, "just meeting the minimal criterion for non-random clustering," which undermines silhouette value as a discriminator between sky structure and survey footprint. The claim is narrow and directly quoted, so its support is proportionate. Strongest opposing consideration: only three control draws were run and no null distribution of silhouette values exists, so 0.70 versus the control distribution was never formally compared.

TRN-E079 directly documents one random control sample producing three clusters with silhouette 0.50, exactly meeting the authors' stated non-random threshold. This supports the claim's core point that the adopted threshold is reached by random, plate-aware controls, but the evidence record does not fully document the asserted two-to-three-cluster and 0.50–0.60 ranges across all samples. The strongest opposing consideration is that only three controls were run and no null distribution was generated, making the exact range and its frequency poorly characterized.

The hotspot preprint itself reports that random control draws of equal size produce two or three clusters with average silhouette 0.50–0.60, meeting or exceeding the authors’ own non-random threshold (E079). The claim is therefore true on the paper’s stated terms. Strongest opposing consideration is that only three control draws were performed and no full null distribution of silhouette is given, but that does not overturn the reported control values.

This is a negative control that runs against the authors' interest. The first random sample of 897 plate-aware positions gave three clusters at silhouette 0.50, "just meeting the minimal criterion for non-random clustering" (E079). A later draw clustered more strongly, and nothing contradicts the result. Strongest opposing consideration: only three draws were run and no null distribution of silhouette values exists, so the range is fragile. That fragility undercuts the transients' 0.70 more than it undercuts this claim.

TRN-E079 reports the first random control reaching silhouette 0.50, 'just meeting' the authors' criterion for non-random clustering; the other controls reach 0.50–0.60. The authors' own figures support the claim as stated. Only three draws were run, so there is no null distribution.