Characterize phantom-set growth with crystal-cell size

Characterize the growth rate of the geometric phantom set governing render-ceiling failures as crystal-cell size increases, thereby determining whether a general cell-size-dependent rate can be established for the frozen-camera reconstruction protocol.

Background

The paper defines a phantom set consisting of spurious species-labelled points produced by projection coincidences between distinct atoms but consistent with all camera views. The render ceiling is exact when this set is empty at the operating tolerance, and the authors certify emptiness for their principal samples and protocol.

The discussion explicitly notes that phantom-set emptiness is not monotone in the extraction tolerance and that the empirical behavior depends on structure and camera configuration. Although the supplementary analysis reports correlations between phantom counts and atom density, the paper does not establish a general rate describing how phantom-set behavior scales with crystal-cell size. Such a result would extend the per-sample certification to a broader theoretical characterization of benchmark difficulty and reconstruction reliability.

References

Exactness is certified sample by sample at a single tolerance: the phantom set is not monotone in that tolerance, no growth rate with cell size is proved, and an independently drawn sample already loses one structure at the certified setting.

— Separating perception from reasoning in vision-language models: a model-free render ceiling for crystal structures  (2609.00663 - Polat et al., 1 Sep 2026) in Discussion, paragraph beginning “Three conditions fix the scope of the instrument”