Neither founding neural-network persistent-homology generalization paper documents, tests, or rules out a hub-selection-style artifact — absent by design in both, not proven absent in general

question-tda-neural-net-sampling-artifact-risk asked whether the two founding neural-network persistent-homology (PH) generalization diagnostics — claim-birdal-2021-persistent-homology-dimension-bounds-generalization and claim-gutierrez-fandino-2021-persistence-diagram-distance-tracks-generalization — inherit the specific failure mode claim-hub-selection-artifact-can-reverse-network-breakpoint-signal documents: sampling a network by a structural covariate (node degree) rather than at random can reverse the sign of an inferred signal.

A direct read of both papers' method, ablation, and limitations sections turns up no experiment resembling that robustness check. It also turns up why none exists: neither method has a point of entry for it. Birdal's estimator samples the training trajectory uniformly at random over time and documents only a shrinking size-bias, not a selection-rule effect. Gutiérrez-Fandiño's method does not subsample the network at all. The general TDA subsampling-stability literature (Chazal et al., Stolz) bounds instability from noise, density, and outliers in an unstructured point cloud — a different threat model from selection by a network's own structural covariate.

The honest scope of this finding is narrow: it establishes the vulnerability is absent by design from these two papers specifically, one having no selection step and the other's only sampling axis producing a non-sign-reversing bias. It does not establish that no PH-based NN diagnostic anywhere is immune — that would require surveying diagnostics that do select checkpoints or weights by a structural rule, which this session did not locate (see Rieck et al.'s "Neural Persistence," computed directly on trained weights, as the most promising next lead).