REVIEW 3 cited by
Gromov-Hausdorff metrics and dimensions of Lorentzian length spaces
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We construct analoga of Gromov-Hausdorff space for Lorentzian distances and show a Gromov precompactness result for one of them. After calculating the Dushnik-Miller dimension of Minkowski spaces (of manifold dimension larger than 2) to be countable infinity, we define a dimension for ordered sets recovering the correct manifold dimension, obtain an obstruction for existence of injective monotonous maps between Lorentzian length spaces, induce functorial pseudo-metrics on Cauchy subsets that in the spacetime case coincide with the Riemannian ones, and prove existence of anti-Lipschitz Cauchy functions with a given Cauchy zero locus, a fundamental ingredient for the Sormani-Vega null distance.
Forward citations
Cited by 3 Pith papers
-
Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry
Normalized bounded Lorentzian metric measure spaces are isomorphic exactly when all of their finite-sample time-separation matrix laws coincide, and three hierarchically related measured Lorentz-Gromov-Hausdorff conve...
-
Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index
Two game-theoretic feature importance scores that include non-WAXp contributions and quantify how effective each feature is at ruling out adversarial examples.
-
New perspectives on the d'Alembertian from general relativity. An invitation
A review of the p-d'Alembertian framework for Lorentzian distance functions, giving distributional comparison theorems across the timelike cut locus.
Discussion (0). Continue with ORCID to comment.