{"paper":{"title":"Volume-Distance-Ratio Asymptote and Spacetime Inextendibility","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"gr-qc","authors_text":"Pengyu Le","submitted_at":"2025-07-30T20:54:58Z","abstract_excerpt":"This paper develops geometric criteria for determining the inextendibility of spacetimes near singularities based on asymptotic analysis of volume-distance relationships. We introduce and analyze the asymptotic behavior of the volume-distance-ratio (VDR), defined as the ratio of volumes of small chronological diamonds to appropriate powers of distances between their vertices. In $\\mathrm{C}^0$ and $\\mathrm{C}^{0,1}$ spacetimes (which are weaker than the classical $\\mathrm{C}^2$ regularity), we prove that VDR converges to the Minkowski value as chronological diamonds approach accumulation point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23097","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.23097/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}