{"paper":{"title":"Lorentzian coarea inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The coarea inequality holds for Lorentzian Hausdorff measure once locally uniformly d-controlling maps are present.","cross_cats":[],"primary_cat":"math.MG","authors_text":"Hikaru Kubota","submitted_at":"2026-05-09T18:16:19Z","abstract_excerpt":"In this article, we introduce the notion of locally uniformly d-controlling map between Lorentzian pre-length spaces which is preserving the diameters of causal diamonds, and through that we establish the coarea inequality for Lorentzian Hausdorff measure which is introduced by McCann and S\\\"{a}mann. Besides that we get a covering lemma for subsets in a Lorentzian pre-length space with a new local assumption named the local causal enlargement property, which enables us to enlarge causal diamonds."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish the coarea inequality for Lorentzian Hausdorff measure which is introduced by McCann and Sämann","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"the existence and properties of locally uniformly d-controlling maps that preserve diameters of causal diamonds, together with the local causal enlargement property needed for the covering lemma","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A coarea inequality holds for Lorentzian Hausdorff measure via diameter-preserving maps on causal pre-length spaces together with a covering lemma under local causal enlargement.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The coarea inequality holds for Lorentzian Hausdorff measure once locally uniformly d-controlling maps are present.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ed710aa02712692fa1de157bb6bbbaf3d69859778447101470027da3dea661be"},"source":{"id":"2605.09101","kind":"arxiv","version":2},"verdict":{"id":"1abc672c-c1fa-4b79-90f4-14dce1c2b88e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T03:07:38.125713Z","strongest_claim":"we establish the coarea inequality for Lorentzian Hausdorff measure which is introduced by McCann and Sämann","one_line_summary":"A coarea inequality holds for Lorentzian Hausdorff measure via diameter-preserving maps on causal pre-length spaces together with a covering lemma under local causal enlargement.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"the existence and properties of locally uniformly d-controlling maps that preserve diameters of causal diamonds, together with the local causal enlargement property needed for the covering lemma","pith_extraction_headline":"The coarea inequality holds for Lorentzian Hausdorff measure once locally uniformly d-controlling maps are present."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09101/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T20:37:53.207164Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:31:18.892166Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:31:07.532218Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"655b72ba3f7a1e85d10e14a7687eef3bb6106510b4fc4567c898d58051b88727"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"fe4e9ce7d28537bfdd6aede35c02f4de95f0de3556290fbc34ecc62314680c73"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}