{"paper":{"title":"A conformal reduction for the X-ADM mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Stephen McCormick","submitted_at":"2026-07-02T14:40:01Z","abstract_excerpt":"The X-ADM mass is a geometric invariant for asymptotically flat manifolds, recently introduced by Mantegazza and Oronzio [arXiv:2602.11372], generalising the weighted mass of Baldauf and Ozuch [arXiv:2201.04475] which itself is a generalisation of the well-known ADM mass.\n  We show that the positivity of the X-ADM mass is in fact equivalent to the standard positive mass theorem for the ADM mass by way of a conformal reduction argument, which in particular proves the X-positive mass theorem in all dimensions, which previously was only established in dimension 3 under a topological condition. As"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03629","kind":"arxiv","version":1},"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/2607.03629/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"}