{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DSXOUQ7F5SVUPFGRA3YNGRD64K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5a875f697bdb75c1af12c96a27351dafd8de9233c1636d1d16c7843ae9a5a27c","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-12T19:31:06Z","title_canon_sha256":"e3ac996aa449701db28002c77afca20b7db7cd80ff51fd04f694491b08b9a238"},"schema_version":"1.0","source":{"id":"2410.09626","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.09626","created_at":"2026-07-05T09:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"2410.09626v1","created_at":"2026-07-05T09:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.09626","created_at":"2026-07-05T09:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"DSXOUQ7F5SVU","created_at":"2026-07-05T09:19:41Z"},{"alias_kind":"pith_short_16","alias_value":"DSXOUQ7F5SVUPFGR","created_at":"2026-07-05T09:19:41Z"},{"alias_kind":"pith_short_8","alias_value":"DSXOUQ7F","created_at":"2026-07-05T09:19:41Z"}],"graph_snapshots":[{"event_id":"sha256:3f4a021f9d1c98695d74a85bc3ec5ce073b66c38ed99de933048e3d642eda45d","target":"graph","created_at":"2026-07-05T09:19:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.09626/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Omega$ be a smooth, bounded subset of $\\mathbb{R}^3$ diffeomorphic to a ball. Consider $M = \\mathbb{R}^3 \\setminus \\Omega$ equipped with an asymptotically flat metric $g = f^4 g_{\\text{euc}}$, where $f\\to 1$ at infinity. Assume that $g$ has non-negative scalar curvature and that $\\Sigma = \\partial M$ is a minimal 2-sphere in the $g$ metric. We prove a sharp inequality relating the ADM mass of $M$ with the conformal capacity of $\\Omega$. As a corollary, we deduce a sharp lower bound for the ADM mass of $M$ in terms of the Euclidean volume of $\\Omega$. We also prove a stability type result","authors_text":"Liam Mazurowski, Xuan Yao","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-12T19:31:06Z","title":"Mass, Conformal Capacity, and the Volumetric Penrose Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.09626","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fbedca48cf53b59fb351d4bb355e3f0a6190a4e2f3bdfb644638b60279fd1934","target":"record","created_at":"2026-07-05T09:19:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5a875f697bdb75c1af12c96a27351dafd8de9233c1636d1d16c7843ae9a5a27c","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-12T19:31:06Z","title_canon_sha256":"e3ac996aa449701db28002c77afca20b7db7cd80ff51fd04f694491b08b9a238"},"schema_version":"1.0","source":{"id":"2410.09626","kind":"arxiv","version":1}},"canonical_sha256":"1caeea43e5ecab4794d106f0d3447ee29f41d62d895bf2a75959a9359622ee36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1caeea43e5ecab4794d106f0d3447ee29f41d62d895bf2a75959a9359622ee36","first_computed_at":"2026-07-05T09:19:41.796147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:19:41.796147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oqE8t3FZEKTN1AAcO+nAY18aQqKfptftV0oCTHidDTMu7106/AwPH2eMV6jRr7WRaIofSDi4HBNmeiOwQMdHAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:19:41.796566Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.09626","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbedca48cf53b59fb351d4bb355e3f0a6190a4e2f3bdfb644638b60279fd1934","sha256:3f4a021f9d1c98695d74a85bc3ec5ce073b66c38ed99de933048e3d642eda45d"],"state_sha256":"d23d735ab92a22804ab0e541ed6f18a0efa91b748f0d5e681984090d975e313d"}