{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7HREZH2C3UPILQQXTKJWGHNHW5","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":"2f20368ebd43b6fca49cd3217bc0ab730556b5af3e33183f594684131da9c4f4","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-31T21:24:58Z","title_canon_sha256":"eea3cf0d3c2ec03698ea98020229a60d15d2338c3569ff54bcc402e6c8aac014"},"schema_version":"1.0","source":{"id":"1209.0019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0019","created_at":"2026-05-18T01:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0019v1","created_at":"2026-05-18T01:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0019","created_at":"2026-05-18T01:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"7HREZH2C3UPI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7HREZH2C3UPILQQX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7HREZH2C","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:023f929773ac6c7a33f39e822240eed454574ffa557e70cdd95cb8956c018011","target":"graph","created_at":"2026-05-18T01:54:48Z","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"},"paper":{"abstract_excerpt":"In this paper, we extend the work in \\cite{D}\\cite{ChrusLiWe}\\cite{ChrusCo}\\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^{6}-$norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr-Newman solution.","authors_text":"Richard Schoen, Xin Zhou","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-31T21:24:58Z","title":"Convexity of reduced energy and mass angular momentum inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0019","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":"sha256:3d3cf3f7d62dd42ad452e9b9c7fa081677341ee46d6e9599d4cbf2a216f7b896","target":"record","created_at":"2026-05-18T01:54:48Z","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":"2f20368ebd43b6fca49cd3217bc0ab730556b5af3e33183f594684131da9c4f4","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-31T21:24:58Z","title_canon_sha256":"eea3cf0d3c2ec03698ea98020229a60d15d2338c3569ff54bcc402e6c8aac014"},"schema_version":"1.0","source":{"id":"1209.0019","kind":"arxiv","version":1}},"canonical_sha256":"f9e24c9f42dd1e85c2179a93631da7b776b9ac8c381214dbcc5ec170223e3429","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9e24c9f42dd1e85c2179a93631da7b776b9ac8c381214dbcc5ec170223e3429","first_computed_at":"2026-05-18T01:54:48.788916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:48.788916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQAkth2EJeOdPY2i3ACbAQdECYNYy2eD9gNvEps1VNE1CS7Jm5ujTB0K2NIHLNVXv6HICvBIwSNXD1kM3N7iBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:48.789639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d3cf3f7d62dd42ad452e9b9c7fa081677341ee46d6e9599d4cbf2a216f7b896","sha256:023f929773ac6c7a33f39e822240eed454574ffa557e70cdd95cb8956c018011"],"state_sha256":"39259a85f467c7c482fde421dfc12a9ab981459698266b26d0468291be6c5b8e"}