{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P5OMYLWLURTMOL3TABLX2MSM3J","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":"83354d38b1db69fb584da3338aeb6b6e4c01b98a52afb9ff0c5cca1f6c33181f","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-04T11:02:49Z","title_canon_sha256":"260594aa6760bb19e2348cb24378644d51a47c198b4288b13ab907c51fecfa96"},"schema_version":"1.0","source":{"id":"1506.01545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01545","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01545v1","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01545","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"pith_short_12","alias_value":"P5OMYLWLURTM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P5OMYLWLURTMOL3T","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P5OMYLWL","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:c3c8de6831df80053492fa6650262135a1c23e5e9a5949fb2b2998367f66e23c","target":"graph","created_at":"2026-05-18T01:32:29Z","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 work we obtain the limit of the Hawking energy of a large class of foliations along general null hypersurfaces $\\Omega$ satisfying a weak notion of asymptotic flatness. The foliations are not required to be either geodesic or approaching large spheres at infinity. The limit is obtained in terms of a reference background geodesic foliation approaching large spheres and a positive function, constant along the null generators on $\\Omega$, which describes the relation between the two foliations at infinity. The integrand in the limit expression has interesting covariance and invariance pro","authors_text":"Alberto Soria, Marc Mars","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-04T11:02:49Z","title":"The asymptotic behaviour of the Hawking energy along null asymptotically flat hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01545","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:c6dc1843dd59a99fee22294f445f1e50c9adec08643539ebc0273c96897f79d8","target":"record","created_at":"2026-05-18T01:32:29Z","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":"83354d38b1db69fb584da3338aeb6b6e4c01b98a52afb9ff0c5cca1f6c33181f","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-06-04T11:02:49Z","title_canon_sha256":"260594aa6760bb19e2348cb24378644d51a47c198b4288b13ab907c51fecfa96"},"schema_version":"1.0","source":{"id":"1506.01545","kind":"arxiv","version":1}},"canonical_sha256":"7f5ccc2ecba466c72f7300577d324cda79722718d3312d12c8249beb89c048ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f5ccc2ecba466c72f7300577d324cda79722718d3312d12c8249beb89c048ca","first_computed_at":"2026-05-18T01:32:29.255849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:29.255849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Nr7Nx5dwI70RhtnB5+sDg717VGQJqPDEIrX8ZfzmMO9IVeVfyRmjotNo8rYrzN4FUCyZg5QPOjecCuf7iNbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:29.256307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6dc1843dd59a99fee22294f445f1e50c9adec08643539ebc0273c96897f79d8","sha256:c3c8de6831df80053492fa6650262135a1c23e5e9a5949fb2b2998367f66e23c"],"state_sha256":"ed5736892435dd85fb5ff63d1174e97d089e3ccb37fcde43b68af48ad17202ca"}