{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GD7LVQ7OWUMVWHW5OBX7DVIBVX","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":"f7940b8eb2198dbebe4210dbd65b57b8c9371a298443407def556c018e85375a","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-06T14:35:16Z","title_canon_sha256":"3a5a281155e34f92ec878700186ce3be9da125fe43235c880fa673f5d1dda954"},"schema_version":"1.0","source":{"id":"1101.1226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1226","created_at":"2026-05-18T04:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1226v2","created_at":"2026-05-18T04:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1226","created_at":"2026-05-18T04:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"GD7LVQ7OWUMV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GD7LVQ7OWUMVWHW5","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GD7LVQ7O","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:0f2be1fdb710fb46f99f809794169a923f7cb3ef7ce7433f1709cde208747e27","target":"graph","created_at":"2026-05-18T04:14:47Z","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 the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with conical initial data. In the second part, we define a geometric invariant lambda_AF for asymptotically flat manifolds with nonnegative scalar curvature. This invariant gives a quantitative lower bound for the ADM-mass from general relativity, motivates a Ricci flow proof of the r","authors_text":"Robert Haslhofer","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-06T14:35:16Z","title":"A renormalized Perelman-functional and a lower bound for the ADM-mass"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1226","kind":"arxiv","version":2},"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":"sha256:7cdb391d2d8747790c1d40313190e3b87e80b76baf6ac4ffe4ae9b7b55bfe2b1","target":"record","created_at":"2026-05-18T04:14:47Z","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":"f7940b8eb2198dbebe4210dbd65b57b8c9371a298443407def556c018e85375a","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-06T14:35:16Z","title_canon_sha256":"3a5a281155e34f92ec878700186ce3be9da125fe43235c880fa673f5d1dda954"},"schema_version":"1.0","source":{"id":"1101.1226","kind":"arxiv","version":2}},"canonical_sha256":"30febac3eeb5195b1edd706ff1d501addaf7cbfa75deca2b7e4b9837b327c5dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30febac3eeb5195b1edd706ff1d501addaf7cbfa75deca2b7e4b9837b327c5dd","first_computed_at":"2026-05-18T04:14:47.288323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:47.288323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqQIsZuedNYMfl8veQhyJX4FiVQLWMWEy1k66rjs8er2KlwQWA10c6Uir09EbkFXtNCEf+RkGLqnGuNeCYKoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:47.288800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cdb391d2d8747790c1d40313190e3b87e80b76baf6ac4ffe4ae9b7b55bfe2b1","sha256:0f2be1fdb710fb46f99f809794169a923f7cb3ef7ce7433f1709cde208747e27"],"state_sha256":"5d466f741575e9ff4663b7da83add570a5f72c5ff133159921734bed010b6cc8"}