{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OGOZELDI2ENKMVK27XMPXJO7ME","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":"9a85a91830c1997e2aebc85b511ad5e35d65d35972845283ecde1be539d1d9a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-05-10T18:25:28Z","title_canon_sha256":"f316d00ac16b5f276b4cd069b80eb997c58b136ef8f054ccbd2df069a7e62be7"},"schema_version":"1.0","source":{"id":"1005.1624","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1624","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1624v2","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1624","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"OGOZELDI2ENK","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OGOZELDI2ENKMVK2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OGOZELDI","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:b4f98b894094b633e488d124cfe42acc87899546aef54fb3229c7b9a0b805aac","target":"graph","created_at":"2026-05-18T01:30:26Z","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":"We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow.","authors_text":"Joerg Enders, Peter M. Topping, Reto M\\\"uller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-05-10T18:25:28Z","title":"On Type I Singularities in Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1624","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":"sha256:9395bebcfed59ae0d691bddeb20c2ba241d147993a955ad897bba547e6947e22","target":"record","created_at":"2026-05-18T01:30:26Z","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":"9a85a91830c1997e2aebc85b511ad5e35d65d35972845283ecde1be539d1d9a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-05-10T18:25:28Z","title_canon_sha256":"f316d00ac16b5f276b4cd069b80eb997c58b136ef8f054ccbd2df069a7e62be7"},"schema_version":"1.0","source":{"id":"1005.1624","kind":"arxiv","version":2}},"canonical_sha256":"719d922c68d11aa6555afdd8fba5df6117829b23f9f730fbce5540b9a5d722d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"719d922c68d11aa6555afdd8fba5df6117829b23f9f730fbce5540b9a5d722d7","first_computed_at":"2026-05-18T01:30:26.269420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:26.269420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JD3PimGdA71Kg4ks/hQbfUOr/kKqxdjfg5v+HHn4GB2S0Db4DikOopJAODPbgn9WPtnF962ZG3/vyncB+FO4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:26.270108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1624","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9395bebcfed59ae0d691bddeb20c2ba241d147993a955ad897bba547e6947e22","sha256:b4f98b894094b633e488d124cfe42acc87899546aef54fb3229c7b9a0b805aac"],"state_sha256":"0b91b025f04d58e19dc4f38a55f77e30aacfea89371bc1e3c81a057f27cf9683"}