{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2SGFCS3F73EJNN5LPBOYPLR5A6","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":"28b5a05c8bdb859a73ed0fe7c69bf2c32345a115b3bcc03fd2f0dee37c506704","cross_cats_sorted":["math.AP","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-24T21:29:26Z","title_canon_sha256":"5a666a9cbe4ee11580021126f8227f776d94d129cafb75c35a967fab14be8ebc"},"schema_version":"1.0","source":{"id":"1411.6655","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6655","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6655v2","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6655","created_at":"2026-05-18T00:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"2SGFCS3F73EJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2SGFCS3F73EJNN5L","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2SGFCS3F","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:e0b0eda52ff96913b86b5a0361df823c9bb57e603c1827fe111b9362ecb52982","target":"graph","created_at":"2026-05-18T00:21:00Z","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":"This is the first of a series of papers on the long-time behavior of 3 dimensional Ricci flows with surgery. In this paper we first fix a notion of Ricci flows with surgery, which will be used in this and the following three papers. Then we review Perelman's long-time estimates and generalize them to the case in which the underlying manifold is allowed to have a boundary. Eventually, making use of Perelman's techniques, we prove new long-time estimates, which hold whenever the metric is sufficiently collapsed.","authors_text":"Richard H. Bamler","cross_cats":["math.AP","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-24T21:29:26Z","title":"Long-time behavior of 3 dimensional Ricci flow -- A: Generalizations of Perelman's long-time estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6655","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:c12bea92e04fc5e3b96e6dc2604ed253ab5d47e444dde7a7a1450add0714ba81","target":"record","created_at":"2026-05-18T00:21:00Z","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":"28b5a05c8bdb859a73ed0fe7c69bf2c32345a115b3bcc03fd2f0dee37c506704","cross_cats_sorted":["math.AP","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-24T21:29:26Z","title_canon_sha256":"5a666a9cbe4ee11580021126f8227f776d94d129cafb75c35a967fab14be8ebc"},"schema_version":"1.0","source":{"id":"1411.6655","kind":"arxiv","version":2}},"canonical_sha256":"d48c514b65fec896b7ab785d87ae3d07ae612050a394502346242876fa70599c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d48c514b65fec896b7ab785d87ae3d07ae612050a394502346242876fa70599c","first_computed_at":"2026-05-18T00:21:00.729362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:00.729362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8YDeh5nBaVkmezQqaQ+WG8x7qEMFnBHQuvJH9l47WET0jYVfeZFKHYIUVQZhvlCIvTMqchVnHmqoATFvDEPgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:00.729859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6655","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c12bea92e04fc5e3b96e6dc2604ed253ab5d47e444dde7a7a1450add0714ba81","sha256:e0b0eda52ff96913b86b5a0361df823c9bb57e603c1827fe111b9362ecb52982"],"state_sha256":"b878696f97e32d1ed11a6581ac7e2eaf00f58a55590bda9c104fb4efd9766ce3"}