{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:YWPNH3ADRLXEEL22THFZHZXKGB","short_pith_number":"pith:YWPNH3AD","schema_version":"1.0","canonical_sha256":"c59ed3ec038aee422f5a99cb93e6ea3075cc1b504ba5f0b08990529bf932894d","source":{"kind":"arxiv","id":"2110.03412","version":2},"attestation_state":"computed","paper":{"title":"Uniqueness and stability of singular Ricci flows in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Robert Haslhofer","submitted_at":"2021-10-07T12:56:04Z","abstract_excerpt":"In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical neighborhood property. In particular, this gives a canonical evolution through singularities for manifolds with positive isotropic curvature. The new ingredients we use are the recent classification of higher dimensional $\\kappa$-solutions by Brendle, Daskalopoulos, Naff and Sesum, and the maximum principle for the linearized Ricci-DeTurck flow on locally conformal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.03412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-10-07T12:56:04Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"07c26ae1639a32778c8dd2dfd2ca6ad70381b7bb04ceb51c8fab94fa2a7a7e5f","abstract_canon_sha256":"b2355ebca97ace1c42987bfb8dc049c3ee857d8e6190aac9fde52b2d3ce05b8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:22:24.342864Z","signature_b64":"7/p16G5xasUMnRcr8uMbcQP10Q01AUNZdW7m9IFrQEmJg0b2PK01LUzJfgXeo+tJkvn06Pl3CbqEBm/rNA91AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c59ed3ec038aee422f5a99cb93e6ea3075cc1b504ba5f0b08990529bf932894d","last_reissued_at":"2026-07-05T03:22:24.342478Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:22:24.342478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness and stability of singular Ricci flows in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Robert Haslhofer","submitted_at":"2021-10-07T12:56:04Z","abstract_excerpt":"In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical neighborhood property. In particular, this gives a canonical evolution through singularities for manifolds with positive isotropic curvature. The new ingredients we use are the recent classification of higher dimensional $\\kappa$-solutions by Brendle, Daskalopoulos, Naff and Sesum, and the maximum principle for the linearized Ricci-DeTurck flow on locally conformal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03412","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.03412/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.03412","created_at":"2026-07-05T03:22:24.342534+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.03412v2","created_at":"2026-07-05T03:22:24.342534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03412","created_at":"2026-07-05T03:22:24.342534+00:00"},{"alias_kind":"pith_short_12","alias_value":"YWPNH3ADRLXE","created_at":"2026-07-05T03:22:24.342534+00:00"},{"alias_kind":"pith_short_16","alias_value":"YWPNH3ADRLXEEL22","created_at":"2026-07-05T03:22:24.342534+00:00"},{"alias_kind":"pith_short_8","alias_value":"YWPNH3AD","created_at":"2026-07-05T03:22:24.342534+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13204","citing_title":"Preserving curvature lower bounds when Ricci flowing non-smooth initial data","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB","json":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB.json","graph_json":"https://pith.science/api/pith-number/YWPNH3ADRLXEEL22THFZHZXKGB/graph.json","events_json":"https://pith.science/api/pith-number/YWPNH3ADRLXEEL22THFZHZXKGB/events.json","paper":"https://pith.science/paper/YWPNH3AD"},"agent_actions":{"view_html":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB","download_json":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB.json","view_paper":"https://pith.science/paper/YWPNH3AD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.03412&json=true","fetch_graph":"https://pith.science/api/pith-number/YWPNH3ADRLXEEL22THFZHZXKGB/graph.json","fetch_events":"https://pith.science/api/pith-number/YWPNH3ADRLXEEL22THFZHZXKGB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB/action/storage_attestation","attest_author":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB/action/author_attestation","sign_citation":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB/action/citation_signature","submit_replication":"https://pith.science/pith/YWPNH3ADRLXEEL22THFZHZXKGB/action/replication_record"}},"created_at":"2026-07-05T03:22:24.342534+00:00","updated_at":"2026-07-05T03:22:24.342534+00:00"}