{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7DK5CALU3NUS3LKEGPCWVXJPAF","short_pith_number":"pith:7DK5CALU","schema_version":"1.0","canonical_sha256":"f8d5d10174db692dad4433c56add2f01571a3ce3331df8beb44faefbbf86da9e","source":{"kind":"arxiv","id":"1904.05388","version":1},"attestation_state":"computed","paper":{"title":"On the rotational symmetry of 3-dimensional $\\kappa$-solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bruce Kleiner, Richard H. Bamler","submitted_at":"2019-04-10T18:48:28Z","abstract_excerpt":"In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional $\\kappa$-solutions. In this paper, we present an alternative proof for this fact and show that compact $\\kappa$-solutions are rotational symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows."},"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":"1904.05388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-10T18:48:28Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"59f208f34c7eee86559f085085f024e74c701eaada5e21db566b077b8583e98c","abstract_canon_sha256":"96756c86e76af27c5bc0181fb4ecbf71c3a024e6359f897cd4304dfb993b4a87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:49.693526Z","signature_b64":"rNsbT9ixM4RqVc3xcLL+oFWUj8LEsgI0xa51/mrTYWG0ZAC4/grOnQIgM3YBWGIBX6a+Nz2Mw0ViTMaduUWuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8d5d10174db692dad4433c56add2f01571a3ce3331df8beb44faefbbf86da9e","last_reissued_at":"2026-05-17T23:48:49.692880Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:49.692880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the rotational symmetry of 3-dimensional $\\kappa$-solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Bruce Kleiner, Richard H. Bamler","submitted_at":"2019-04-10T18:48:28Z","abstract_excerpt":"In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional $\\kappa$-solutions. In this paper, we present an alternative proof for this fact and show that compact $\\kappa$-solutions are rotational symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05388","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1904.05388","created_at":"2026-05-17T23:48:49.692979+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.05388v1","created_at":"2026-05-17T23:48:49.692979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05388","created_at":"2026-05-17T23:48:49.692979+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DK5CALU3NUS","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DK5CALU3NUS3LKE","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DK5CALU","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.11967","citing_title":"Unique asymptotics of ancient compact non-collapsed solutions to the 3-dimensional Ricci flow","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF","json":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF.json","graph_json":"https://pith.science/api/pith-number/7DK5CALU3NUS3LKEGPCWVXJPAF/graph.json","events_json":"https://pith.science/api/pith-number/7DK5CALU3NUS3LKEGPCWVXJPAF/events.json","paper":"https://pith.science/paper/7DK5CALU"},"agent_actions":{"view_html":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF","download_json":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF.json","view_paper":"https://pith.science/paper/7DK5CALU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.05388&json=true","fetch_graph":"https://pith.science/api/pith-number/7DK5CALU3NUS3LKEGPCWVXJPAF/graph.json","fetch_events":"https://pith.science/api/pith-number/7DK5CALU3NUS3LKEGPCWVXJPAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF/action/storage_attestation","attest_author":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF/action/author_attestation","sign_citation":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF/action/citation_signature","submit_replication":"https://pith.science/pith/7DK5CALU3NUS3LKEGPCWVXJPAF/action/replication_record"}},"created_at":"2026-05-17T23:48:49.692979+00:00","updated_at":"2026-05-17T23:48:49.692979+00:00"}