{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LCNAESGKJWDV4Y3XQK5ZX4HEZ2","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":"2b60011c28f99da38bbb666310f11f4e46cfce61cfa81d0f4f2ecf4fe85e873d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-14T13:45:10Z","title_canon_sha256":"d3172ded97de39738f4cc1508669b4c203f66213ab821c3277cb9fea4585f2f1"},"schema_version":"1.0","source":{"id":"1303.3446","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3446","created_at":"2026-05-18T03:19:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3446v2","created_at":"2026-05-18T03:19:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3446","created_at":"2026-05-18T03:19:43Z"},{"alias_kind":"pith_short_12","alias_value":"LCNAESGKJWDV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LCNAESGKJWDV4Y3X","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LCNAESGK","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:4583a888f8ea3c51d88278902fea5cf1d68aa2996e2263dfc8f30fac21570e4d","target":"graph","created_at":"2026-05-18T03:19:43Z","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":"Let $(M^n,g,\\nabla f)$, $n\\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\\mathbb{S}^{n-1}(c))$ where $\\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of curvature $1/c^2$, with $c\\in(0,1)$. We prove that if the convergence to the asymptotic cone is smooth, $(M^n,g,\\nabla f)$ is rotationally symmetric. This is the expanding analogue of the Perelman conjecture on the Bryant soliton and this work is based on the proof by Brendle \\cite{Bre-Rot-3d}. This has also been proved recently by Chodosh \\cite{Cho-EGS}.","authors_text":"Alix Deruelle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-14T13:45:10Z","title":"Rotational symmetry of non negatively curved expanding gradient Ricci solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3446","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":"sha256:4c20055ced2120ba2d5db8a7853179bc1d0e111e37fd1627b37c207a0c96aecd","target":"record","created_at":"2026-05-18T03:19:43Z","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":"2b60011c28f99da38bbb666310f11f4e46cfce61cfa81d0f4f2ecf4fe85e873d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-14T13:45:10Z","title_canon_sha256":"d3172ded97de39738f4cc1508669b4c203f66213ab821c3277cb9fea4585f2f1"},"schema_version":"1.0","source":{"id":"1303.3446","kind":"arxiv","version":2}},"canonical_sha256":"589a0248ca4d875e637782bb9bf0e4ceb433bcb02db218200537e2484dcbd70b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"589a0248ca4d875e637782bb9bf0e4ceb433bcb02db218200537e2484dcbd70b","first_computed_at":"2026-05-18T03:19:43.847497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:43.847497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gn05xCiiEUVRLOP21DTGEvF6wnruV/GufacoNtbIfAbwR752oomkWfsVOPLAYPO37ofXj+i9q12wQyUPsoKoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:43.848234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3446","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c20055ced2120ba2d5db8a7853179bc1d0e111e37fd1627b37c207a0c96aecd","sha256:4583a888f8ea3c51d88278902fea5cf1d68aa2996e2263dfc8f30fac21570e4d"],"state_sha256":"bcf2977e38f19c4a87e4d0f5c314c206e4704583a60f8b7d3145f7bb024677c6"}