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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}."},"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":"1303.3446","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-14T13:45:10Z","cross_cats_sorted":[],"title_canon_sha256":"d3172ded97de39738f4cc1508669b4c203f66213ab821c3277cb9fea4585f2f1","abstract_canon_sha256":"2b60011c28f99da38bbb666310f11f4e46cfce61cfa81d0f4f2ecf4fe85e873d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:43.848234Z","signature_b64":"gn05xCiiEUVRLOP21DTGEvF6wnruV/GufacoNtbIfAbwR752oomkWfsVOPLAYPO37ofXj+i9q12wQyUPsoKoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"589a0248ca4d875e637782bb9bf0e4ceb433bcb02db218200537e2484dcbd70b","last_reissued_at":"2026-05-18T03:19:43.847497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:43.847497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotational symmetry of non negatively curved expanding gradient Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alix Deruelle","submitted_at":"2013-03-14T13:45:10Z","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}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3446","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":""},"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":"1303.3446","created_at":"2026-05-18T03:19:43.847626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3446v2","created_at":"2026-05-18T03:19:43.847626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3446","created_at":"2026-05-18T03:19:43.847626+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCNAESGKJWDV","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCNAESGKJWDV4Y3X","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCNAESGK","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2","json":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2.json","graph_json":"https://pith.science/api/pith-number/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/graph.json","events_json":"https://pith.science/api/pith-number/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/events.json","paper":"https://pith.science/paper/LCNAESGK"},"agent_actions":{"view_html":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2","download_json":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2.json","view_paper":"https://pith.science/paper/LCNAESGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3446&json=true","fetch_graph":"https://pith.science/api/pith-number/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/graph.json","fetch_events":"https://pith.science/api/pith-number/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/action/storage_attestation","attest_author":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/action/author_attestation","sign_citation":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/action/citation_signature","submit_replication":"https://pith.science/pith/LCNAESGKJWDV4Y3XQK5ZX4HEZ2/action/replication_record"}},"created_at":"2026-05-18T03:19:43.847626+00:00","updated_at":"2026-05-18T03:19:43.847626+00:00"}