{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2RG6XBUMJVN5BRD26X5RFVD5SY","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":"3d5a8ac481dba337a669464e0b041f7d57d67de3a6f5a575c58f99b0713de187","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-02-12T15:34:01Z","title_canon_sha256":"12989600524250f1eb6ec79e78523df18c9369c1cc814c2a135bc153e235df72"},"schema_version":"1.0","source":{"id":"2502.08500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08500","created_at":"2026-07-05T10:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08500v1","created_at":"2026-07-05T10:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08500","created_at":"2026-07-05T10:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"2RG6XBUMJVN5","created_at":"2026-07-05T10:13:23Z"},{"alias_kind":"pith_short_16","alias_value":"2RG6XBUMJVN5BRD2","created_at":"2026-07-05T10:13:23Z"},{"alias_kind":"pith_short_8","alias_value":"2RG6XBUM","created_at":"2026-07-05T10:13:23Z"}],"graph_snapshots":[{"event_id":"sha256:28cce65e84cc3d0257a6ab10e171a8703e37453834e80e2e26fc7fe76d184908","target":"graph","created_at":"2026-07-05T10:13:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.08500/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We demonstrate that any four-dimensional shrinking Ricci soliton $(\\mathcal B \\times {\\mathbb S^2}, g)$, where $\\mathcal B$ is any two-dimensional complete noncompact surface and $g$ is a warped product metric over the base $\\mathcal B$, has to be isometric to the generalized cylinder $\\mathbb R^2\\times\\mathbb S^2$ equipped with the standard cylindrical metric. After completing this classification, we study Ricci flow solutions that are multiply warped products -- but not products -- and provide rigorous examples of the formation of generalized cylinder singularity models $\\mathbb R^k\\times\\ma","authors_text":"Dan Knopf, James Isenberg, Natasa Sesum, Zilu Ma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-02-12T15:34:01Z","title":"Local singularities of compact multiply warped Ricci flow solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08500","kind":"arxiv","version":1},"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":"sha256:14af8ac292d01762785050fce795d2d0ec11a84e7f0e2cb6e0516bc311072b5e","target":"record","created_at":"2026-07-05T10:13:23Z","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":"3d5a8ac481dba337a669464e0b041f7d57d67de3a6f5a575c58f99b0713de187","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-02-12T15:34:01Z","title_canon_sha256":"12989600524250f1eb6ec79e78523df18c9369c1cc814c2a135bc153e235df72"},"schema_version":"1.0","source":{"id":"2502.08500","kind":"arxiv","version":1}},"canonical_sha256":"d44deb868c4d5bd0c47af5fb12d47d963e0e5ff3b8ef42ca057d3a87b4c749c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d44deb868c4d5bd0c47af5fb12d47d963e0e5ff3b8ef42ca057d3a87b4c749c6","first_computed_at":"2026-07-05T10:13:23.902341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:23.902341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v+7Sz7358LPLnjtmhvW3EoTL6J5we1j+aYSuAyVjKaCvyW0fwinS984xEy6aJ0SqwgODkW5br9ZYR2RLod1VBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:23.902938Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14af8ac292d01762785050fce795d2d0ec11a84e7f0e2cb6e0516bc311072b5e","sha256:28cce65e84cc3d0257a6ab10e171a8703e37453834e80e2e26fc7fe76d184908"],"state_sha256":"4db4c8c53915e32d9f886a7fdbc663e4dfe1a5c06ed532de1229fe62c4f67386"}