{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LG4EH4MPEDLSAF3SGEZEVXBZUH","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":"a5e05f026452b81ce0df7d8c2a0da57ab25ab32c60ee62c1c30264b8e2d78397","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-27T16:47:03Z","title_canon_sha256":"b6fe2e7220871054b2099cad48f1b9df8547f6d5388de30dacfee023496d411f"},"schema_version":"1.0","source":{"id":"1410.7303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7303","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7303v1","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7303","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"LG4EH4MPEDLS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LG4EH4MPEDLSAF3S","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LG4EH4MP","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:29fd05fe97d2d8a0748453f332c6448f94b1e956c9a5b18b9d518df9c66ab5cf","target":"graph","created_at":"2026-05-18T02:39:17Z","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":"We prove that a four-dimensional gradient shrinking Ricci soliton with $\\delta W^{\\pm}=0$ is either Einstein, or a finite quotient of $S^3\\times\\mathbb{R}$, $S^2\\times\\mathbb{R}^2$ or $\\mathbb{R}^4$. We also prove that a four-dimensional cscK gradient Ricci soliton is either K\\\"ahler-Einstein, or a finite quotient of $M\\times\\mathbb{C}$, where $M$ is a Riemann surface. The main arguments are curvature decompositions, the Weitzenb\\\"ock formula for half Weyl curvature, and the maximum principle.","authors_text":"Jia-Yong Wu, Peng Wu, William Wylie","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-27T16:47:03Z","title":"Gradient shrinking Ricci solitons of half harmonic Weyl curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7303","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:a566606928a956f21526ce0bb28866b2f6a86d56712f009c72df6df3bc7c9d26","target":"record","created_at":"2026-05-18T02:39:17Z","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":"a5e05f026452b81ce0df7d8c2a0da57ab25ab32c60ee62c1c30264b8e2d78397","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2014-10-27T16:47:03Z","title_canon_sha256":"b6fe2e7220871054b2099cad48f1b9df8547f6d5388de30dacfee023496d411f"},"schema_version":"1.0","source":{"id":"1410.7303","kind":"arxiv","version":1}},"canonical_sha256":"59b843f18f20d720177231324adc39a1e3f6fd4d19694fb1f86df9689bb2973b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59b843f18f20d720177231324adc39a1e3f6fd4d19694fb1f86df9689bb2973b","first_computed_at":"2026-05-18T02:39:17.624764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:17.624764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MuWGPTQ4jcFyb9CuNy6Zu31A5/VEB0kMtEcHgQ7z6BIB7PjC0Vnb1dxvsAsDV+c2Z4e/ugu/SA8B2IEirqN5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:17.625264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a566606928a956f21526ce0bb28866b2f6a86d56712f009c72df6df3bc7c9d26","sha256:29fd05fe97d2d8a0748453f332c6448f94b1e956c9a5b18b9d518df9c66ab5cf"],"state_sha256":"0859082faed049bb13d0109bd09fd5fce8c5ee639648b88d0fdd426bf6d1b7f1"}