{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:SKDMHSVDUE2BZDGZAWUZSIILOH","short_pith_number":"pith:SKDMHSVD","canonical_record":{"source":{"id":"0910.4761","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-25T19:10:29Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e3f6267c0a618d773d755c94453b2b6e6ea5ef0efd88d5c2a36f5a28cfcd8d4b","abstract_canon_sha256":"b25d336d2f00ff86528394d33282a9f47191950d6ec673d0a86f469fb29c5b9f"},"schema_version":"1.0"},"canonical_sha256":"9286c3caa3a1341c8cd905a999210b71d376361152b849fe2a0ded4a12682c9c","source":{"kind":"arxiv","id":"0910.4761","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4761","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4761v7","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4761","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"SKDMHSVDUE2B","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SKDMHSVDUE2BZDGZ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SKDMHSVD","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:SKDMHSVDUE2BZDGZAWUZSIILOH","target":"record","payload":{"canonical_record":{"source":{"id":"0910.4761","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-25T19:10:29Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e3f6267c0a618d773d755c94453b2b6e6ea5ef0efd88d5c2a36f5a28cfcd8d4b","abstract_canon_sha256":"b25d336d2f00ff86528394d33282a9f47191950d6ec673d0a86f469fb29c5b9f"},"schema_version":"1.0"},"canonical_sha256":"9286c3caa3a1341c8cd905a999210b71d376361152b849fe2a0ded4a12682c9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:47.526813Z","signature_b64":"TEvu5guh43IJvEKuQTzntkS2fqyZwLlRtz4msrVM1Wr91odmmBM+s0o80k0Ym7kkBQJtj6b8d8Y8ECpENKfZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9286c3caa3a1341c8cd905a999210b71d376361152b849fe2a0ded4a12682c9c","last_reissued_at":"2026-05-18T03:11:47.526098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:47.526098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.4761","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PLmevMXmCmG7+wDEU3kOqziZV7/CDErEROPzb0ejanTMzsANt6bmPJD6IX72r1snoQ9M5uvlbzaQMtEieY5IBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:09:27.393648Z"},"content_sha256":"f765ebf3ef3f1f8465a69b1e477040e1e96b068d8a1c176d1a247549bedf6472","schema_version":"1.0","event_id":"sha256:f765ebf3ef3f1f8465a69b1e477040e1e96b068d8a1c176d1a247549bedf6472"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:SKDMHSVDUE2BZDGZAWUZSIILOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolution of the Weyl Tensor under the Ricci Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Carlo Mantegazza, Giovanni Catino","submitted_at":"2009-10-25T19:10:29Z","abstract_excerpt":"We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4761","kind":"arxiv","version":7},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9RJmo77Xk7GHLWNIT+86aLXxugkktQ27Liay7GMTr/qsoM4a2rFJUfpefKcoLkQSsti4tpnKQlbAeDZG+InAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:09:27.394676Z"},"content_sha256":"a8c77db1b7bde2fe0f5b33bf56b7124b428f9c42c0d27fd602cdcd1c3f141d57","schema_version":"1.0","event_id":"sha256:a8c77db1b7bde2fe0f5b33bf56b7124b428f9c42c0d27fd602cdcd1c3f141d57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKDMHSVDUE2BZDGZAWUZSIILOH/bundle.json","state_url":"https://pith.science/pith/SKDMHSVDUE2BZDGZAWUZSIILOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKDMHSVDUE2BZDGZAWUZSIILOH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T08:09:27Z","links":{"resolver":"https://pith.science/pith/SKDMHSVDUE2BZDGZAWUZSIILOH","bundle":"https://pith.science/pith/SKDMHSVDUE2BZDGZAWUZSIILOH/bundle.json","state":"https://pith.science/pith/SKDMHSVDUE2BZDGZAWUZSIILOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKDMHSVDUE2BZDGZAWUZSIILOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SKDMHSVDUE2BZDGZAWUZSIILOH","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":"b25d336d2f00ff86528394d33282a9f47191950d6ec673d0a86f469fb29c5b9f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-25T19:10:29Z","title_canon_sha256":"e3f6267c0a618d773d755c94453b2b6e6ea5ef0efd88d5c2a36f5a28cfcd8d4b"},"schema_version":"1.0","source":{"id":"0910.4761","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4761","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4761v7","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4761","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"SKDMHSVDUE2B","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SKDMHSVDUE2BZDGZ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SKDMHSVD","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:a8c77db1b7bde2fe0f5b33bf56b7124b428f9c42c0d27fd602cdcd1c3f141d57","target":"graph","created_at":"2026-05-18T03:11:47Z","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 compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.","authors_text":"Carlo Mantegazza, Giovanni Catino","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-25T19:10:29Z","title":"Evolution of the Weyl Tensor under the Ricci Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4761","kind":"arxiv","version":7},"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:f765ebf3ef3f1f8465a69b1e477040e1e96b068d8a1c176d1a247549bedf6472","target":"record","created_at":"2026-05-18T03:11:47Z","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":"b25d336d2f00ff86528394d33282a9f47191950d6ec673d0a86f469fb29c5b9f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-25T19:10:29Z","title_canon_sha256":"e3f6267c0a618d773d755c94453b2b6e6ea5ef0efd88d5c2a36f5a28cfcd8d4b"},"schema_version":"1.0","source":{"id":"0910.4761","kind":"arxiv","version":7}},"canonical_sha256":"9286c3caa3a1341c8cd905a999210b71d376361152b849fe2a0ded4a12682c9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9286c3caa3a1341c8cd905a999210b71d376361152b849fe2a0ded4a12682c9c","first_computed_at":"2026-05-18T03:11:47.526098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:47.526098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TEvu5guh43IJvEKuQTzntkS2fqyZwLlRtz4msrVM1Wr91odmmBM+s0o80k0Ym7kkBQJtj6b8d8Y8ECpENKfZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:47.526813Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.4761","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f765ebf3ef3f1f8465a69b1e477040e1e96b068d8a1c176d1a247549bedf6472","sha256:a8c77db1b7bde2fe0f5b33bf56b7124b428f9c42c0d27fd602cdcd1c3f141d57"],"state_sha256":"3477ad6121f07c8f87ad03fcb754f8845af825502dc1b1cf11dc6fb191a7c908"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4FRztEnMhzsKQ9Zp8rOplk1wuB97Nv/3sVlhg78+WrtGVD7P3F6MyQZu+8wG+MoV3IZiu2RTsPrz8fKE1Z6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:09:27.398233Z","bundle_sha256":"ff8770dd8dbab81e2ed96de0499c570afcc78f50869257ca04a5838905b8180d"}}