{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:X5MOSSWM3O2VDEUFJ76XQM2O7A","short_pith_number":"pith:X5MOSSWM","canonical_record":{"source":{"id":"0705.4048","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-05-28T14:06:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a661acd4daabbd5c74d051e1830d06035ecb56c4781dbfb9a48db341e645b844","abstract_canon_sha256":"4d63c2b942b2c0a208d015925667e28c4da4cd5706224b0b84c2f31a4a4c1082"},"schema_version":"1.0"},"canonical_sha256":"bf58e94accdbb55192854ffd78334ef821ea362f7c960424aa16ef80433f9023","source":{"kind":"arxiv","id":"0705.4048","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.4048","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"0705.4048v2","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.4048","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"X5MOSSWM3O2V","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"X5MOSSWM3O2VDEUF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"X5MOSSWM","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:X5MOSSWM3O2VDEUFJ76XQM2O7A","target":"record","payload":{"canonical_record":{"source":{"id":"0705.4048","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-05-28T14:06:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a661acd4daabbd5c74d051e1830d06035ecb56c4781dbfb9a48db341e645b844","abstract_canon_sha256":"4d63c2b942b2c0a208d015925667e28c4da4cd5706224b0b84c2f31a4a4c1082"},"schema_version":"1.0"},"canonical_sha256":"bf58e94accdbb55192854ffd78334ef821ea362f7c960424aa16ef80433f9023","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:00.103247Z","signature_b64":"iQxnLD66Q2Mg+8WTM0yzhBYrP98gCgYY1Afahtsp6e+22pvI4HlO18k8kaOaJlZXMNELIWu3mU0FwMtweUFZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf58e94accdbb55192854ffd78334ef821ea362f7c960424aa16ef80433f9023","last_reissued_at":"2026-05-17T23:58:00.102671Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:00.102671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.4048","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJX0fTgaAutyd9COfe8aELp+qqGsj/+RzB1GrQOo1jxHq75kLJAlZNnmk1SMUzoND4rG7Mp0rIQJliyKYoYXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T15:39:55.470286Z"},"content_sha256":"5d41ee1d7a459dc65e5aaf93c80441a03890863f0ee148b16bc14505993c965f","schema_version":"1.0","event_id":"sha256:5d41ee1d7a459dc65e5aaf93c80441a03890863f0ee148b16bc14505993c965f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:X5MOSSWM3O2VDEUFJ76XQM2O7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The K\\\"ahler-Ricci flow and the $\\bar\\partial$ operator on vector fields","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ben Weinkove, D.H. Phong, Jacob Sturm, Jian Song","submitted_at":"2007-05-28T14:06:38Z","abstract_excerpt":"The limiting behavior of the normalized K\\\"ahler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi K-energy is bounded from below, then the scalar curvature converges uniformly to a constant. Second, it is shown that if the Mabuchi K-energy is bounded from below and if the lowest positive eigenvalue of the $\\bar\\partial^\\dagger \\bar\\partial$ operator on smooth vector fields is bounded away from 0 along the flow, then the metrics converge exponentially fast in $C^\\infty$ to a K\\\"ahler-Einstein metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4048","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1T3s5SULhvF+uaNcu8L2Xp3ghLGcoNNbjKCo9ZPDURjOSwC59kQkHQAv8wo/gqG/P7JS3kDxffHlqIvlpP/4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T15:39:55.470650Z"},"content_sha256":"5f10a5c29743ad4a54640d4dc9a2c564462b093b73f63f407e10f3027aa98c8e","schema_version":"1.0","event_id":"sha256:5f10a5c29743ad4a54640d4dc9a2c564462b093b73f63f407e10f3027aa98c8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A/bundle.json","state_url":"https://pith.science/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A/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":"2026-06-25T15:39:55Z","links":{"resolver":"https://pith.science/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A","bundle":"https://pith.science/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A/bundle.json","state":"https://pith.science/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5MOSSWM3O2VDEUFJ76XQM2O7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:X5MOSSWM3O2VDEUFJ76XQM2O7A","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":"4d63c2b942b2c0a208d015925667e28c4da4cd5706224b0b84c2f31a4a4c1082","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.DG","submitted_at":"2007-05-28T14:06:38Z","title_canon_sha256":"a661acd4daabbd5c74d051e1830d06035ecb56c4781dbfb9a48db341e645b844"},"schema_version":"1.0","source":{"id":"0705.4048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.4048","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"0705.4048v2","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.4048","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"X5MOSSWM3O2V","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"X5MOSSWM3O2VDEUF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"X5MOSSWM","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:5f10a5c29743ad4a54640d4dc9a2c564462b093b73f63f407e10f3027aa98c8e","target":"graph","created_at":"2026-05-17T23:58:00Z","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":"The limiting behavior of the normalized K\\\"ahler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi K-energy is bounded from below, then the scalar curvature converges uniformly to a constant. Second, it is shown that if the Mabuchi K-energy is bounded from below and if the lowest positive eigenvalue of the $\\bar\\partial^\\dagger \\bar\\partial$ operator on smooth vector fields is bounded away from 0 along the flow, then the metrics converge exponentially fast in $C^\\infty$ to a K\\\"ahler-Einstein metric.","authors_text":"Ben Weinkove, D.H. Phong, Jacob Sturm, Jian Song","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-05-28T14:06:38Z","title":"The K\\\"ahler-Ricci flow and the $\\bar\\partial$ operator on vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4048","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":"sha256:5d41ee1d7a459dc65e5aaf93c80441a03890863f0ee148b16bc14505993c965f","target":"record","created_at":"2026-05-17T23:58:00Z","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":"4d63c2b942b2c0a208d015925667e28c4da4cd5706224b0b84c2f31a4a4c1082","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.DG","submitted_at":"2007-05-28T14:06:38Z","title_canon_sha256":"a661acd4daabbd5c74d051e1830d06035ecb56c4781dbfb9a48db341e645b844"},"schema_version":"1.0","source":{"id":"0705.4048","kind":"arxiv","version":2}},"canonical_sha256":"bf58e94accdbb55192854ffd78334ef821ea362f7c960424aa16ef80433f9023","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf58e94accdbb55192854ffd78334ef821ea362f7c960424aa16ef80433f9023","first_computed_at":"2026-05-17T23:58:00.102671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:00.102671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iQxnLD66Q2Mg+8WTM0yzhBYrP98gCgYY1Afahtsp6e+22pvI4HlO18k8kaOaJlZXMNELIWu3mU0FwMtweUFZDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:00.103247Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.4048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d41ee1d7a459dc65e5aaf93c80441a03890863f0ee148b16bc14505993c965f","sha256:5f10a5c29743ad4a54640d4dc9a2c564462b093b73f63f407e10f3027aa98c8e"],"state_sha256":"7b94c9bd6892c3a7bb0c29339efa8565bd11a9fc951d2fddeb60541461099fb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEOENvf8JtoxrDXXfDTCZnJzbeQg8Cu5ViBHRMk/lrts7xHJ0hE3Y+PGriculrCGyjRhAToAoNuTSFvKjezxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T15:39:55.472644Z","bundle_sha256":"3dc7846dcf88d863ebf62bb477e8d9d9335acf651cbcf67a96e32a19e8685218"}}