{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:EJUODLRKE4DYNUMCXFAUO5NZIC","short_pith_number":"pith:EJUODLRK","canonical_record":{"source":{"id":"0710.3919","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-10-22T03:18:35Z","cross_cats_sorted":[],"title_canon_sha256":"29273cee26e4e7a48250263e898f931f5830547e052b0e3abd11041b49278f43","abstract_canon_sha256":"d50d92859ddb35161129cbb346cb16626063dcfff6ee2a20b88b79c7de5bfbf1"},"schema_version":"1.0"},"canonical_sha256":"2268e1ae2a270786d182b9414775b940bee0b2252508fa8876fbf76558922e12","source":{"kind":"arxiv","id":"0710.3919","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3919","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3919v2","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3919","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"EJUODLRKE4DY","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"EJUODLRKE4DYNUMC","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"EJUODLRK","created_at":"2026-07-04T15:09:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:EJUODLRKE4DYNUMCXFAUO5NZIC","target":"record","payload":{"canonical_record":{"source":{"id":"0710.3919","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-10-22T03:18:35Z","cross_cats_sorted":[],"title_canon_sha256":"29273cee26e4e7a48250263e898f931f5830547e052b0e3abd11041b49278f43","abstract_canon_sha256":"d50d92859ddb35161129cbb346cb16626063dcfff6ee2a20b88b79c7de5bfbf1"},"schema_version":"1.0"},"canonical_sha256":"2268e1ae2a270786d182b9414775b940bee0b2252508fa8876fbf76558922e12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:09:54.528438Z","signature_b64":"prFPuzjLottSXqsY4d4j/uwp8wauLixCy6M2g+42gbHVAPiVDMSo0RrWoi3TvBlJWVJ3afxsEUbTWvGc5mhOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2268e1ae2a270786d182b9414775b940bee0b2252508fa8876fbf76558922e12","last_reissued_at":"2026-07-04T15:09:54.528028Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:09:54.528028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.3919","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":"2026-07-04T15:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4lD7pGwPr/5f9+/tl3luo0HU5GHThHlBbJyQdAvFI26QnLCCHgoTjrKKJM1ftZuSNHOYvDC53DX03cw6gf6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:53:39.647617Z"},"content_sha256":"a95651e157bac71bb18b6e3b0bd3359b2b56c86a15e1149070cef18f386ad297","schema_version":"1.0","event_id":"sha256:a95651e157bac71bb18b6e3b0bd3359b2b56c86a15e1149070cef18f386ad297"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:EJUODLRKE4DYNUMCXFAUO5NZIC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounding sectional curvature along a K\\\"ahler-Ricci flow","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wei-Dong Ruan, Yuguang Zhang, Zhenlei Zhang","submitted_at":"2007-10-22T03:18:35Z","abstract_excerpt":"If a normalized K\\\"{a}hler-Ricci flow $g(t),t\\in[0,\\infty),$ on a compact K\\\"{a}hler $n$-manifold, $n\\geq 3$, of positive first Chern class satisfies $g(t)\\in 2\\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a K\\\"{a}hler-Ricci soliton."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3919","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0710.3919/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LiyiKuSvIOHoWRvrH46ex7n7qtj/epZt3eYqb+AHHxELxrw1nnD4eHrCLxIZNrdfKqcmxV7kE2oSRNoZFbpPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:53:39.648096Z"},"content_sha256":"0e7562b655cde503dbda2e09d36441312c9c89eff16863928bb8c50c6db30972","schema_version":"1.0","event_id":"sha256:0e7562b655cde503dbda2e09d36441312c9c89eff16863928bb8c50c6db30972"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJUODLRKE4DYNUMCXFAUO5NZIC/bundle.json","state_url":"https://pith.science/pith/EJUODLRKE4DYNUMCXFAUO5NZIC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJUODLRKE4DYNUMCXFAUO5NZIC/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":"2026-08-06T03:53:39Z","links":{"resolver":"https://pith.science/pith/EJUODLRKE4DYNUMCXFAUO5NZIC","bundle":"https://pith.science/pith/EJUODLRKE4DYNUMCXFAUO5NZIC/bundle.json","state":"https://pith.science/pith/EJUODLRKE4DYNUMCXFAUO5NZIC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJUODLRKE4DYNUMCXFAUO5NZIC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EJUODLRKE4DYNUMCXFAUO5NZIC","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":"d50d92859ddb35161129cbb346cb16626063dcfff6ee2a20b88b79c7de5bfbf1","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-10-22T03:18:35Z","title_canon_sha256":"29273cee26e4e7a48250263e898f931f5830547e052b0e3abd11041b49278f43"},"schema_version":"1.0","source":{"id":"0710.3919","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3919","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3919v2","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3919","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"EJUODLRKE4DY","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"EJUODLRKE4DYNUMC","created_at":"2026-07-04T15:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"EJUODLRK","created_at":"2026-07-04T15:09:54Z"}],"graph_snapshots":[{"event_id":"sha256:0e7562b655cde503dbda2e09d36441312c9c89eff16863928bb8c50c6db30972","target":"graph","created_at":"2026-07-04T15:09:54Z","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/0710.3919/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If a normalized K\\\"{a}hler-Ricci flow $g(t),t\\in[0,\\infty),$ on a compact K\\\"{a}hler $n$-manifold, $n\\geq 3$, of positive first Chern class satisfies $g(t)\\in 2\\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a K\\\"{a}hler-Ricci soliton.","authors_text":"Wei-Dong Ruan, Yuguang Zhang, Zhenlei Zhang","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-10-22T03:18:35Z","title":"Bounding sectional curvature along a K\\\"ahler-Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3919","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:a95651e157bac71bb18b6e3b0bd3359b2b56c86a15e1149070cef18f386ad297","target":"record","created_at":"2026-07-04T15:09:54Z","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":"d50d92859ddb35161129cbb346cb16626063dcfff6ee2a20b88b79c7de5bfbf1","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-10-22T03:18:35Z","title_canon_sha256":"29273cee26e4e7a48250263e898f931f5830547e052b0e3abd11041b49278f43"},"schema_version":"1.0","source":{"id":"0710.3919","kind":"arxiv","version":2}},"canonical_sha256":"2268e1ae2a270786d182b9414775b940bee0b2252508fa8876fbf76558922e12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2268e1ae2a270786d182b9414775b940bee0b2252508fa8876fbf76558922e12","first_computed_at":"2026-07-04T15:09:54.528028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:09:54.528028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prFPuzjLottSXqsY4d4j/uwp8wauLixCy6M2g+42gbHVAPiVDMSo0RrWoi3TvBlJWVJ3afxsEUbTWvGc5mhOAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:09:54.528438Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3919","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a95651e157bac71bb18b6e3b0bd3359b2b56c86a15e1149070cef18f386ad297","sha256:0e7562b655cde503dbda2e09d36441312c9c89eff16863928bb8c50c6db30972"],"state_sha256":"ac6301e2912387105e8fabeaed658f9e648bc5eefff17f529194fe8473d9ba72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nhRaRYTrogm03Mc2+P+grZ02GJa3XwDtlP/e51DIaTkaLscHd6S2hJZ36wNmi10a44VdnSVAyjXjZYmKFX1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T03:53:39.651383Z","bundle_sha256":"464c585c8c311019a83c486f25ca7c2db4e4d81e468ec4b94f2c85ef409f4740"}}