{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:CRTCYW7EJFRBMESU6JNLPI6NU2","short_pith_number":"pith:CRTCYW7E","canonical_record":{"source":{"id":"math/0410418","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-10-19T14:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"0cd8d2e97ced4cc7591ec1f942d848e5394716e87cf25552450371872bf2be5e","abstract_canon_sha256":"74f7a22c873c6598ce80820743087333510a34c8fc5fe018a8335b57ae977051"},"schema_version":"1.0"},"canonical_sha256":"14662c5be44962161254f25ab7a3cda6bb82a797bb4b647304ceea1275177641","source":{"kind":"arxiv","id":"math/0410418","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410418","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410418v1","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410418","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"CRTCYW7EJFRB","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"pith_short_16","alias_value":"CRTCYW7EJFRBMESU","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"pith_short_8","alias_value":"CRTCYW7E","created_at":"2026-07-04T15:35:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:CRTCYW7EJFRBMESU6JNLPI6NU2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0410418","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-10-19T14:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"0cd8d2e97ced4cc7591ec1f942d848e5394716e87cf25552450371872bf2be5e","abstract_canon_sha256":"74f7a22c873c6598ce80820743087333510a34c8fc5fe018a8335b57ae977051"},"schema_version":"1.0"},"canonical_sha256":"14662c5be44962161254f25ab7a3cda6bb82a797bb4b647304ceea1275177641","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:35:58.028416Z","signature_b64":"ku/meSmMSixgG/RynqLsXziEdFm5nEPgsuuAL2YSCAmfP0MpmhgBtXGfW6NsnhafQO2Z6I1wOmyCCyAP17AKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14662c5be44962161254f25ab7a3cda6bb82a797bb4b647304ceea1275177641","last_reissued_at":"2026-07-04T15:35:58.028051Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:35:58.028051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0410418","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:35:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lo8cKFkKlof3P6eadQAx4YkWMs22fB7zOIcwI7MK+2RiXK7VyK6nML9i6gr+afqEYY4S2xh8sJ4+QEaJFi5QDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:10:46.411641Z"},"content_sha256":"671519134131c0397ea9359a6ef009ad0eeb47dca7d9624c8ddbfe3484c97f9c","schema_version":"1.0","event_id":"sha256:671519134131c0397ea9359a6ef009ad0eeb47dca7d9624c8ddbfe3484c97f9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:CRTCYW7EJFRBMESU6JNLPI6NU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the convergence and singularities of the J-flow with applications to the Mabuchi energy","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ben Weinkove, Jian Song","submitted_at":"2004-10-19T14:04:47Z","abstract_excerpt":"The J-flow of S. K. Donaldson and X. X. Chen is a parabolic flow on Kahler manifolds with two Kahler metrics. It is the gradient flow of the J-functional which appears in Chen's formula for the Mabuchi energy. We find a positivity condition in terms of the two metrics which is both necessary and sufficient for the convergence of the J-flow to a critical metric. We use this result to show that on manifolds with ample canonical bundle, the Mabuchi energy is proper on all Kahler classes in an open neighborhood of the canonical class defined by a positivity condition. This improves previous result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410418","kind":"arxiv","version":1},"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/math/0410418/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":"2026-07-04T15:35:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BhD6wPF16bBpIooP5r7fEK4cgzWQ8fVtNW73VwLLLdUUoU1NEzuQSKeY1qLbLVhoPRqkUNaiDhlAJQz2HshCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:10:46.412284Z"},"content_sha256":"f2d0a3e9310044052d7c9d76783fc477ffff971d36f28f098884a84f38c1564d","schema_version":"1.0","event_id":"sha256:f2d0a3e9310044052d7c9d76783fc477ffff971d36f28f098884a84f38c1564d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRTCYW7EJFRBMESU6JNLPI6NU2/bundle.json","state_url":"https://pith.science/pith/CRTCYW7EJFRBMESU6JNLPI6NU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRTCYW7EJFRBMESU6JNLPI6NU2/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":"2026-08-09T14:10:46Z","links":{"resolver":"https://pith.science/pith/CRTCYW7EJFRBMESU6JNLPI6NU2","bundle":"https://pith.science/pith/CRTCYW7EJFRBMESU6JNLPI6NU2/bundle.json","state":"https://pith.science/pith/CRTCYW7EJFRBMESU6JNLPI6NU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRTCYW7EJFRBMESU6JNLPI6NU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:CRTCYW7EJFRBMESU6JNLPI6NU2","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":"74f7a22c873c6598ce80820743087333510a34c8fc5fe018a8335b57ae977051","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2004-10-19T14:04:47Z","title_canon_sha256":"0cd8d2e97ced4cc7591ec1f942d848e5394716e87cf25552450371872bf2be5e"},"schema_version":"1.0","source":{"id":"math/0410418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410418","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410418v1","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410418","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"CRTCYW7EJFRB","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"pith_short_16","alias_value":"CRTCYW7EJFRBMESU","created_at":"2026-07-04T15:35:58Z"},{"alias_kind":"pith_short_8","alias_value":"CRTCYW7E","created_at":"2026-07-04T15:35:58Z"}],"graph_snapshots":[{"event_id":"sha256:f2d0a3e9310044052d7c9d76783fc477ffff971d36f28f098884a84f38c1564d","target":"graph","created_at":"2026-07-04T15:35:58Z","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/math/0410418/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The J-flow of S. K. Donaldson and X. X. Chen is a parabolic flow on Kahler manifolds with two Kahler metrics. It is the gradient flow of the J-functional which appears in Chen's formula for the Mabuchi energy. We find a positivity condition in terms of the two metrics which is both necessary and sufficient for the convergence of the J-flow to a critical metric. We use this result to show that on manifolds with ample canonical bundle, the Mabuchi energy is proper on all Kahler classes in an open neighborhood of the canonical class defined by a positivity condition. This improves previous result","authors_text":"Ben Weinkove, Jian Song","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2004-10-19T14:04:47Z","title":"On the convergence and singularities of the J-flow with applications to the Mabuchi energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410418","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":"sha256:671519134131c0397ea9359a6ef009ad0eeb47dca7d9624c8ddbfe3484c97f9c","target":"record","created_at":"2026-07-04T15:35:58Z","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":"74f7a22c873c6598ce80820743087333510a34c8fc5fe018a8335b57ae977051","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2004-10-19T14:04:47Z","title_canon_sha256":"0cd8d2e97ced4cc7591ec1f942d848e5394716e87cf25552450371872bf2be5e"},"schema_version":"1.0","source":{"id":"math/0410418","kind":"arxiv","version":1}},"canonical_sha256":"14662c5be44962161254f25ab7a3cda6bb82a797bb4b647304ceea1275177641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14662c5be44962161254f25ab7a3cda6bb82a797bb4b647304ceea1275177641","first_computed_at":"2026-07-04T15:35:58.028051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:35:58.028051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ku/meSmMSixgG/RynqLsXziEdFm5nEPgsuuAL2YSCAmfP0MpmhgBtXGfW6NsnhafQO2Z6I1wOmyCCyAP17AKBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:35:58.028416Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0410418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:671519134131c0397ea9359a6ef009ad0eeb47dca7d9624c8ddbfe3484c97f9c","sha256:f2d0a3e9310044052d7c9d76783fc477ffff971d36f28f098884a84f38c1564d"],"state_sha256":"2ab29a2f8a4e7d2bc349df48bc9b9fbe720c11046a563c090e70eee0b9e7c2d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rW+GEb8bcipSbKHmIvq0FARTSui4FUVcTg0x+3ggloTn4gEXf+StyuOOVfTcTIXnT5y9IB2MyMlfXD3H7v7cAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T14:10:46.416978Z","bundle_sha256":"8a67689035d7dbbe0d62f412770cdd83baec0a429fe5afe38dd293c1e3037103"}}