{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:F5ZSPJXIC5E522A25HFTAGREND","short_pith_number":"pith:F5ZSPJXI","canonical_record":{"source":{"id":"math/0010283","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2000-10-29T11:44:13Z","cross_cats_sorted":[],"title_canon_sha256":"a5686533ec13bcbe872fa0d25f4a70b07640165d8fdb373a0d25a0289f82303d","abstract_canon_sha256":"403e46517af2cd1ac98c088a8babf2959d82b2f7b5bd840485bb491059844d7d"},"schema_version":"1.0"},"canonical_sha256":"2f7327a6e81749dd681ae9cb301a2468eb727260835ecb60fa0525de9b2c302c","source":{"kind":"arxiv","id":"math/0010283","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0010283","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0010283v1","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0010283","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"F5ZSPJXIC5E5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"F5ZSPJXIC5E522A2","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"F5ZSPJXI","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:F5ZSPJXIC5E522A25HFTAGREND","target":"record","payload":{"canonical_record":{"source":{"id":"math/0010283","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2000-10-29T11:44:13Z","cross_cats_sorted":[],"title_canon_sha256":"a5686533ec13bcbe872fa0d25f4a70b07640165d8fdb373a0d25a0289f82303d","abstract_canon_sha256":"403e46517af2cd1ac98c088a8babf2959d82b2f7b5bd840485bb491059844d7d"},"schema_version":"1.0"},"canonical_sha256":"2f7327a6e81749dd681ae9cb301a2468eb727260835ecb60fa0525de9b2c302c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:38.154546Z","signature_b64":"O+ETs0PiUzFbc124gzHSfOC+iBeMHrCskVPyzBVcjSE10/HMm5M4TRxYXazoW2F535GP2M9K/zaSGQb+JfvWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7327a6e81749dd681ae9cb301a2468eb727260835ecb60fa0525de9b2c302c","last_reissued_at":"2026-05-18T01:05:38.154063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:38.154063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0010283","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":"2026-05-18T01:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6O9jV8dNic7rEQXNspu+2LifKXR6IjA3c51tVFNyesOYFLlNo3fKS+Z0SwJOiMWLeh39ZoTYL+0kEdT/xTuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:36:34.078976Z"},"content_sha256":"fa24496f7cbc30ebb9132e49e279ae30c45c95bf5296a674bd2946e2d06df4fb","schema_version":"1.0","event_id":"sha256:fa24496f7cbc30ebb9132e49e279ae30c45c95bf5296a674bd2946e2d06df4fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:F5ZSPJXIC5E522A25HFTAGREND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher direct images of Lagrangian fibrations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daisuke Matsushita","submitted_at":"2000-10-29T11:44:13Z","abstract_excerpt":"We prove that the higher direct images of the dualizing sheaf of a Lagrangian fibration between smooth projective manifolds are isomorphic to the cotangent bundles of base space.\n As a corollary, we obtain that every Hodge number of the base space of a fibre space of an irreducible symplectic manifold is the same to that of a projective space if the base space is smooth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0010283","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":""},"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":"2026-05-18T01:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQWHX0G7L0QKH37GfHoM6IGSSQXeNrO0oTZD5kv5NmZDoU6U4mnCpXgtuk4y9GzI+vF+/I95J9esTex9Iyq6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:36:34.079323Z"},"content_sha256":"dd1347654ff79d1898f2827b0c1ff89dc6ca4732307bc6adeba31f089768f725","schema_version":"1.0","event_id":"sha256:dd1347654ff79d1898f2827b0c1ff89dc6ca4732307bc6adeba31f089768f725"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5ZSPJXIC5E522A25HFTAGREND/bundle.json","state_url":"https://pith.science/pith/F5ZSPJXIC5E522A25HFTAGREND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5ZSPJXIC5E522A25HFTAGREND/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":"2026-06-20T07:36:34Z","links":{"resolver":"https://pith.science/pith/F5ZSPJXIC5E522A25HFTAGREND","bundle":"https://pith.science/pith/F5ZSPJXIC5E522A25HFTAGREND/bundle.json","state":"https://pith.science/pith/F5ZSPJXIC5E522A25HFTAGREND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5ZSPJXIC5E522A25HFTAGREND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:F5ZSPJXIC5E522A25HFTAGREND","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":"403e46517af2cd1ac98c088a8babf2959d82b2f7b5bd840485bb491059844d7d","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-10-29T11:44:13Z","title_canon_sha256":"a5686533ec13bcbe872fa0d25f4a70b07640165d8fdb373a0d25a0289f82303d"},"schema_version":"1.0","source":{"id":"math/0010283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0010283","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0010283v1","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0010283","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"F5ZSPJXIC5E5","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"F5ZSPJXIC5E522A2","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"F5ZSPJXI","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:dd1347654ff79d1898f2827b0c1ff89dc6ca4732307bc6adeba31f089768f725","target":"graph","created_at":"2026-05-18T01:05:38Z","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 the higher direct images of the dualizing sheaf of a Lagrangian fibration between smooth projective manifolds are isomorphic to the cotangent bundles of base space.\n As a corollary, we obtain that every Hodge number of the base space of a fibre space of an irreducible symplectic manifold is the same to that of a projective space if the base space is smooth.","authors_text":"Daisuke Matsushita","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2000-10-29T11:44:13Z","title":"Higher direct images of Lagrangian fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0010283","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:fa24496f7cbc30ebb9132e49e279ae30c45c95bf5296a674bd2946e2d06df4fb","target":"record","created_at":"2026-05-18T01:05:38Z","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":"403e46517af2cd1ac98c088a8babf2959d82b2f7b5bd840485bb491059844d7d","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-10-29T11:44:13Z","title_canon_sha256":"a5686533ec13bcbe872fa0d25f4a70b07640165d8fdb373a0d25a0289f82303d"},"schema_version":"1.0","source":{"id":"math/0010283","kind":"arxiv","version":1}},"canonical_sha256":"2f7327a6e81749dd681ae9cb301a2468eb727260835ecb60fa0525de9b2c302c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f7327a6e81749dd681ae9cb301a2468eb727260835ecb60fa0525de9b2c302c","first_computed_at":"2026-05-18T01:05:38.154063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:38.154063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O+ETs0PiUzFbc124gzHSfOC+iBeMHrCskVPyzBVcjSE10/HMm5M4TRxYXazoW2F535GP2M9K/zaSGQb+JfvWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:38.154546Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0010283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa24496f7cbc30ebb9132e49e279ae30c45c95bf5296a674bd2946e2d06df4fb","sha256:dd1347654ff79d1898f2827b0c1ff89dc6ca4732307bc6adeba31f089768f725"],"state_sha256":"0a2fab54b320bd5901223b7ca6c8055a927ecb9b189f5d1a93af00760e263db8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qty8n5pqV96PgZUEz/t12qIF0t5FtutO7fwHS1D3p+H/mCfXBiD9mp4rLZVglBMQIqmJGVYuDTgueTuj2UsGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:36:34.081262Z","bundle_sha256":"faefff670f2b500d8a439dd1d251ffe2533b6083734c2c4ae840ac571df52c93"}}