{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2JY4QXF3UF5RFPDGO4DDXX25GW","short_pith_number":"pith:2JY4QXF3","canonical_record":{"source":{"id":"1110.2680","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-12T15:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"5498856e37c0221db5d078068c047da6c13dbde37428074c5184adb486f65722","abstract_canon_sha256":"8580113625f49b39210d85bc69b4d9fe091eae58ac156b0a6d85b44d67189171"},"schema_version":"1.0"},"canonical_sha256":"d271c85cbba17b12bc6677063bdf5d358c6b248fd915fb192e3b66c64a2b0502","source":{"kind":"arxiv","id":"1110.2680","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2680","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2680v3","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2680","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"2JY4QXF3UF5R","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2JY4QXF3UF5RFPDG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2JY4QXF3","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2JY4QXF3UF5RFPDGO4DDXX25GW","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2680","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-12T15:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"5498856e37c0221db5d078068c047da6c13dbde37428074c5184adb486f65722","abstract_canon_sha256":"8580113625f49b39210d85bc69b4d9fe091eae58ac156b0a6d85b44d67189171"},"schema_version":"1.0"},"canonical_sha256":"d271c85cbba17b12bc6677063bdf5d358c6b248fd915fb192e3b66c64a2b0502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:41.333112Z","signature_b64":"ZGucEx4A0xj9CchBd8aCRv1LeiRSIqftB9Nqwjg/buNhfyulvuaRDh65B/wCK3itcOzjVXlm2vI/hWcMUzUuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d271c85cbba17b12bc6677063bdf5d358c6b248fd915fb192e3b66c64a2b0502","last_reissued_at":"2026-05-18T02:18:41.332591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:41.332591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2680","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bStCG6/+ax5b3rgSZN777jiBj2rS0xxRdSaKWwQUUClDfgsA3GfsDWK15Vrn5B054m7kdSthRLVghT37TZ+bCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:12:15.464884Z"},"content_sha256":"837eba3795821ac8eb1ac33d667b0893e62cdd083b191c2c7e8a12c9137bc9d5","schema_version":"1.0","event_id":"sha256:837eba3795821ac8eb1ac33d667b0893e62cdd083b191c2c7e8a12c9137bc9d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2JY4QXF3UF5RFPDGO4DDXX25GW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangian fibrations on hyperk\\\"ahler fourfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Lehn, Daniel Greb, S\\\"onke Rollenske","submitted_at":"2011-10-12T15:26:28Z","abstract_excerpt":"Let X be a projective hyperk\\\"ahler manifold containing a Lagrangian subtorus L. We study intersections of deformations of L, defining a canonical almost holomorphic map called L-reduction, which is not birational if and only if X admits an almost holomorphic Lagrangian fibration with (strong) fibre L.\n  In dimension four we prove that in the above situation there is always a holomorphic Lagrangian fibration with fibre L, thus answering a question of Beauville in this particular case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2680","kind":"arxiv","version":3},"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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRR9m8APolxwfTSDtTg6LffmAqyE8J91PgXvP/OIdmPHqg2HUdQEzGbdZpp5ZCa1JxYhACeUfjv3bchAIS9FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:12:15.465637Z"},"content_sha256":"7ef548d0e44505c7f6bbd0c12aaeb6cdc7b91d7fe9596a06e00368b44ceea606","schema_version":"1.0","event_id":"sha256:7ef548d0e44505c7f6bbd0c12aaeb6cdc7b91d7fe9596a06e00368b44ceea606"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JY4QXF3UF5RFPDGO4DDXX25GW/bundle.json","state_url":"https://pith.science/pith/2JY4QXF3UF5RFPDGO4DDXX25GW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JY4QXF3UF5RFPDGO4DDXX25GW/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":"2026-06-06T18:12:15Z","links":{"resolver":"https://pith.science/pith/2JY4QXF3UF5RFPDGO4DDXX25GW","bundle":"https://pith.science/pith/2JY4QXF3UF5RFPDGO4DDXX25GW/bundle.json","state":"https://pith.science/pith/2JY4QXF3UF5RFPDGO4DDXX25GW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JY4QXF3UF5RFPDGO4DDXX25GW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2JY4QXF3UF5RFPDGO4DDXX25GW","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":"8580113625f49b39210d85bc69b4d9fe091eae58ac156b0a6d85b44d67189171","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-12T15:26:28Z","title_canon_sha256":"5498856e37c0221db5d078068c047da6c13dbde37428074c5184adb486f65722"},"schema_version":"1.0","source":{"id":"1110.2680","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2680","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2680v3","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2680","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"2JY4QXF3UF5R","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2JY4QXF3UF5RFPDG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2JY4QXF3","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:7ef548d0e44505c7f6bbd0c12aaeb6cdc7b91d7fe9596a06e00368b44ceea606","target":"graph","created_at":"2026-05-18T02:18:41Z","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":"Let X be a projective hyperk\\\"ahler manifold containing a Lagrangian subtorus L. We study intersections of deformations of L, defining a canonical almost holomorphic map called L-reduction, which is not birational if and only if X admits an almost holomorphic Lagrangian fibration with (strong) fibre L.\n  In dimension four we prove that in the above situation there is always a holomorphic Lagrangian fibration with fibre L, thus answering a question of Beauville in this particular case.","authors_text":"Christian Lehn, Daniel Greb, S\\\"onke Rollenske","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-12T15:26:28Z","title":"Lagrangian fibrations on hyperk\\\"ahler fourfolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2680","kind":"arxiv","version":3},"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":"sha256:837eba3795821ac8eb1ac33d667b0893e62cdd083b191c2c7e8a12c9137bc9d5","target":"record","created_at":"2026-05-18T02:18:41Z","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":"8580113625f49b39210d85bc69b4d9fe091eae58ac156b0a6d85b44d67189171","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-12T15:26:28Z","title_canon_sha256":"5498856e37c0221db5d078068c047da6c13dbde37428074c5184adb486f65722"},"schema_version":"1.0","source":{"id":"1110.2680","kind":"arxiv","version":3}},"canonical_sha256":"d271c85cbba17b12bc6677063bdf5d358c6b248fd915fb192e3b66c64a2b0502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d271c85cbba17b12bc6677063bdf5d358c6b248fd915fb192e3b66c64a2b0502","first_computed_at":"2026-05-18T02:18:41.332591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:41.332591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGucEx4A0xj9CchBd8aCRv1LeiRSIqftB9Nqwjg/buNhfyulvuaRDh65B/wCK3itcOzjVXlm2vI/hWcMUzUuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:41.333112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2680","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:837eba3795821ac8eb1ac33d667b0893e62cdd083b191c2c7e8a12c9137bc9d5","sha256:7ef548d0e44505c7f6bbd0c12aaeb6cdc7b91d7fe9596a06e00368b44ceea606"],"state_sha256":"49679fbf26a01dab9c963c904c8c41986533b371d425285743dcfd58554a76ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRs2OeVFiFrpQ+pA6IZeaOfonLD/D0uAuzj5OsZxzGrqIWpg2/47cO9F0G+UjN9TISRlnFIM5tc8QntHcROCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:12:15.469352Z","bundle_sha256":"12dd4e9bb686b602a756b2ea251e032ceffcde0f3a31f9832851b36b5a9bd839"}}