{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U4LXRMHZW3AW2ZEJNQQ3SMCQ6T","short_pith_number":"pith:U4LXRMHZ","canonical_record":{"source":{"id":"1812.10673","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2018-12-27T09:32:30Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c823165e2af74d59752e9156777f3ecc55123fa112beccf0eda8cfdbb51c61bc","abstract_canon_sha256":"a3dea99d64208a736c692302e1d143605dc3ebe700a98749866457235e006bbd"},"schema_version":"1.0"},"canonical_sha256":"a71778b0f9b6c16d64896c21b93050f4eb19ba2637160433ab46dafeca60e017","source":{"kind":"arxiv","id":"1812.10673","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10673","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10673v5","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10673","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"U4LXRMHZW3AW","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"U4LXRMHZW3AW2ZEJ","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"U4LXRMHZ","created_at":"2026-07-05T02:08:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U4LXRMHZW3AW2ZEJNQQ3SMCQ6T","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10673","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2018-12-27T09:32:30Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c823165e2af74d59752e9156777f3ecc55123fa112beccf0eda8cfdbb51c61bc","abstract_canon_sha256":"a3dea99d64208a736c692302e1d143605dc3ebe700a98749866457235e006bbd"},"schema_version":"1.0"},"canonical_sha256":"a71778b0f9b6c16d64896c21b93050f4eb19ba2637160433ab46dafeca60e017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:08:58.196886Z","signature_b64":"iDEARUmamLFoRDFjxbXYZuxXkVpX2eVcg5iCo+TX+EixgEboBoZvI8K5X8aluSG6u/kFEVHg+5vYE0yhRnenCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a71778b0f9b6c16d64896c21b93050f4eb19ba2637160433ab46dafeca60e017","last_reissued_at":"2026-07-05T02:08:58.196348Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:08:58.196348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10673","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4N7II+MKn6D4I2cGOB+weZMNTWE6BH8o54qyOUt9ac6IfXJ713H/PnsZQogOr2zvFJRdkPnzH7orMJRxuUdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:08:23.551949Z"},"content_sha256":"55cb4cce4859a8978a70ecf318e9d6e3c233f967b4d4de1a4c36333702efe632","schema_version":"1.0","event_id":"sha256:55cb4cce4859a8978a70ecf318e9d6e3c233f967b4d4de1a4c36333702efe632"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U4LXRMHZW3AW2ZEJNQQ3SMCQ6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of Lagrangian fibrations and Hodge theory of hyper-K\\\"ahler manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Junliang Shen, Qizheng Yin","submitted_at":"2018-12-27T09:32:30Z","abstract_excerpt":"We establish a compact analog of the P = W conjecture. For a holomorphic symplectic variety with a Lagrangian fibration, we show that the perverse numbers associated with the fibration match perfectly with the Hodge numbers of the total space. This builds a new connection between the topology of Lagrangian fibrations and the Hodge theory of hyper-K\\\"ahler manifolds. We present two applications of our result, one on the topology of the base and fibers of a Lagrangian fibration, the other on the refined Gopakumar-Vafa invariants of a K3 surface. Furthermore, we show that the perverse filtration "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10673","kind":"arxiv","version":5},"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/1812.10673/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":"2026-07-05T02:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHV3DZdTt+bzoGZhe1H4NWPDU2wInV4HGkeyb64LpVU9V5ozDdfHJS+HM+HBXoJ8HfFWWksmSJOymyp2FoFABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:08:23.552482Z"},"content_sha256":"18637e632c88222839fcf6c940f6657f01e72d620075a878dcda5b66a690d756","schema_version":"1.0","event_id":"sha256:18637e632c88222839fcf6c940f6657f01e72d620075a878dcda5b66a690d756"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T/bundle.json","state_url":"https://pith.science/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T/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":"2026-08-20T22:08:23Z","links":{"resolver":"https://pith.science/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T","bundle":"https://pith.science/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T/bundle.json","state":"https://pith.science/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4LXRMHZW3AW2ZEJNQQ3SMCQ6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U4LXRMHZW3AW2ZEJNQQ3SMCQ6T","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":"a3dea99d64208a736c692302e1d143605dc3ebe700a98749866457235e006bbd","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2018-12-27T09:32:30Z","title_canon_sha256":"c823165e2af74d59752e9156777f3ecc55123fa112beccf0eda8cfdbb51c61bc"},"schema_version":"1.0","source":{"id":"1812.10673","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10673","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10673v5","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10673","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"U4LXRMHZW3AW","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"U4LXRMHZW3AW2ZEJ","created_at":"2026-07-05T02:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"U4LXRMHZ","created_at":"2026-07-05T02:08:58Z"}],"graph_snapshots":[{"event_id":"sha256:18637e632c88222839fcf6c940f6657f01e72d620075a878dcda5b66a690d756","target":"graph","created_at":"2026-07-05T02:08:58Z","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/1812.10673/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a compact analog of the P = W conjecture. For a holomorphic symplectic variety with a Lagrangian fibration, we show that the perverse numbers associated with the fibration match perfectly with the Hodge numbers of the total space. This builds a new connection between the topology of Lagrangian fibrations and the Hodge theory of hyper-K\\\"ahler manifolds. We present two applications of our result, one on the topology of the base and fibers of a Lagrangian fibration, the other on the refined Gopakumar-Vafa invariants of a K3 surface. Furthermore, we show that the perverse filtration ","authors_text":"Junliang Shen, Qizheng Yin","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2018-12-27T09:32:30Z","title":"Topology of Lagrangian fibrations and Hodge theory of hyper-K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10673","kind":"arxiv","version":5},"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":"sha256:55cb4cce4859a8978a70ecf318e9d6e3c233f967b4d4de1a4c36333702efe632","target":"record","created_at":"2026-07-05T02:08:58Z","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":"a3dea99d64208a736c692302e1d143605dc3ebe700a98749866457235e006bbd","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2018-12-27T09:32:30Z","title_canon_sha256":"c823165e2af74d59752e9156777f3ecc55123fa112beccf0eda8cfdbb51c61bc"},"schema_version":"1.0","source":{"id":"1812.10673","kind":"arxiv","version":5}},"canonical_sha256":"a71778b0f9b6c16d64896c21b93050f4eb19ba2637160433ab46dafeca60e017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a71778b0f9b6c16d64896c21b93050f4eb19ba2637160433ab46dafeca60e017","first_computed_at":"2026-07-05T02:08:58.196348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:08:58.196348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iDEARUmamLFoRDFjxbXYZuxXkVpX2eVcg5iCo+TX+EixgEboBoZvI8K5X8aluSG6u/kFEVHg+5vYE0yhRnenCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:08:58.196886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10673","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55cb4cce4859a8978a70ecf318e9d6e3c233f967b4d4de1a4c36333702efe632","sha256:18637e632c88222839fcf6c940f6657f01e72d620075a878dcda5b66a690d756"],"state_sha256":"c807adb43c541db3dbc69f551ba6978acdcb99dce5a0e07b06ad6a2ef0d61bad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6U95b/97jV31KH3CncHX4huf3KtpuetSJNDLHp4qmQ7NciWKY0EZPelSA6OQCIGC6fD1qDrfoPV6iQf/WxtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T22:08:23.557045Z","bundle_sha256":"99b82cc0ee67da62674081564a0829c8a9ddcedf49ec66eade05b11167b90e72"}}