{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:H35YDPYBSMZIJ43HFH6DCPKKTP","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":"31f22184e4d1b8f273e5cec03b33ccec8a7850a7ec148fd38685febd3ca8595b","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"1999-07-14T00:00:00Z","title_canon_sha256":"3fa959f4c51a95fa58f72c501a977c3ced71b6e2765a7154d10e8b04050fb7d6"},"schema_version":"1.0","source":{"id":"math/9907200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9907200","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/9907200v1","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9907200","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"H35YDPYBSMZI","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"H35YDPYBSMZIJ43H","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"H35YDPYB","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:ef0c4c9fae9ecbe83e0a70896073e364b6924f7d9e6c7b2493bc2670b84e767b","target":"graph","created_at":"2026-05-18T02:37:59Z","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":"Integral symplectic 4-manifolds may be described in terms of Lefschetz fibrations. In this note we give a formula for the signature of any Lefschetz fibration in terms of the second cohomology of the moduli space of stable curves. As a consequence we see that the sphere in moduli space defined by any (not necessarily holomorphic) Lefschetz fibration has positive \"symplectic volume\"; it evaluates positively with the Kahler class. Some other applications of the signature formula and some more general results for genus two fibrations are discussed.","authors_text":"Ivan Smith","cross_cats":[],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"1999-07-14T00:00:00Z","title":"Lefschetz fibrations and the Hodge bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9907200","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:bb938dfaed8863a554d4872b29a1e269cd7fe9b64b9cf46feda8a798d47da217","target":"record","created_at":"2026-05-18T02:37:59Z","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":"31f22184e4d1b8f273e5cec03b33ccec8a7850a7ec148fd38685febd3ca8595b","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"1999-07-14T00:00:00Z","title_canon_sha256":"3fa959f4c51a95fa58f72c501a977c3ced71b6e2765a7154d10e8b04050fb7d6"},"schema_version":"1.0","source":{"id":"math/9907200","kind":"arxiv","version":1}},"canonical_sha256":"3efb81bf01933284f36729fc313d4a9bd2ea1646f6f0983968f3a398add5a191","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3efb81bf01933284f36729fc313d4a9bd2ea1646f6f0983968f3a398add5a191","first_computed_at":"2026-05-18T02:37:59.213336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.213336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7y958b28ABpl2eLO/3yaIzLkRC4z3qEm08ZLmJVHCfdBgcaNEdT6hKYB/VpLjicBH5j+KmomNDuEtOmzGtN7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.213734Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9907200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb938dfaed8863a554d4872b29a1e269cd7fe9b64b9cf46feda8a798d47da217","sha256:ef0c4c9fae9ecbe83e0a70896073e364b6924f7d9e6c7b2493bc2670b84e767b"],"state_sha256":"38ed0109246ad98db46eb79f392c45317840473530749aeb5e2580ae43f45068"}