{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5354L2VGTWMFCZPXROTXUYZUIK","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":"7a2f2c1b4f479c349c852089cfe5ddc3dc8ed9a0fdc46596c30ec3a04a54cddc","cross_cats_sorted":["math.CV","math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-11T19:38:04Z","title_canon_sha256":"fb030ad81e1c15ffb606ef346305de1d1c17241cef35bcf2efee5ba8aa1814aa"},"schema_version":"1.0","source":{"id":"1908.03955","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03955","created_at":"2026-07-05T04:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03955v3","created_at":"2026-07-05T04:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03955","created_at":"2026-07-05T04:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"5354L2VGTWMF","created_at":"2026-07-05T04:55:14Z"},{"alias_kind":"pith_short_16","alias_value":"5354L2VGTWMFCZPX","created_at":"2026-07-05T04:55:14Z"},{"alias_kind":"pith_short_8","alias_value":"5354L2VG","created_at":"2026-07-05T04:55:14Z"}],"graph_snapshots":[{"event_id":"sha256:3a1e8e1693cb6453eeb6a9e11e42681b0c55792b9e18da25d8bf3b92d87521ee","target":"graph","created_at":"2026-07-05T04:55:14Z","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/1908.03955/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider a special relative K\\\"ahler fibration that satisfies a homogenous Monge-Amp\\`ere equation, which is called a Monge-Amp\\`ere fibration. There exist two canonical types of generalized Weil-Petersson metrics on the base complex manifold of the fibration. For the second generalized Weil-Petersson metric, we obtain an explicit curvature formula and prove that the holomorphic bisectional curvature is non-positive, the holomorphic sectional curvature, the Ricci curvature, and the scalar curvature are all bounded from above by a negative constant. For a holomorphic vector bu","authors_text":"Xueyuan Wan, Xu Wang","cross_cats":["math.CV","math.DG","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-11T19:38:04Z","title":"Curvature of the base manifold of a Monge-Amp\\`ere fibration and its existence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03955","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:ba274f7871d9a53364063f26e89060461c7acc07abaab313d8ffad33fe422e88","target":"record","created_at":"2026-07-05T04:55:14Z","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":"7a2f2c1b4f479c349c852089cfe5ddc3dc8ed9a0fdc46596c30ec3a04a54cddc","cross_cats_sorted":["math.CV","math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-11T19:38:04Z","title_canon_sha256":"fb030ad81e1c15ffb606ef346305de1d1c17241cef35bcf2efee5ba8aa1814aa"},"schema_version":"1.0","source":{"id":"1908.03955","kind":"arxiv","version":3}},"canonical_sha256":"eefbc5eaa69d985165f78ba77a633442ba40f7a7450ce266df35b2c8a3d38462","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eefbc5eaa69d985165f78ba77a633442ba40f7a7450ce266df35b2c8a3d38462","first_computed_at":"2026-07-05T04:55:14.282864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:55:14.282864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuG4s50XQ3Knawa2eidSuDUB1iEP5pZkCH/fajW806NMtvw7dwPptwAXj3ecV/UqJnwUCK38jBIDvTA0Er3mAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:55:14.283249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03955","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba274f7871d9a53364063f26e89060461c7acc07abaab313d8ffad33fe422e88","sha256:3a1e8e1693cb6453eeb6a9e11e42681b0c55792b9e18da25d8bf3b92d87521ee"],"state_sha256":"92df6cacd84feaa58dc3144bc2cab7b475aa6f43fddef2402ad36d9d7011441e"}