{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2RNEFVI2YVDBVCIC6FWOSUOPTP","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":"95a206f0681692c69ecd258c42e2d816d3a9acf5710128e45da7575b3f74aa67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-09-01T06:52:04Z","title_canon_sha256":"b448b760d07a10f858fbf849b9556fbc942c5e4fa9e4a95edb1914eecff4b21a"},"schema_version":"1.0","source":{"id":"2509.01176","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.01176","created_at":"2026-06-12T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.01176v7","created_at":"2026-06-12T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01176","created_at":"2026-06-12T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"2RNEFVI2YVDB","created_at":"2026-06-12T01:09:12Z"},{"alias_kind":"pith_short_16","alias_value":"2RNEFVI2YVDBVCIC","created_at":"2026-06-12T01:09:12Z"},{"alias_kind":"pith_short_8","alias_value":"2RNEFVI2","created_at":"2026-06-12T01:09:12Z"}],"graph_snapshots":[{"event_id":"sha256:cebbd40b877fd1db8d3986a77b7f36451ef9e21094d9b1f07335d7ec75410638","target":"graph","created_at":"2026-06-12T01:09:12Z","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/2509.01176/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the global topological constraints and structural properties of compact Hessian manifolds. By establishing novel fibration and splitting theorems, we confirm Chern's conjecture on the vanishing of the Euler characteristic for this class of affine manifolds. Applying these techniques to low dimensions, we provide a topological classification of complete Hessian surfaces. Furthermore, utilizing the theory of Hitchin systems and the Cheng-Yau solution to the real Monge-Amp\\`ere equation, we establish a geometric classification of closed orientable Hessian $3$-manifolds.","authors_text":"Hanwen Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-09-01T06:52:04Z","title":"On Topology of Compact Hessian Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01176","kind":"arxiv","version":7},"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:d50eaaca0f1eb2f76600b27f38e30f0f33c6408dc4a8c21b981659b5cf353a99","target":"record","created_at":"2026-06-12T01:09:12Z","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":"95a206f0681692c69ecd258c42e2d816d3a9acf5710128e45da7575b3f74aa67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-09-01T06:52:04Z","title_canon_sha256":"b448b760d07a10f858fbf849b9556fbc942c5e4fa9e4a95edb1914eecff4b21a"},"schema_version":"1.0","source":{"id":"2509.01176","kind":"arxiv","version":7}},"canonical_sha256":"d45a42d51ac5461a8902f16ce951cf9bee302cc7aeba1641fb1616fa78e33f6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d45a42d51ac5461a8902f16ce951cf9bee302cc7aeba1641fb1616fa78e33f6a","first_computed_at":"2026-06-12T01:09:12.963675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:12.963675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JsVrOIBtAJMDmP7hrVtJVRv1+RGRIflJGv0R8GGYSx12KjmR49PR9MHuZMkKpw+jldgJBedgvVv7+o9fcIxaDA==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:12.964674Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.01176","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50eaaca0f1eb2f76600b27f38e30f0f33c6408dc4a8c21b981659b5cf353a99","sha256:cebbd40b877fd1db8d3986a77b7f36451ef9e21094d9b1f07335d7ec75410638"],"state_sha256":"8ba665b145711fa5207dd2635103495f230cc440ebb9b8205c81768dcbc64448"}