{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PTUNH6L66NHWUTSLVDLH5B6CT3","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":"e96f4be8941cfcf17c5fbe107e1cae8f349d1b560ccf5ff77b4691476b54725f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-11T06:43:27Z","title_canon_sha256":"cf3cdb07b1db1275804c1342eb48b4938f9e4aa5ae8fa94c0ee1139508d6a10d"},"schema_version":"1.0","source":{"id":"1010.2013","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2013","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2013v2","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2013","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"pith_short_12","alias_value":"PTUNH6L66NHW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PTUNH6L66NHWUTSL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PTUNH6L6","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:aeabb439e0ffbcf0dbf020aaaf6de2a9c26e5e4c22459278a3480548ac53956a","target":"graph","created_at":"2026-05-18T04:26:55Z","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":"In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the $\\gamma_k$ functions on the space of its hermitian metrics.","authors_text":"Damin Wu, Jixiang Fu, Zhizhang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-11T06:43:27Z","title":"Semilinear equations, the $\\gamma_k$ function, and generalized Gauduchon metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2013","kind":"arxiv","version":2},"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":"sha256:6e04c61e9dae3e635ca3cc9deb02a0d23eb3009d8110906d6d69c3ec5704443c","target":"record","created_at":"2026-05-18T04:26:55Z","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":"e96f4be8941cfcf17c5fbe107e1cae8f349d1b560ccf5ff77b4691476b54725f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-11T06:43:27Z","title_canon_sha256":"cf3cdb07b1db1275804c1342eb48b4938f9e4aa5ae8fa94c0ee1139508d6a10d"},"schema_version":"1.0","source":{"id":"1010.2013","kind":"arxiv","version":2}},"canonical_sha256":"7ce8d3f97ef34f6a4e4ba8d67e87c29ecaea2a56df37778451f4618a8cc8b136","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ce8d3f97ef34f6a4e4ba8d67e87c29ecaea2a56df37778451f4618a8cc8b136","first_computed_at":"2026-05-18T04:26:55.544835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:55.544835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yIK4T5Yvu7rn0lw2BUVYxpwVlcM3b2yLginQt9W2rBLN3/auVxHgDt7nALqUhP6jEqmQLHqVaB7Lm1vBJkiHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:55.545220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2013","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e04c61e9dae3e635ca3cc9deb02a0d23eb3009d8110906d6d69c3ec5704443c","sha256:aeabb439e0ffbcf0dbf020aaaf6de2a9c26e5e4c22459278a3480548ac53956a"],"state_sha256":"599e8cd9dd100d19aa71e8831a6f18fb2fdde887918a518096d96e4bfd517138"}