{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DNZZGLTJNUEPRZEQOPVBNSAGEI","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":"01dfe68b8a53dc580bbdabac4d0c55a5c9f351c7853a56b54648d38d0500e969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T12:42:06Z","title_canon_sha256":"f9d59d9000f583b553a1904ed64875c8ca16bfecb20feec9199ca38335f6006a"},"schema_version":"1.0","source":{"id":"1103.6158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6158","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6158v1","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6158","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"DNZZGLTJNUEP","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DNZZGLTJNUEPRZEQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DNZZGLTJ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:5eae28413bd6b34014eaa3b17cd705111d24dcc9728f5aaa89a3db4d1e08245d","target":"graph","created_at":"2026-05-18T04:25:13Z","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 investigate the balanced condition (in the sense of Donaldson) and the existence of an Englis expansion for the LeBrun's metrics on $C^2$. Our first result shows that a LeBrun's metric on $C^2$ is never balanced unless it is the flat metric. The second one shows that an Englis expansion of the Rawnsley's function associated to a LeBrun's metric always exists, while the coefficient $a_3$ of the expansion vanishes if and only if the LeBrun's metric is indeed the flat one.","authors_text":"Andrea Loi, Fabio Zuddas, Michela Zedda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T12:42:06Z","title":"Some remarks on the Kaehler geometry of LeBrun's Ricci flat metrics on C^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6158","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":"sha256:3fd3eddfd3ed67700cb130d521a75f5b21a833c4538e75f7b23fb5ce7d317a34","target":"record","created_at":"2026-05-18T04:25:13Z","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":"01dfe68b8a53dc580bbdabac4d0c55a5c9f351c7853a56b54648d38d0500e969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-31T12:42:06Z","title_canon_sha256":"f9d59d9000f583b553a1904ed64875c8ca16bfecb20feec9199ca38335f6006a"},"schema_version":"1.0","source":{"id":"1103.6158","kind":"arxiv","version":1}},"canonical_sha256":"1b73932e696d08f8e49073ea16c806222054592310ac3e5f645f9796b09d34cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b73932e696d08f8e49073ea16c806222054592310ac3e5f645f9796b09d34cb","first_computed_at":"2026-05-18T04:25:13.881702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:13.881702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GSYfhIx0mNLHLibB7yEiA1f57xs9n+C2kI+neSKK2uYRQ+xyGgj/PawSkHzQPvZ7x/9b1QnHf/+ZRGOzpk7MDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:13.882199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.6158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fd3eddfd3ed67700cb130d521a75f5b21a833c4538e75f7b23fb5ce7d317a34","sha256:5eae28413bd6b34014eaa3b17cd705111d24dcc9728f5aaa89a3db4d1e08245d"],"state_sha256":"f08781c26d415a9adbfbf0fe3d0f9eb6428fd10d07f2a32c82e189d39f35eeb1"}