{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:TEIZ57XQKBC3RXIQSP525KON6F","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":"0a308837ebc49d3b24b55079859cf9c0d76366c5ac3bc899318c9ce82719045b","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2006-09-18T08:36:45Z","title_canon_sha256":"a5283c7bca05c27b0b8f443c77e47c641bbe1283ee106208d70975751219e2de"},"schema_version":"1.0","source":{"id":"math/0609487","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609487","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609487v2","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609487","created_at":"2026-05-18T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"TEIZ57XQKBC3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"TEIZ57XQKBC3RXIQ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"TEIZ57XQ","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:46a28d11edcd2d3d277eb15984741d96b724c59df85220a4d3c48ff475e0a2cb","target":"graph","created_at":"2026-05-18T00:48:01Z","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":"Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen (math.DG/0105263), who describe where the Einstein metrics appear amongst the Joyce spaces, leading to a different classification. Taking the twistor transform of our result gives a new proof of their theorem.","authors_text":"Joel Fine","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2006-09-18T08:36:45Z","title":"Toric anti-self-dual Einstein metrics via complex geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609487","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":"sha256:47b214938a553a4583d44cfce632a931b153338e4408d572996ce931654c306e","target":"record","created_at":"2026-05-18T00:48:01Z","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":"0a308837ebc49d3b24b55079859cf9c0d76366c5ac3bc899318c9ce82719045b","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2006-09-18T08:36:45Z","title_canon_sha256":"a5283c7bca05c27b0b8f443c77e47c641bbe1283ee106208d70975751219e2de"},"schema_version":"1.0","source":{"id":"math/0609487","kind":"arxiv","version":2}},"canonical_sha256":"99119efef05045b8dd1093fbaea9cdf15be2a4d77d8a324b3e646e7c2bdfeb67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99119efef05045b8dd1093fbaea9cdf15be2a4d77d8a324b3e646e7c2bdfeb67","first_computed_at":"2026-05-18T00:48:01.639258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:01.639258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gz3hp8ZrZuu/GI8ccIKJaUEiXOyjchNHV++oJSBgkr3SQPhkLJF5XdfXfHEdyzg2CWlpI4RabfcjR+lP8VKOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:01.639749Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609487","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47b214938a553a4583d44cfce632a931b153338e4408d572996ce931654c306e","sha256:46a28d11edcd2d3d277eb15984741d96b724c59df85220a4d3c48ff475e0a2cb"],"state_sha256":"004ebd048366890a6f5a9cdc6c8249d0c5a558b0376d6a1b7d4690420493af4e"}