{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:TEIZ57XQKBC3RXIQSP525KON6F","short_pith_number":"pith:TEIZ57XQ","canonical_record":{"source":{"id":"math/0609487","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-09-18T08:36:45Z","cross_cats_sorted":[],"title_canon_sha256":"a5283c7bca05c27b0b8f443c77e47c641bbe1283ee106208d70975751219e2de","abstract_canon_sha256":"0a308837ebc49d3b24b55079859cf9c0d76366c5ac3bc899318c9ce82719045b"},"schema_version":"1.0"},"canonical_sha256":"99119efef05045b8dd1093fbaea9cdf15be2a4d77d8a324b3e646e7c2bdfeb67","source":{"kind":"arxiv","id":"math/0609487","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:TEIZ57XQKBC3RXIQSP525KON6F","target":"record","payload":{"canonical_record":{"source":{"id":"math/0609487","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-09-18T08:36:45Z","cross_cats_sorted":[],"title_canon_sha256":"a5283c7bca05c27b0b8f443c77e47c641bbe1283ee106208d70975751219e2de","abstract_canon_sha256":"0a308837ebc49d3b24b55079859cf9c0d76366c5ac3bc899318c9ce82719045b"},"schema_version":"1.0"},"canonical_sha256":"99119efef05045b8dd1093fbaea9cdf15be2a4d77d8a324b3e646e7c2bdfeb67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:01.639749Z","signature_b64":"Gz3hp8ZrZuu/GI8ccIKJaUEiXOyjchNHV++oJSBgkr3SQPhkLJF5XdfXfHEdyzg2CWlpI4RabfcjR+lP8VKOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99119efef05045b8dd1093fbaea9cdf15be2a4d77d8a324b3e646e7c2bdfeb67","last_reissued_at":"2026-05-18T00:48:01.639258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:01.639258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0609487","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGxZWiUCY2cm3VxY9yAS3SZy6oVHlvpBSD+ZA+9joXpf2C+7NQ13sFU8/SRtTIvbzkg7wOdDgZM4KBhVToEtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:02:43.592191Z"},"content_sha256":"47b214938a553a4583d44cfce632a931b153338e4408d572996ce931654c306e","schema_version":"1.0","event_id":"sha256:47b214938a553a4583d44cfce632a931b153338e4408d572996ce931654c306e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:TEIZ57XQKBC3RXIQSP525KON6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric anti-self-dual Einstein metrics via complex geometry","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Joel Fine","submitted_at":"2006-09-18T08:36:45Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609487","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrX4nYdXhlSmJ6z7+uRxGJ7p801ezlEARSWOL1MW/ukS+Ad0lMEfOosuYfmr2Xx6SUiNdObKmLF6Tze6oW5MCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:02:43.593092Z"},"content_sha256":"46a28d11edcd2d3d277eb15984741d96b724c59df85220a4d3c48ff475e0a2cb","schema_version":"1.0","event_id":"sha256:46a28d11edcd2d3d277eb15984741d96b724c59df85220a4d3c48ff475e0a2cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEIZ57XQKBC3RXIQSP525KON6F/bundle.json","state_url":"https://pith.science/pith/TEIZ57XQKBC3RXIQSP525KON6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEIZ57XQKBC3RXIQSP525KON6F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T20:02:43Z","links":{"resolver":"https://pith.science/pith/TEIZ57XQKBC3RXIQSP525KON6F","bundle":"https://pith.science/pith/TEIZ57XQKBC3RXIQSP525KON6F/bundle.json","state":"https://pith.science/pith/TEIZ57XQKBC3RXIQSP525KON6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEIZ57XQKBC3RXIQSP525KON6F/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kY0WMicyeeAN1GP259qkasTZ6VyLPgCCRupbq4PBKEl7078/wamOiZXZuEFNF3bjdl2DNHh5HhFPIJ4cyVFFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:02:43.597772Z","bundle_sha256":"e695f78c4150ed11ffb136c86882dece6c966b699eceea8db5693f945069f2ea"}}