{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:J3VXFDM2ABLJLU7ZTMIONXIHRH","short_pith_number":"pith:J3VXFDM2","canonical_record":{"source":{"id":"1304.7772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-04-29T20:00:01Z","cross_cats_sorted":["gr-qc","math.DG"],"title_canon_sha256":"51f182e135aab539027d1f2955e90824545ce4f58058e97268804b204b410c61","abstract_canon_sha256":"5ea0f904545142771a47c8a92cd2fc221f5eb53df710146e9d7b8033dd294bb0"},"schema_version":"1.0"},"canonical_sha256":"4eeb728d9a005695d3f99b10e6dd0789f871a69bc7fd590c96c3ffcfe471bfc9","source":{"kind":"arxiv","id":"1304.7772","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7772","created_at":"2026-05-18T01:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7772v2","created_at":"2026-05-18T01:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7772","created_at":"2026-05-18T01:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"J3VXFDM2ABLJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J3VXFDM2ABLJLU7Z","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J3VXFDM2","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:J3VXFDM2ABLJLU7ZTMIONXIHRH","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-04-29T20:00:01Z","cross_cats_sorted":["gr-qc","math.DG"],"title_canon_sha256":"51f182e135aab539027d1f2955e90824545ce4f58058e97268804b204b410c61","abstract_canon_sha256":"5ea0f904545142771a47c8a92cd2fc221f5eb53df710146e9d7b8033dd294bb0"},"schema_version":"1.0"},"canonical_sha256":"4eeb728d9a005695d3f99b10e6dd0789f871a69bc7fd590c96c3ffcfe471bfc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:14.476074Z","signature_b64":"cKraXtSDjfleFeE4x/a3gYUczmeAQhuvXsUfvRoHflTtcv4mF+Su1myFk5WBpMzsC94i0Rfrkx2rZw6x0XIKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eeb728d9a005695d3f99b10e6dd0789f871a69bc7fd590c96c3ffcfe471bfc9","last_reissued_at":"2026-05-18T01:50:14.475516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:14.475516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7772","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":"2026-05-18T01:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pCh5FscHyWnAokOeoBXZpkISbdrauud6z1MvmdKbP5Uh9x9vXozrfYrA4MbM9GdmuYhT8lRyG1dKWnSUh946BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:54:36.180272Z"},"content_sha256":"a642e705a4c75cded9fded0009d2378949660433eb40608ba18f138618fd762b","schema_version":"1.0","event_id":"sha256:a642e705a4c75cded9fded0009d2378949660433eb40608ba18f138618fd762b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:J3VXFDM2ABLJLU7ZTMIONXIHRH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Dual Conformal Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"hep-th","authors_text":"Maciej Dunajski, Paul Tod","submitted_at":"2013-04-29T20:00:01Z","abstract_excerpt":"We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and tensor conformal invariants. The invariants obstruct the existence of parallel sections of a certain connection on a complex rank-four vector bundle over $M$. They provide a natural generalisation of the Bach tensor which vanishes identically for anti-self-dual conformal structures. We use the obstructions to demonstrate that LeBrun's anti-self-dual metrics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7772","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":"2026-05-18T01:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ov+hVoMXfft0CQgLFhsdp6CeQoRRHcOWbrS4FhixcYet3/fj5GdCoMO2V8Ki0sWRW9llsmZ/VloR2kPblhjhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T11:54:36.180959Z"},"content_sha256":"0af3ce11e485e90aa6a6d8aeb94501d5c288bea74ac1155a3552916441c09154","schema_version":"1.0","event_id":"sha256:0af3ce11e485e90aa6a6d8aeb94501d5c288bea74ac1155a3552916441c09154"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH/bundle.json","state_url":"https://pith.science/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH/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":"2026-05-25T11:54:36Z","links":{"resolver":"https://pith.science/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH","bundle":"https://pith.science/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH/bundle.json","state":"https://pith.science/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3VXFDM2ABLJLU7ZTMIONXIHRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J3VXFDM2ABLJLU7ZTMIONXIHRH","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":"5ea0f904545142771a47c8a92cd2fc221f5eb53df710146e9d7b8033dd294bb0","cross_cats_sorted":["gr-qc","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-04-29T20:00:01Z","title_canon_sha256":"51f182e135aab539027d1f2955e90824545ce4f58058e97268804b204b410c61"},"schema_version":"1.0","source":{"id":"1304.7772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7772","created_at":"2026-05-18T01:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7772v2","created_at":"2026-05-18T01:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7772","created_at":"2026-05-18T01:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"J3VXFDM2ABLJ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J3VXFDM2ABLJLU7Z","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J3VXFDM2","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:0af3ce11e485e90aa6a6d8aeb94501d5c288bea74ac1155a3552916441c09154","target":"graph","created_at":"2026-05-18T01:50:14Z","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":"We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and tensor conformal invariants. The invariants obstruct the existence of parallel sections of a certain connection on a complex rank-four vector bundle over $M$. They provide a natural generalisation of the Bach tensor which vanishes identically for anti-self-dual conformal structures. We use the obstructions to demonstrate that LeBrun's anti-self-dual metrics","authors_text":"Maciej Dunajski, Paul Tod","cross_cats":["gr-qc","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-04-29T20:00:01Z","title":"Self-Dual Conformal Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7772","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:a642e705a4c75cded9fded0009d2378949660433eb40608ba18f138618fd762b","target":"record","created_at":"2026-05-18T01:50:14Z","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":"5ea0f904545142771a47c8a92cd2fc221f5eb53df710146e9d7b8033dd294bb0","cross_cats_sorted":["gr-qc","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-04-29T20:00:01Z","title_canon_sha256":"51f182e135aab539027d1f2955e90824545ce4f58058e97268804b204b410c61"},"schema_version":"1.0","source":{"id":"1304.7772","kind":"arxiv","version":2}},"canonical_sha256":"4eeb728d9a005695d3f99b10e6dd0789f871a69bc7fd590c96c3ffcfe471bfc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eeb728d9a005695d3f99b10e6dd0789f871a69bc7fd590c96c3ffcfe471bfc9","first_computed_at":"2026-05-18T01:50:14.475516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:14.475516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cKraXtSDjfleFeE4x/a3gYUczmeAQhuvXsUfvRoHflTtcv4mF+Su1myFk5WBpMzsC94i0Rfrkx2rZw6x0XIKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:14.476074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a642e705a4c75cded9fded0009d2378949660433eb40608ba18f138618fd762b","sha256:0af3ce11e485e90aa6a6d8aeb94501d5c288bea74ac1155a3552916441c09154"],"state_sha256":"556e97dd4fc321c3df2bbe5f3dfc85fe97fcc6d2ab9b22c5554a8eab8d6fd547"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DYMJVh59Y0cmfWdfip2+73NbRrDF06c8hY1/XMR/7/Ax9mTHnndTJ8Y4HcBqVSJmFTPEgF33U0nWT2LEyyC7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T11:54:36.184682Z","bundle_sha256":"5146e5ded0bafed4262c86c216229243db33ccf6fd7f976b5123ce6f62d926f0"}}