{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BJ7YVQ5MVI7T2HQNDUIWXUOY53","short_pith_number":"pith:BJ7YVQ5M","canonical_record":{"source":{"id":"1112.0284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-01T20:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"4b5561f666b70da9f9c3a30379a88051f0e0d5c1e7e017db1cb6317b52b35f7f","abstract_canon_sha256":"7be9de316574b089a5ba8343ee9d97ef69c0b5d1c257c8294efd5ee976ab4a60"},"schema_version":"1.0"},"canonical_sha256":"0a7f8ac3acaa3f3d1e0d1d116bd1d8eec59ff2b6c492bec4c2260f0c49f70e93","source":{"kind":"arxiv","id":"1112.0284","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0284","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0284v1","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0284","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"BJ7YVQ5MVI7T","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BJ7YVQ5MVI7T2HQN","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BJ7YVQ5M","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BJ7YVQ5MVI7T2HQNDUIWXUOY53","target":"record","payload":{"canonical_record":{"source":{"id":"1112.0284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-01T20:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"4b5561f666b70da9f9c3a30379a88051f0e0d5c1e7e017db1cb6317b52b35f7f","abstract_canon_sha256":"7be9de316574b089a5ba8343ee9d97ef69c0b5d1c257c8294efd5ee976ab4a60"},"schema_version":"1.0"},"canonical_sha256":"0a7f8ac3acaa3f3d1e0d1d116bd1d8eec59ff2b6c492bec4c2260f0c49f70e93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:32.775093Z","signature_b64":"Ufa7gHyCOcb3GMop3wEr6GCIkYK+HDjqSqilff6l+XnHQ+Y+Z6VuUD1QdB3M1b8228Ta3OYNT24iW2myZDL8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a7f8ac3acaa3f3d1e0d1d116bd1d8eec59ff2b6c492bec4c2260f0c49f70e93","last_reissued_at":"2026-05-18T03:49:32.774257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:32.774257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.0284","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/LZPljuH53QkTpi39fCXQeP+0DYRZVn3pe0fxeiaMduubUGpWgeWRzMz12miRawNfr+1+QwfwTVwLb8SidKRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:30:41.454426Z"},"content_sha256":"f7633d4098138975aa254b045086071f1b1c5767f3e838b4f42e0638bbd7d19b","schema_version":"1.0","event_id":"sha256:f7633d4098138975aa254b045086071f1b1c5767f3e838b4f42e0638bbd7d19b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BJ7YVQ5MVI7T2HQNDUIWXUOY53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-jets of conformal fields along their zero sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrzej Derdzinski","submitted_at":"2011-12-01T20:01:22Z","abstract_excerpt":"The connected components of the zero set of any conformal vector field $v$, in a pseudo-Riemannian manifold $(M,g)$ of arbitrary signature, are of two types, which may be called `essential' and `nonessential'. The former consist of points at which $v$ is essential, that is, cannot be turned into a Killing field by a local conformal change of the metric. In a component of the latter type, points at which $v$ is nonessential form a relatively-open dense subset that is at the same time a totally umbilical submanifold of $(M,g)$. An essential component is always a null totally geodesic submanifold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0284","kind":"arxiv","version":1},"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":"2026-05-18T03:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"480E8+TRLzmJsWH46oA65FZS33031dEsjoIzNYbmR9x++m9dlWFcapC1cfrv0jxfJLzrHJhxJWNCBZxoT7YZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:30:41.454878Z"},"content_sha256":"259f5f2aaa41a1f15bd51fc0c3c17068cc23e04410c3e4cd8aced3f5d91c8518","schema_version":"1.0","event_id":"sha256:259f5f2aaa41a1f15bd51fc0c3c17068cc23e04410c3e4cd8aced3f5d91c8518"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53/bundle.json","state_url":"https://pith.science/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53/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":"2026-05-27T08:30:41Z","links":{"resolver":"https://pith.science/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53","bundle":"https://pith.science/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53/bundle.json","state":"https://pith.science/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJ7YVQ5MVI7T2HQNDUIWXUOY53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BJ7YVQ5MVI7T2HQNDUIWXUOY53","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":"7be9de316574b089a5ba8343ee9d97ef69c0b5d1c257c8294efd5ee976ab4a60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-01T20:01:22Z","title_canon_sha256":"4b5561f666b70da9f9c3a30379a88051f0e0d5c1e7e017db1cb6317b52b35f7f"},"schema_version":"1.0","source":{"id":"1112.0284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0284","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0284v1","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0284","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"BJ7YVQ5MVI7T","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BJ7YVQ5MVI7T2HQN","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BJ7YVQ5M","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:259f5f2aaa41a1f15bd51fc0c3c17068cc23e04410c3e4cd8aced3f5d91c8518","target":"graph","created_at":"2026-05-18T03:49:32Z","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":"The connected components of the zero set of any conformal vector field $v$, in a pseudo-Riemannian manifold $(M,g)$ of arbitrary signature, are of two types, which may be called `essential' and `nonessential'. The former consist of points at which $v$ is essential, that is, cannot be turned into a Killing field by a local conformal change of the metric. In a component of the latter type, points at which $v$ is nonessential form a relatively-open dense subset that is at the same time a totally umbilical submanifold of $(M,g)$. An essential component is always a null totally geodesic submanifold","authors_text":"Andrzej Derdzinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-01T20:01:22Z","title":"Two-jets of conformal fields along their zero sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0284","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:f7633d4098138975aa254b045086071f1b1c5767f3e838b4f42e0638bbd7d19b","target":"record","created_at":"2026-05-18T03:49:32Z","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":"7be9de316574b089a5ba8343ee9d97ef69c0b5d1c257c8294efd5ee976ab4a60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-01T20:01:22Z","title_canon_sha256":"4b5561f666b70da9f9c3a30379a88051f0e0d5c1e7e017db1cb6317b52b35f7f"},"schema_version":"1.0","source":{"id":"1112.0284","kind":"arxiv","version":1}},"canonical_sha256":"0a7f8ac3acaa3f3d1e0d1d116bd1d8eec59ff2b6c492bec4c2260f0c49f70e93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a7f8ac3acaa3f3d1e0d1d116bd1d8eec59ff2b6c492bec4c2260f0c49f70e93","first_computed_at":"2026-05-18T03:49:32.774257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:32.774257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ufa7gHyCOcb3GMop3wEr6GCIkYK+HDjqSqilff6l+XnHQ+Y+Z6VuUD1QdB3M1b8228Ta3OYNT24iW2myZDL8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:32.775093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7633d4098138975aa254b045086071f1b1c5767f3e838b4f42e0638bbd7d19b","sha256:259f5f2aaa41a1f15bd51fc0c3c17068cc23e04410c3e4cd8aced3f5d91c8518"],"state_sha256":"15c659b26bdf04628ff7d66c19951e75596d5c2af829a2b88df020041cfb19dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyvFv82v2+3gszr+7mrTprsmhfMmHvguHzImgvnyQ00dirpb5NHwyQC0gKdvwEMJEYBN6R9vshvfP+lugWosBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:30:41.457280Z","bundle_sha256":"90fef0a166bec9f392a5e4323f8b8c5b7d0cf2e0c4dde248195006246d4bdc0b"}}