{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2ZFQ52FFV26ZXPIQMNE3O476QL","short_pith_number":"pith:2ZFQ52FF","canonical_record":{"source":{"id":"1008.3781","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-23T09:29:26Z","cross_cats_sorted":["gr-qc","math.DS"],"title_canon_sha256":"f54ba3602470a9878262f49112658e6aec96ca79cd9eb6593d558f9b8c024d8e","abstract_canon_sha256":"f949a84726affb9016807c35f40b17d6df0a816297b2bc72f38a1860bb5ba452"},"schema_version":"1.0"},"canonical_sha256":"d64b0ee8a5aebd9bbd106349b773fe82ca6dc1f1a48ddeb877e86716069f9907","source":{"kind":"arxiv","id":"1008.3781","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3781","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3781v2","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3781","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"2ZFQ52FFV26Z","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ZFQ52FFV26ZXPIQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ZFQ52FF","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2ZFQ52FFV26ZXPIQMNE3O476QL","target":"record","payload":{"canonical_record":{"source":{"id":"1008.3781","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-23T09:29:26Z","cross_cats_sorted":["gr-qc","math.DS"],"title_canon_sha256":"f54ba3602470a9878262f49112658e6aec96ca79cd9eb6593d558f9b8c024d8e","abstract_canon_sha256":"f949a84726affb9016807c35f40b17d6df0a816297b2bc72f38a1860bb5ba452"},"schema_version":"1.0"},"canonical_sha256":"d64b0ee8a5aebd9bbd106349b773fe82ca6dc1f1a48ddeb877e86716069f9907","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.408341Z","signature_b64":"C8kslivk71vwuB763Tv9mn5ttE4WjURie83xom9ygJ58Rmq3YSYqfV60Hk+F3oyucmFyCuyfaCEBTC+DdN5oAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d64b0ee8a5aebd9bbd106349b773fe82ca6dc1f1a48ddeb877e86716069f9907","last_reissued_at":"2026-05-18T03:45:23.407777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.407777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.3781","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":"2026-05-18T03:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0uemKRoVVC0tXglYWNJjoW3gEhkai9gxi1WaRyz99f2OTAVebf+RMDCsSyf1vfK9pRZr1XHRR2Kl8YpCKRrjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:17:48.118990Z"},"content_sha256":"eac785022b09bc9be9e91064c6efe08616b6d6b5a9c59635ce6c9a8f83640d36","schema_version":"1.0","event_id":"sha256:eac785022b09bc9be9e91064c6efe08616b6d6b5a9c59635ce6c9a8f83640d36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2ZFQ52FFV26ZXPIQMNE3O476QL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Formes normales pour les champs conformes pseudo-riemanniens","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DS"],"primary_cat":"math.DG","authors_text":"Charles Frances, Karin Melnick","submitted_at":"2010-08-23T09:29:26Z","abstract_excerpt":"We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is conformally flat. In either case, the vector field is locally conjugate to a normal form on a model space. For smooth metrics of general signature, we obtain the analogous result under the additional assumption that the differential of the flow at the fixed point is bounded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3781","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":"2026-05-18T03:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qlxKfIRMMv3es3SB+uQ+aoHojeg97WbXBs1o1CUdJc46oRtvGVPzqdkvrEwGUFzOlCI0vd6nyTugprhee4NBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:17:48.119345Z"},"content_sha256":"3dfce43b6b5aaa42bd0e14a2481b6fbb432dd78dd9ed21f29a8e3b70674f8d89","schema_version":"1.0","event_id":"sha256:3dfce43b6b5aaa42bd0e14a2481b6fbb432dd78dd9ed21f29a8e3b70674f8d89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZFQ52FFV26ZXPIQMNE3O476QL/bundle.json","state_url":"https://pith.science/pith/2ZFQ52FFV26ZXPIQMNE3O476QL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZFQ52FFV26ZXPIQMNE3O476QL/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":"2026-06-21T09:17:48Z","links":{"resolver":"https://pith.science/pith/2ZFQ52FFV26ZXPIQMNE3O476QL","bundle":"https://pith.science/pith/2ZFQ52FFV26ZXPIQMNE3O476QL/bundle.json","state":"https://pith.science/pith/2ZFQ52FFV26ZXPIQMNE3O476QL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZFQ52FFV26ZXPIQMNE3O476QL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2ZFQ52FFV26ZXPIQMNE3O476QL","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":"f949a84726affb9016807c35f40b17d6df0a816297b2bc72f38a1860bb5ba452","cross_cats_sorted":["gr-qc","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-23T09:29:26Z","title_canon_sha256":"f54ba3602470a9878262f49112658e6aec96ca79cd9eb6593d558f9b8c024d8e"},"schema_version":"1.0","source":{"id":"1008.3781","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3781","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3781v2","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3781","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"2ZFQ52FFV26Z","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ZFQ52FFV26ZXPIQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ZFQ52FF","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:3dfce43b6b5aaa42bd0e14a2481b6fbb432dd78dd9ed21f29a8e3b70674f8d89","target":"graph","created_at":"2026-05-18T03:45:23Z","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 establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is conformally flat. In either case, the vector field is locally conjugate to a normal form on a model space. For smooth metrics of general signature, we obtain the analogous result under the additional assumption that the differential of the flow at the fixed point is bounded.","authors_text":"Charles Frances, Karin Melnick","cross_cats":["gr-qc","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-23T09:29:26Z","title":"Formes normales pour les champs conformes pseudo-riemanniens"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3781","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:eac785022b09bc9be9e91064c6efe08616b6d6b5a9c59635ce6c9a8f83640d36","target":"record","created_at":"2026-05-18T03:45:23Z","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":"f949a84726affb9016807c35f40b17d6df0a816297b2bc72f38a1860bb5ba452","cross_cats_sorted":["gr-qc","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-23T09:29:26Z","title_canon_sha256":"f54ba3602470a9878262f49112658e6aec96ca79cd9eb6593d558f9b8c024d8e"},"schema_version":"1.0","source":{"id":"1008.3781","kind":"arxiv","version":2}},"canonical_sha256":"d64b0ee8a5aebd9bbd106349b773fe82ca6dc1f1a48ddeb877e86716069f9907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d64b0ee8a5aebd9bbd106349b773fe82ca6dc1f1a48ddeb877e86716069f9907","first_computed_at":"2026-05-18T03:45:23.407777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:23.407777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C8kslivk71vwuB763Tv9mn5ttE4WjURie83xom9ygJ58Rmq3YSYqfV60Hk+F3oyucmFyCuyfaCEBTC+DdN5oAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:23.408341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3781","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eac785022b09bc9be9e91064c6efe08616b6d6b5a9c59635ce6c9a8f83640d36","sha256:3dfce43b6b5aaa42bd0e14a2481b6fbb432dd78dd9ed21f29a8e3b70674f8d89"],"state_sha256":"2c3d0626d9a9de5c843c66f9a064beaac515e39d8148c6e42b2bd0e4863d9cf7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b52lWQfmrrd59AuUW/JPRbiZCDvU6GOM4B4Gts8j4hMHfNsn/jdoP1IGOtsUCRdZKc69WmDtqM8xjC5riv5wCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:17:48.121273Z","bundle_sha256":"9cfccea668cbfe7d3e2e28dad16583c2af74b00a1da7ad9f6a5afa0bfa0ee584"}}