{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M6Q642LAU4LXVSETAZ4CYQRJFT","short_pith_number":"pith:M6Q642LA","canonical_record":{"source":{"id":"1512.06724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-21T17:40:18Z","cross_cats_sorted":[],"title_canon_sha256":"b6e109899141b49df4a85cc90d9ea3a24d5bdaa6710ef956861187eacd156843","abstract_canon_sha256":"3a2b8aba84c4d175914b33c6e8fc347c9f2ff1ef3c15fbe6d624cf7c957814bb"},"schema_version":"1.0"},"canonical_sha256":"67a1ee6960a7177ac89306782c42292ccd7f1fe678dcd593e4f6a67c278ff7d2","source":{"kind":"arxiv","id":"1512.06724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06724","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06724v1","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06724","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"M6Q642LAU4LX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M6Q642LAU4LXVSET","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M6Q642LA","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M6Q642LAU4LXVSETAZ4CYQRJFT","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-21T17:40:18Z","cross_cats_sorted":[],"title_canon_sha256":"b6e109899141b49df4a85cc90d9ea3a24d5bdaa6710ef956861187eacd156843","abstract_canon_sha256":"3a2b8aba84c4d175914b33c6e8fc347c9f2ff1ef3c15fbe6d624cf7c957814bb"},"schema_version":"1.0"},"canonical_sha256":"67a1ee6960a7177ac89306782c42292ccd7f1fe678dcd593e4f6a67c278ff7d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:59.834119Z","signature_b64":"uDrHOskZ7dIviG68t9X7UTmO/fiZlN7mEQK4zX/Rjvl4ILY0uQH6/7IvnmQTO5lZ0s2j1QRKpaIvP1IocodMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67a1ee6960a7177ac89306782c42292ccd7f1fe678dcd593e4f6a67c278ff7d2","last_reissued_at":"2026-05-18T01:23:59.833394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:59.833394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06724","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":"2026-05-18T01:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TDN2zCidk7/yTgwUN1LeB6EArDg0MIMKtkno/ZZeYTPDd1J2reYHUTZoeg7BGB06VBTRscm7OeeA0WD6M98DDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:06:36.035062Z"},"content_sha256":"a143fea48637c399bd3529831de2faae3f72a6dcfb21de147fca64810600c91a","schema_version":"1.0","event_id":"sha256:a143fea48637c399bd3529831de2faae3f72a6dcfb21de147fca64810600c91a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M6Q642LAU4LXVSETAZ4CYQRJFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prescribed curvature tensor in locally conformally flat manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mauricio Pieterzack, Romildo Pina","submitted_at":"2015-12-21T17:40:18Z","abstract_excerpt":"Our principal goal is to study the Prescribed Curvature Tensor problem in locally conformally flat manifolds. The solution to this problem is given explicitly for the special cases of the tensor R, including a case where the metric g is complete on Rn. Similar problems are considered for locally conformally flat manifolds. As applications of these results we exhibit explicit examples of metrics g, conformal to g they are solutions for this problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06724","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":"2026-05-18T01:23:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fqJTl8zfT1h5kGTG0Vnxd6bVgn82Q49keAS6NmHdrIpTpw23fdN/cjHNE0QFc0dCICuMkh/+2B13g/XUOSFYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:06:36.035429Z"},"content_sha256":"0d03b62dce6aa3c9496129b8fdd222a414e29efb9023eaa0f232c96a0ce6f39b","schema_version":"1.0","event_id":"sha256:0d03b62dce6aa3c9496129b8fdd222a414e29efb9023eaa0f232c96a0ce6f39b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6Q642LAU4LXVSETAZ4CYQRJFT/bundle.json","state_url":"https://pith.science/pith/M6Q642LAU4LXVSETAZ4CYQRJFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6Q642LAU4LXVSETAZ4CYQRJFT/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":"2026-06-24T03:06:36Z","links":{"resolver":"https://pith.science/pith/M6Q642LAU4LXVSETAZ4CYQRJFT","bundle":"https://pith.science/pith/M6Q642LAU4LXVSETAZ4CYQRJFT/bundle.json","state":"https://pith.science/pith/M6Q642LAU4LXVSETAZ4CYQRJFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6Q642LAU4LXVSETAZ4CYQRJFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M6Q642LAU4LXVSETAZ4CYQRJFT","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":"3a2b8aba84c4d175914b33c6e8fc347c9f2ff1ef3c15fbe6d624cf7c957814bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-21T17:40:18Z","title_canon_sha256":"b6e109899141b49df4a85cc90d9ea3a24d5bdaa6710ef956861187eacd156843"},"schema_version":"1.0","source":{"id":"1512.06724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06724","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06724v1","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06724","created_at":"2026-05-18T01:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"M6Q642LAU4LX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M6Q642LAU4LXVSET","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M6Q642LA","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:0d03b62dce6aa3c9496129b8fdd222a414e29efb9023eaa0f232c96a0ce6f39b","target":"graph","created_at":"2026-05-18T01:23:59Z","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":"Our principal goal is to study the Prescribed Curvature Tensor problem in locally conformally flat manifolds. The solution to this problem is given explicitly for the special cases of the tensor R, including a case where the metric g is complete on Rn. Similar problems are considered for locally conformally flat manifolds. As applications of these results we exhibit explicit examples of metrics g, conformal to g they are solutions for this problem.","authors_text":"Mauricio Pieterzack, Romildo Pina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-21T17:40:18Z","title":"Prescribed curvature tensor in locally conformally flat manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06724","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:a143fea48637c399bd3529831de2faae3f72a6dcfb21de147fca64810600c91a","target":"record","created_at":"2026-05-18T01:23:59Z","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":"3a2b8aba84c4d175914b33c6e8fc347c9f2ff1ef3c15fbe6d624cf7c957814bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-21T17:40:18Z","title_canon_sha256":"b6e109899141b49df4a85cc90d9ea3a24d5bdaa6710ef956861187eacd156843"},"schema_version":"1.0","source":{"id":"1512.06724","kind":"arxiv","version":1}},"canonical_sha256":"67a1ee6960a7177ac89306782c42292ccd7f1fe678dcd593e4f6a67c278ff7d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67a1ee6960a7177ac89306782c42292ccd7f1fe678dcd593e4f6a67c278ff7d2","first_computed_at":"2026-05-18T01:23:59.833394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:59.833394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uDrHOskZ7dIviG68t9X7UTmO/fiZlN7mEQK4zX/Rjvl4ILY0uQH6/7IvnmQTO5lZ0s2j1QRKpaIvP1IocodMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:59.834119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a143fea48637c399bd3529831de2faae3f72a6dcfb21de147fca64810600c91a","sha256:0d03b62dce6aa3c9496129b8fdd222a414e29efb9023eaa0f232c96a0ce6f39b"],"state_sha256":"17db8c8b19a9f4bafb96111724fdfc5e277dd22b553a96e2d17635b5607bad20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uF4dsH2CS30/MZ2dBO5zimiZzNqhsgMb1DfoMqXfN0RsqNEnxB7I9YMBbF69sueEHFjnl1OBJCLph/kCJCeSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T03:06:36.037330Z","bundle_sha256":"dbf5d7d27a08f95b349f638b644e2b76e2639a5ea35b21cceebacb90245c91a2"}}