{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EGRTQK2IE6E4YKRPYVFVWQ4ZAV","short_pith_number":"pith:EGRTQK2I","canonical_record":{"source":{"id":"1101.4157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-21T15:20:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e30bb5a18b7164382a8b88c9c9ebbe1fd120a9769eb55016eff9a437d1abcd4f","abstract_canon_sha256":"db008f7e2742b0d2f24b259810b9345afb72721947c14941d0be23314f45a11c"},"schema_version":"1.0"},"canonical_sha256":"21a3382b482789cc2a2fc54b5b4399057c32433ca28b786ad609c5c8d6021779","source":{"kind":"arxiv","id":"1101.4157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4157","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4157v1","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4157","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"pith_short_12","alias_value":"EGRTQK2IE6E4","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EGRTQK2IE6E4YKRP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EGRTQK2I","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EGRTQK2IE6E4YKRPYVFVWQ4ZAV","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-21T15:20:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e30bb5a18b7164382a8b88c9c9ebbe1fd120a9769eb55016eff9a437d1abcd4f","abstract_canon_sha256":"db008f7e2742b0d2f24b259810b9345afb72721947c14941d0be23314f45a11c"},"schema_version":"1.0"},"canonical_sha256":"21a3382b482789cc2a2fc54b5b4399057c32433ca28b786ad609c5c8d6021779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:59.036634Z","signature_b64":"6rLSMnPLunPlSYPP5qUYOqYSx0gZVUB7ruJ4v0K4DC1Eexqbca8z4q398zeKKh2N7ADTA+lOFUG4wE5/5zzACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21a3382b482789cc2a2fc54b5b4399057c32433ca28b786ad609c5c8d6021779","last_reissued_at":"2026-05-18T03:41:59.036037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:59.036037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4157","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":"2026-05-18T03:41:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPPdbLbqst4Jc/q23JiD4/NPH0Fi9QwH5LOlPTaAVx+X6nsIYYDpv/nB0Ys0HWDNw7mxSfnCoL5B9MGNgKGKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:57:54.366121Z"},"content_sha256":"406df0f22ebabd90cd38903aa87ffca0fe9ed9afdca35d0f48155c871dcc0f48","schema_version":"1.0","event_id":"sha256:406df0f22ebabd90cd38903aa87ffca0fe9ed9afdca35d0f48155c871dcc0f48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EGRTQK2IE6E4YKRPYVFVWQ4ZAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended Derdzinski-Shen theorem for the Riemann tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Carlo Alberto Mantica, Luca Guido Molinari","submitted_at":"2011-01-21T15:20:35Z","abstract_excerpt":"We extend a classical result by Derdzinski and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms) as well as tensors with gauged Codazzi condition (i.e. \"recurrent 1-forms\"), typical of some well known differential structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4157","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":"2026-05-18T03:41:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEqGxkeN7FF2drMlk8pKmt+zoCxnixtCmAHv7tl54VNLWLUmMrsJ2yJGaMO3sdN3NkEnol7SXZACkcftFvzBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:57:54.366500Z"},"content_sha256":"32bf955c77be35e68122211c166f0cd1dea083f631f2fe60778a3a3620e4346a","schema_version":"1.0","event_id":"sha256:32bf955c77be35e68122211c166f0cd1dea083f631f2fe60778a3a3620e4346a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV/bundle.json","state_url":"https://pith.science/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV/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":"2026-05-25T08:57:54Z","links":{"resolver":"https://pith.science/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV","bundle":"https://pith.science/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV/bundle.json","state":"https://pith.science/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGRTQK2IE6E4YKRPYVFVWQ4ZAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EGRTQK2IE6E4YKRPYVFVWQ4ZAV","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":"db008f7e2742b0d2f24b259810b9345afb72721947c14941d0be23314f45a11c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-21T15:20:35Z","title_canon_sha256":"e30bb5a18b7164382a8b88c9c9ebbe1fd120a9769eb55016eff9a437d1abcd4f"},"schema_version":"1.0","source":{"id":"1101.4157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4157","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4157v1","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4157","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"pith_short_12","alias_value":"EGRTQK2IE6E4","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EGRTQK2IE6E4YKRP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EGRTQK2I","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:32bf955c77be35e68122211c166f0cd1dea083f631f2fe60778a3a3620e4346a","target":"graph","created_at":"2026-05-18T03:41:59Z","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":"We extend a classical result by Derdzinski and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms) as well as tensors with gauged Codazzi condition (i.e. \"recurrent 1-forms\"), typical of some well known differential structures.","authors_text":"Carlo Alberto Mantica, Luca Guido Molinari","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-21T15:20:35Z","title":"Extended Derdzinski-Shen theorem for the Riemann tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4157","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":"sha256:406df0f22ebabd90cd38903aa87ffca0fe9ed9afdca35d0f48155c871dcc0f48","target":"record","created_at":"2026-05-18T03:41:59Z","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":"db008f7e2742b0d2f24b259810b9345afb72721947c14941d0be23314f45a11c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-21T15:20:35Z","title_canon_sha256":"e30bb5a18b7164382a8b88c9c9ebbe1fd120a9769eb55016eff9a437d1abcd4f"},"schema_version":"1.0","source":{"id":"1101.4157","kind":"arxiv","version":1}},"canonical_sha256":"21a3382b482789cc2a2fc54b5b4399057c32433ca28b786ad609c5c8d6021779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a3382b482789cc2a2fc54b5b4399057c32433ca28b786ad609c5c8d6021779","first_computed_at":"2026-05-18T03:41:59.036037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:59.036037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6rLSMnPLunPlSYPP5qUYOqYSx0gZVUB7ruJ4v0K4DC1Eexqbca8z4q398zeKKh2N7ADTA+lOFUG4wE5/5zzACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:59.036634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:406df0f22ebabd90cd38903aa87ffca0fe9ed9afdca35d0f48155c871dcc0f48","sha256:32bf955c77be35e68122211c166f0cd1dea083f631f2fe60778a3a3620e4346a"],"state_sha256":"c2eebe5cfb1a169e9c9161cdb119b8dc714a3f924ee001ed129fe7a9b08efd22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggKn3jlJlNKZ8DBFxtB4sHgMeKQCYYP1mpMHGVpYCzDY1JbUXUHTCRRgnk31TOuVJ9Tw2XR/Mfy1JrXeGPUGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:57:54.369028Z","bundle_sha256":"21a4fbea4e761320104e2f99b6239a50fba7c86f738fa42acdfde2ee2669ae80"}}