{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XVTT5OCJOYO6QJNXEGZS65FAX4","short_pith_number":"pith:XVTT5OCJ","canonical_record":{"source":{"id":"1109.6258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-28T16:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"5610a42843617c2e9c84b57fd7cb54b3290f58bd356c5c65f34d1cf9e21f4aeb","abstract_canon_sha256":"0b37c9c8db1918319c3c4712ed84be5db486aaf46c93385de97f8a152cb3dfb5"},"schema_version":"1.0"},"canonical_sha256":"bd673eb849761de825b721b32f74a0bf2fb1b25db827bd08e6fa04aedcedc644","source":{"kind":"arxiv","id":"1109.6258","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6258","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6258v1","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6258","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"XVTT5OCJOYO6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XVTT5OCJOYO6QJNX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XVTT5OCJ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XVTT5OCJOYO6QJNXEGZS65FAX4","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-28T16:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"5610a42843617c2e9c84b57fd7cb54b3290f58bd356c5c65f34d1cf9e21f4aeb","abstract_canon_sha256":"0b37c9c8db1918319c3c4712ed84be5db486aaf46c93385de97f8a152cb3dfb5"},"schema_version":"1.0"},"canonical_sha256":"bd673eb849761de825b721b32f74a0bf2fb1b25db827bd08e6fa04aedcedc644","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.301334Z","signature_b64":"bOCDqbuYffHSAYGC8L8dmEQ0DESIZxn3c2GNjGwWEYjrjvSjKZXsPSEKpZDV++i3EkmpE6zHscTEOMjcdod2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd673eb849761de825b721b32f74a0bf2fb1b25db827bd08e6fa04aedcedc644","last_reissued_at":"2026-05-18T01:36:21.300881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.300881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6258","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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6/gdYU3TZhqpCay6scoMHCddo81kyAX1mxzkImxcSUj4y7jVeva9MMERBnPSCCrmn7qfvvEMcVV5JGjosLr8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:23:38.850150Z"},"content_sha256":"9d0f67ba881c37d198c80455a03d2ed4a849423e1cf5d04954d231f7b35b50e1","schema_version":"1.0","event_id":"sha256:9d0f67ba881c37d198c80455a03d2ed4a849423e1cf5d04954d231f7b35b50e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XVTT5OCJOYO6QJNXEGZS65FAX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The curvature tensor of (\\ka,\\mu,\\nu)-contact metric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfonso Carriazo, Cengizhan Murathan, Kadri Arslan, Ver\\'onica Mart\\'in-Molina","submitted_at":"2011-09-28T16:11:12Z","abstract_excerpt":"We study the Riemann curvature tensor of (\\kappa,\\mu,\\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (\\kappa,\\mu,\\nu)-space forms and of the necessary and sufficient conditions for them to be conformally flat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6258","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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4r41f/widZ5cFeV2X1KzO8e0TM4ZJlISAKdB+q3qhp08KmVkReQE+sSj49UngBHdFJgawWB2G20CPBTtN/1KBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:23:38.850517Z"},"content_sha256":"4b7f7a710f68cd980f594bd7b7867408767ac472dfc46ca57ec0a0b7ef2c600e","schema_version":"1.0","event_id":"sha256:4b7f7a710f68cd980f594bd7b7867408767ac472dfc46ca57ec0a0b7ef2c600e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVTT5OCJOYO6QJNXEGZS65FAX4/bundle.json","state_url":"https://pith.science/pith/XVTT5OCJOYO6QJNXEGZS65FAX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVTT5OCJOYO6QJNXEGZS65FAX4/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":"2026-06-03T18:23:38Z","links":{"resolver":"https://pith.science/pith/XVTT5OCJOYO6QJNXEGZS65FAX4","bundle":"https://pith.science/pith/XVTT5OCJOYO6QJNXEGZS65FAX4/bundle.json","state":"https://pith.science/pith/XVTT5OCJOYO6QJNXEGZS65FAX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVTT5OCJOYO6QJNXEGZS65FAX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XVTT5OCJOYO6QJNXEGZS65FAX4","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":"0b37c9c8db1918319c3c4712ed84be5db486aaf46c93385de97f8a152cb3dfb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-28T16:11:12Z","title_canon_sha256":"5610a42843617c2e9c84b57fd7cb54b3290f58bd356c5c65f34d1cf9e21f4aeb"},"schema_version":"1.0","source":{"id":"1109.6258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6258","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6258v1","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6258","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"XVTT5OCJOYO6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XVTT5OCJOYO6QJNX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XVTT5OCJ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:4b7f7a710f68cd980f594bd7b7867408767ac472dfc46ca57ec0a0b7ef2c600e","target":"graph","created_at":"2026-05-18T01:36:21Z","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 study the Riemann curvature tensor of (\\kappa,\\mu,\\nu)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (\\kappa,\\mu,\\nu)-space forms and of the necessary and sufficient conditions for them to be conformally flat.","authors_text":"Alfonso Carriazo, Cengizhan Murathan, Kadri Arslan, Ver\\'onica Mart\\'in-Molina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-28T16:11:12Z","title":"The curvature tensor of (\\ka,\\mu,\\nu)-contact metric manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6258","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":"sha256:9d0f67ba881c37d198c80455a03d2ed4a849423e1cf5d04954d231f7b35b50e1","target":"record","created_at":"2026-05-18T01:36:21Z","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":"0b37c9c8db1918319c3c4712ed84be5db486aaf46c93385de97f8a152cb3dfb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-28T16:11:12Z","title_canon_sha256":"5610a42843617c2e9c84b57fd7cb54b3290f58bd356c5c65f34d1cf9e21f4aeb"},"schema_version":"1.0","source":{"id":"1109.6258","kind":"arxiv","version":1}},"canonical_sha256":"bd673eb849761de825b721b32f74a0bf2fb1b25db827bd08e6fa04aedcedc644","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd673eb849761de825b721b32f74a0bf2fb1b25db827bd08e6fa04aedcedc644","first_computed_at":"2026-05-18T01:36:21.300881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.300881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bOCDqbuYffHSAYGC8L8dmEQ0DESIZxn3c2GNjGwWEYjrjvSjKZXsPSEKpZDV++i3EkmpE6zHscTEOMjcdod2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.301334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d0f67ba881c37d198c80455a03d2ed4a849423e1cf5d04954d231f7b35b50e1","sha256:4b7f7a710f68cd980f594bd7b7867408767ac472dfc46ca57ec0a0b7ef2c600e"],"state_sha256":"91a8bcadfeeab6c0bb1e4d05af32a757f832f83e8934abf16aa71a7585a02e54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PXiMchFO/pNmnM+8svWGC7KEMBM9eyqQ8DXBL9V6eYMYmSyQPNI5GG3cwritF6JeO7Aex2wnscDfgWIF1s+BDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:23:38.852495Z","bundle_sha256":"580e0ad51f4664ae7b7151454d9fc0e982fdb04177d9b47c49f5141c1835f3f0"}}