{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4V5SFUVGKPE4HB5LSNSSYOU3BT","short_pith_number":"pith:4V5SFUVG","canonical_record":{"source":{"id":"1509.06997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-09-21T21:18:55Z","cross_cats_sorted":[],"title_canon_sha256":"6cdacf5b32da40f9905d04b1004878e9ca26787542d399ec95b5301d2f084ab0","abstract_canon_sha256":"0923c3d7ffce190d249906f89252e2a9b3e8a41e186ecfe5937d835a4da8c09d"},"schema_version":"1.0"},"canonical_sha256":"e57b22d2a653c9c387ab93652c3a9b0cc5e451a64d09441f2d5c68a3ec2a48c7","source":{"kind":"arxiv","id":"1509.06997","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06997","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06997v1","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06997","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"4V5SFUVGKPE4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4V5SFUVGKPE4HB5L","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4V5SFUVG","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4V5SFUVGKPE4HB5LSNSSYOU3BT","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-09-21T21:18:55Z","cross_cats_sorted":[],"title_canon_sha256":"6cdacf5b32da40f9905d04b1004878e9ca26787542d399ec95b5301d2f084ab0","abstract_canon_sha256":"0923c3d7ffce190d249906f89252e2a9b3e8a41e186ecfe5937d835a4da8c09d"},"schema_version":"1.0"},"canonical_sha256":"e57b22d2a653c9c387ab93652c3a9b0cc5e451a64d09441f2d5c68a3ec2a48c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:08.594027Z","signature_b64":"MLcYe+bDOCcqBBouhtvAPXPPc8xexFTK9EC0UJMz52nl40W0AQOTBeKgeS1VJpSIyelBThRfO6SIuQZKZNZBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e57b22d2a653c9c387ab93652c3a9b0cc5e451a64d09441f2d5c68a3ec2a48c7","last_reissued_at":"2026-05-18T00:45:08.593370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:08.593370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06997","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":"2026-05-18T00:45:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAhKr1wnXFJhTbfvLuCXXu9DyKP8mX3JBn13dxHaHGxvYZfReAgGAcmrV3GqCOCwIMMQrU2ZZ2VXa5zU6MInCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:15:52.627698Z"},"content_sha256":"a076fdd95b6581fa115a884c07711f78af1307fbc92c53eecd45919d1e1b146d","schema_version":"1.0","event_id":"sha256:a076fdd95b6581fa115a884c07711f78af1307fbc92c53eecd45919d1e1b146d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4V5SFUVGKPE4HB5LSNSSYOU3BT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesic Deviation Equation in $f (R,T)$ Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"A. V. Kpadonou, E. H. Baffou, J. Tossa, M. E. Rodrigues, M. J. S. Houndjo","submitted_at":"2015-09-21T21:18:55Z","abstract_excerpt":"In this paper, we investigate the modified Geodesic Deviation Equation (GDE) in the framework of $f(R,T)$ theory of gravity where $R$ and $T$ are the curvature scalar and the trace of the energy-momentum tensor, respectively, using the FLRW background. In this way, we obtain the GR equivalent (GDE) in $f(R,T)$ metric formalism. We also extend our work to the generalization of the Matting relation and perform the numerical analysis with GDE for null vector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06997","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":"2026-05-18T00:45:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cBzwqxCH4GM1pJUOwjmPw4sNF54i6z5Qgz4gopR6dQde3lMwVRCwUqyKF4qBdeJj4ymBZ+JG4HOVpIm1YOeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:15:52.628396Z"},"content_sha256":"f0fc2b83dab8cafdce84c3a464ec9f297002348a5205a68e761e8f56541b51c1","schema_version":"1.0","event_id":"sha256:f0fc2b83dab8cafdce84c3a464ec9f297002348a5205a68e761e8f56541b51c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT/bundle.json","state_url":"https://pith.science/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT/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":"2026-06-08T01:15:52Z","links":{"resolver":"https://pith.science/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT","bundle":"https://pith.science/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT/bundle.json","state":"https://pith.science/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4V5SFUVGKPE4HB5LSNSSYOU3BT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4V5SFUVGKPE4HB5LSNSSYOU3BT","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":"0923c3d7ffce190d249906f89252e2a9b3e8a41e186ecfe5937d835a4da8c09d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-09-21T21:18:55Z","title_canon_sha256":"6cdacf5b32da40f9905d04b1004878e9ca26787542d399ec95b5301d2f084ab0"},"schema_version":"1.0","source":{"id":"1509.06997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06997","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06997v1","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06997","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"4V5SFUVGKPE4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4V5SFUVGKPE4HB5L","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4V5SFUVG","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:f0fc2b83dab8cafdce84c3a464ec9f297002348a5205a68e761e8f56541b51c1","target":"graph","created_at":"2026-05-18T00:45:08Z","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":"In this paper, we investigate the modified Geodesic Deviation Equation (GDE) in the framework of $f(R,T)$ theory of gravity where $R$ and $T$ are the curvature scalar and the trace of the energy-momentum tensor, respectively, using the FLRW background. In this way, we obtain the GR equivalent (GDE) in $f(R,T)$ metric formalism. We also extend our work to the generalization of the Matting relation and perform the numerical analysis with GDE for null vector.","authors_text":"A. V. Kpadonou, E. H. Baffou, J. Tossa, M. E. Rodrigues, M. J. S. Houndjo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-09-21T21:18:55Z","title":"Geodesic Deviation Equation in $f (R,T)$ Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06997","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:a076fdd95b6581fa115a884c07711f78af1307fbc92c53eecd45919d1e1b146d","target":"record","created_at":"2026-05-18T00:45:08Z","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":"0923c3d7ffce190d249906f89252e2a9b3e8a41e186ecfe5937d835a4da8c09d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-09-21T21:18:55Z","title_canon_sha256":"6cdacf5b32da40f9905d04b1004878e9ca26787542d399ec95b5301d2f084ab0"},"schema_version":"1.0","source":{"id":"1509.06997","kind":"arxiv","version":1}},"canonical_sha256":"e57b22d2a653c9c387ab93652c3a9b0cc5e451a64d09441f2d5c68a3ec2a48c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e57b22d2a653c9c387ab93652c3a9b0cc5e451a64d09441f2d5c68a3ec2a48c7","first_computed_at":"2026-05-18T00:45:08.593370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:08.593370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MLcYe+bDOCcqBBouhtvAPXPPc8xexFTK9EC0UJMz52nl40W0AQOTBeKgeS1VJpSIyelBThRfO6SIuQZKZNZBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:08.594027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a076fdd95b6581fa115a884c07711f78af1307fbc92c53eecd45919d1e1b146d","sha256:f0fc2b83dab8cafdce84c3a464ec9f297002348a5205a68e761e8f56541b51c1"],"state_sha256":"d586b064dc6ebdc84aed5ecf1acd6fe2f54726cb0bb3102fb1a10184d675fc0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LslgT2U29/j8jksY4LzZcbXF6m2OSn2QLH28/D7175XNZU+Arqd2WHo//jJQVh4CGS3lYm36d7H4dkZcJ/Z+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:15:52.632279Z","bundle_sha256":"245b22e93c0b7bda485517a5da55671d97370c2e10c05934058751e21015cf9c"}}