{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RRM6UTKN6ABVLLMTJ7Q3G66SFF","short_pith_number":"pith:RRM6UTKN","canonical_record":{"source":{"id":"1605.07611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-05-24T15:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"7d50d3b88a0549f855c68d2de04431e62552eda0b324ae8110060e5c89ffeda3","abstract_canon_sha256":"0b921786e4d1390dc270badf75c157bb0fa37bc1a540d8e43b607bcb069e60a1"},"schema_version":"1.0"},"canonical_sha256":"8c59ea4d4df00355ad934fe1b37bd2296b7b4b215ee28fef0ae3a3afe86eb0ee","source":{"kind":"arxiv","id":"1605.07611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07611","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07611v1","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07611","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"RRM6UTKN6ABV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RRM6UTKN6ABVLLMT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RRM6UTKN","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RRM6UTKN6ABVLLMTJ7Q3G66SFF","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-05-24T15:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"7d50d3b88a0549f855c68d2de04431e62552eda0b324ae8110060e5c89ffeda3","abstract_canon_sha256":"0b921786e4d1390dc270badf75c157bb0fa37bc1a540d8e43b607bcb069e60a1"},"schema_version":"1.0"},"canonical_sha256":"8c59ea4d4df00355ad934fe1b37bd2296b7b4b215ee28fef0ae3a3afe86eb0ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:45.396807Z","signature_b64":"vn3Dx5lYovwMJrqFmLdlFpDxUrkQOn0+VfFZ/M78qcrWiJlOE9zpOCJwOzPEQnQ177chBv33G4FDxSB4BVrAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c59ea4d4df00355ad934fe1b37bd2296b7b4b215ee28fef0ae3a3afe86eb0ee","last_reissued_at":"2026-05-18T01:13:45.396254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:45.396254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07611","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":"2026-05-18T01:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PJul/Td7fQr1BO2BT75CvmRGwoKcxqZSpaIRGisO7V/nTk5QcL+5R5ZoruhrJ0o4DydnAqFTzzUk37FIHwAwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:38:50.085355Z"},"content_sha256":"32ff554a339318bdfbe3d56df7824341808123c94576b461e3959f8bb086ccdf","schema_version":"1.0","event_id":"sha256:32ff554a339318bdfbe3d56df7824341808123c94576b461e3959f8bb086ccdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RRM6UTKN6ABVLLMTJ7Q3G66SFF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Mattig's relation in Brans-Dicke-Rastall gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Abdul Jawad, Ines G. Salako, M. J. S. Houndjo","submitted_at":"2016-05-24T15:47:25Z","abstract_excerpt":"The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $\\eta(z)$ and observer area distance $r_0(z)$ and compare the results with $\\Lambda$CDM model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07611","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":"2026-05-18T01:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WD6lgVClJBagLUm132Ncq2CVOeUIrESbuyuNMXt+nWT1i100H9+e9gAujr+0t+MfJPd1/vTcwyARRcCJa3q0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:38:50.085704Z"},"content_sha256":"214955a344a4170913988c5156ffd972073b8b4203118b08444dc9dcfe5780fe","schema_version":"1.0","event_id":"sha256:214955a344a4170913988c5156ffd972073b8b4203118b08444dc9dcfe5780fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF/bundle.json","state_url":"https://pith.science/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF/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":"2026-06-05T13:38:50Z","links":{"resolver":"https://pith.science/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF","bundle":"https://pith.science/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF/bundle.json","state":"https://pith.science/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RRM6UTKN6ABVLLMTJ7Q3G66SFF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RRM6UTKN6ABVLLMTJ7Q3G66SFF","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":"0b921786e4d1390dc270badf75c157bb0fa37bc1a540d8e43b607bcb069e60a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-05-24T15:47:25Z","title_canon_sha256":"7d50d3b88a0549f855c68d2de04431e62552eda0b324ae8110060e5c89ffeda3"},"schema_version":"1.0","source":{"id":"1605.07611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07611","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07611v1","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07611","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"RRM6UTKN6ABV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RRM6UTKN6ABVLLMT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RRM6UTKN","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:214955a344a4170913988c5156ffd972073b8b4203118b08444dc9dcfe5780fe","target":"graph","created_at":"2026-05-18T01:13:45Z","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":"The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $\\eta(z)$ and observer area distance $r_0(z)$ and compare the results with $\\Lambda$CDM model.","authors_text":"Abdul Jawad, Ines G. Salako, M. J. S. Houndjo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-05-24T15:47:25Z","title":"Generalized Mattig's relation in Brans-Dicke-Rastall gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07611","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":"sha256:32ff554a339318bdfbe3d56df7824341808123c94576b461e3959f8bb086ccdf","target":"record","created_at":"2026-05-18T01:13:45Z","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":"0b921786e4d1390dc270badf75c157bb0fa37bc1a540d8e43b607bcb069e60a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-05-24T15:47:25Z","title_canon_sha256":"7d50d3b88a0549f855c68d2de04431e62552eda0b324ae8110060e5c89ffeda3"},"schema_version":"1.0","source":{"id":"1605.07611","kind":"arxiv","version":1}},"canonical_sha256":"8c59ea4d4df00355ad934fe1b37bd2296b7b4b215ee28fef0ae3a3afe86eb0ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c59ea4d4df00355ad934fe1b37bd2296b7b4b215ee28fef0ae3a3afe86eb0ee","first_computed_at":"2026-05-18T01:13:45.396254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:45.396254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vn3Dx5lYovwMJrqFmLdlFpDxUrkQOn0+VfFZ/M78qcrWiJlOE9zpOCJwOzPEQnQ177chBv33G4FDxSB4BVrAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:45.396807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32ff554a339318bdfbe3d56df7824341808123c94576b461e3959f8bb086ccdf","sha256:214955a344a4170913988c5156ffd972073b8b4203118b08444dc9dcfe5780fe"],"state_sha256":"9dee4108f5e9ceb1a4fbd64980355a1e71ea0f2e10ca7ce1a860f5d13c4a77f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8GAelxjmPBMdhPBKHnG57DlqO0T0ogdxJp5S5ZRJyLRN+D0ZLRruHc5kuGcTAuQeCsecqVfOs5iGqeFOjMWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T13:38:50.087606Z","bundle_sha256":"ac1688b9fd45e466f0a5d0c18226d03f2840fb3af97bcfd9f03fa5178e18cf0c"}}