{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IL6TPYGPS6QYGM53B3ULIO75CE","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":"44e18fdacaadb4bfc8552ae5b14fb0ab63435873e80cf3a34d41f827bcc18ea6","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-02-23T17:48:19Z","title_canon_sha256":"377a60442aa6beba593fd6b6576a631e461f64635d3fad816d2001f7ab89f953"},"schema_version":"1.0","source":{"id":"1902.08820","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08820","created_at":"2026-05-17T23:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08820v1","created_at":"2026-05-17T23:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08820","created_at":"2026-05-17T23:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"IL6TPYGPS6QY","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IL6TPYGPS6QYGM53","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IL6TPYGP","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:ea28f986c28b7169982a06364d9439e3a43ff95f9877d0d2360fc4df8a6389b2","target":"graph","created_at":"2026-05-17T23:52:49Z","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 consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form $P(R) F(\\Box) Q(R)$. For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein-Hilbert modified action and basics of gravity perturbations.","authors_text":"Branko Dragovich, Ivan Dimitrijevic, Jelena Stankovic, Zoran Rakic","cross_cats":["astro-ph.CO","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-02-23T17:48:19Z","title":"Variations of Infinite Derivative Modified Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08820","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:c40f0c4a9c316830ad2694ff2522dae5dd390c62c1cc197cd5e202c54b9cc7f2","target":"record","created_at":"2026-05-17T23:52:49Z","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":"44e18fdacaadb4bfc8552ae5b14fb0ab63435873e80cf3a34d41f827bcc18ea6","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-02-23T17:48:19Z","title_canon_sha256":"377a60442aa6beba593fd6b6576a631e461f64635d3fad816d2001f7ab89f953"},"schema_version":"1.0","source":{"id":"1902.08820","kind":"arxiv","version":1}},"canonical_sha256":"42fd37e0cf97a18333bb0ee8b43bfd1107d4cc10c2d58d4aeec215a6a4a120e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42fd37e0cf97a18333bb0ee8b43bfd1107d4cc10c2d58d4aeec215a6a4a120e0","first_computed_at":"2026-05-17T23:52:49.813444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:49.813444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mSezYmnvvQWWF6eVuikZz9tRzoirF85cIZyV2sg7gcaW1+F9TkkS5Ye/tdu0Tmy68/2YgMstxAM3TxQ5FG4WAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:49.814334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c40f0c4a9c316830ad2694ff2522dae5dd390c62c1cc197cd5e202c54b9cc7f2","sha256:ea28f986c28b7169982a06364d9439e3a43ff95f9877d0d2360fc4df8a6389b2"],"state_sha256":"a0f196a114abbedc083c4c5d2f334df617c237ffc0db2a89f1144e471a49a7c9"}