{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:POPMAKVPJ7G6DRJY2OYO5WPS5G","short_pith_number":"pith:POPMAKVP","canonical_record":{"source":{"id":"1202.2352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-10T16:26:11Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"7f203c2eb613ff0ce4e523c2a4f53371c9dab9d1659d6750decb493af5b195b7","abstract_canon_sha256":"9c6995199f3a0ded59e11e86df59b9365e29482ce755697c67dac6c5420fb0fd"},"schema_version":"1.0"},"canonical_sha256":"7b9ec02aaf4fcde1c538d3b0eed9f2e9a401938e7b13e2c9d4a5d043e670b612","source":{"kind":"arxiv","id":"1202.2352","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2352","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2352v2","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2352","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"POPMAKVPJ7G6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"POPMAKVPJ7G6DRJY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"POPMAKVP","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:POPMAKVPJ7G6DRJY2OYO5WPS5G","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-10T16:26:11Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"7f203c2eb613ff0ce4e523c2a4f53371c9dab9d1659d6750decb493af5b195b7","abstract_canon_sha256":"9c6995199f3a0ded59e11e86df59b9365e29482ce755697c67dac6c5420fb0fd"},"schema_version":"1.0"},"canonical_sha256":"7b9ec02aaf4fcde1c538d3b0eed9f2e9a401938e7b13e2c9d4a5d043e670b612","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:12.774067Z","signature_b64":"0Ez2s+UNTwd4pZhhQqWWldc3e1m431HI24fsWizuSUpifTgr0S62awqpGXVmkaLw6SD4vbT+6YkdKJ8CH9z0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b9ec02aaf4fcde1c538d3b0eed9f2e9a401938e7b13e2c9d4a5d043e670b612","last_reissued_at":"2026-05-18T00:53:12.773576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:12.773576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2352","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2U5imdSqoXTiE6qTSHH8Vb8O3eeghtDCOTh6RbLldVVyT8pvTaPvsX+FfVgwe4Z+vdNoRkZ7kKNMI0Cq5YekAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:30:16.552353Z"},"content_sha256":"26324a4e8ec49558e4fdc591fac7331de2a70635bfbd837318ccba3429e0919e","schema_version":"1.0","event_id":"sha256:26324a4e8ec49558e4fdc591fac7331de2a70635bfbd837318ccba3429e0919e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:POPMAKVPJ7G6DRJY2OYO5WPS5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Modified Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc"],"primary_cat":"hep-th","authors_text":"Branko Dragovich, Ivan Dimitrijevic, Jelena Grujic, Zoran Rakic","submitted_at":"2012-02-10T16:26:11Z","abstract_excerpt":"We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \\mathcal{F}(\\Box) R$. In particular, using ansatz of the form $\\Box R = c R^\\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2352","kind":"arxiv","version":2},"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":"2026-05-18T00:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XremSOjw4uXUkVG2PWhVg9P4eYmJB2WFb06WqNUOOA7/FXBir2p1/x3mxg3ACu4MYyEcnGIWp2tf8XWfHY1KBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:30:16.552709Z"},"content_sha256":"1f5533006aaaa94379fd8219d273b8035e9e248611ffb4f387761a52c6e910f5","schema_version":"1.0","event_id":"sha256:1f5533006aaaa94379fd8219d273b8035e9e248611ffb4f387761a52c6e910f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G/bundle.json","state_url":"https://pith.science/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G/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":"2026-05-31T14:30:16Z","links":{"resolver":"https://pith.science/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G","bundle":"https://pith.science/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G/bundle.json","state":"https://pith.science/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/POPMAKVPJ7G6DRJY2OYO5WPS5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:POPMAKVPJ7G6DRJY2OYO5WPS5G","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":"9c6995199f3a0ded59e11e86df59b9365e29482ce755697c67dac6c5420fb0fd","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-10T16:26:11Z","title_canon_sha256":"7f203c2eb613ff0ce4e523c2a4f53371c9dab9d1659d6750decb493af5b195b7"},"schema_version":"1.0","source":{"id":"1202.2352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2352","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2352v2","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2352","created_at":"2026-05-18T00:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"POPMAKVPJ7G6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"POPMAKVPJ7G6DRJY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"POPMAKVP","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:1f5533006aaaa94379fd8219d273b8035e9e248611ffb4f387761a52c6e910f5","target":"graph","created_at":"2026-05-18T00:53:12Z","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 some aspects of nonlocal modified gravity, where nonlocality is of the type $R \\mathcal{F}(\\Box) R$. In particular, using ansatz of the form $\\Box R = c R^\\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.","authors_text":"Branko Dragovich, Ivan Dimitrijevic, Jelena Grujic, 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":"2012-02-10T16:26:11Z","title":"On Modified Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2352","kind":"arxiv","version":2},"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":"sha256:26324a4e8ec49558e4fdc591fac7331de2a70635bfbd837318ccba3429e0919e","target":"record","created_at":"2026-05-18T00:53:12Z","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":"9c6995199f3a0ded59e11e86df59b9365e29482ce755697c67dac6c5420fb0fd","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-02-10T16:26:11Z","title_canon_sha256":"7f203c2eb613ff0ce4e523c2a4f53371c9dab9d1659d6750decb493af5b195b7"},"schema_version":"1.0","source":{"id":"1202.2352","kind":"arxiv","version":2}},"canonical_sha256":"7b9ec02aaf4fcde1c538d3b0eed9f2e9a401938e7b13e2c9d4a5d043e670b612","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b9ec02aaf4fcde1c538d3b0eed9f2e9a401938e7b13e2c9d4a5d043e670b612","first_computed_at":"2026-05-18T00:53:12.773576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:12.773576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Ez2s+UNTwd4pZhhQqWWldc3e1m431HI24fsWizuSUpifTgr0S62awqpGXVmkaLw6SD4vbT+6YkdKJ8CH9z0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:12.774067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26324a4e8ec49558e4fdc591fac7331de2a70635bfbd837318ccba3429e0919e","sha256:1f5533006aaaa94379fd8219d273b8035e9e248611ffb4f387761a52c6e910f5"],"state_sha256":"566b8f9fbf29922795e1052e05e9833e68f593255040349329d3cd35a354ec67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J50IdY0MFWjOPHKerD7jmrWYMQpkpdSd1KYEpJ+tDTgZhwOyInaOs8kCBAImOEx2npYn+EJqQxwuFGNsqZa+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:30:16.554779Z","bundle_sha256":"424bdb8bf6fb481daa2e101e0214de547b58c5e58603620e64b15ab1e4167343"}}