{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:Y4RARUTBELWFSN3YT7ZAOWZD5L","short_pith_number":"pith:Y4RARUTB","canonical_record":{"source":{"id":"2206.11259","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-06-22T01:55:34Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"13ec80a6ca8eea565b5c74358efb998caa89f74c7269707434efbf56fe7283f4","abstract_canon_sha256":"ef1074b87ddec6f75576963f9c728ebfb0b1b7a00817aa851bc733d9c7842761"},"schema_version":"1.0"},"canonical_sha256":"c72208d26122ec5937789ff2075b23eaf9b37fc09ffc0d6e870e005558055dcc","source":{"kind":"arxiv","id":"2206.11259","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.11259","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"2206.11259v2","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.11259","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"Y4RARUTBELWF","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_16","alias_value":"Y4RARUTBELWFSN3Y","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_8","alias_value":"Y4RARUTB","created_at":"2026-07-05T10:18:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:Y4RARUTBELWFSN3YT7ZAOWZD5L","target":"record","payload":{"canonical_record":{"source":{"id":"2206.11259","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-06-22T01:55:34Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"13ec80a6ca8eea565b5c74358efb998caa89f74c7269707434efbf56fe7283f4","abstract_canon_sha256":"ef1074b87ddec6f75576963f9c728ebfb0b1b7a00817aa851bc733d9c7842761"},"schema_version":"1.0"},"canonical_sha256":"c72208d26122ec5937789ff2075b23eaf9b37fc09ffc0d6e870e005558055dcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:18:30.518232Z","signature_b64":"Pl8LJSMppy1Umb81bmIkc0cbml3lC4tSkyceNZaoFZ7dl+ZwWlK7BIuIMIb9ACfIGMrqgkQFpLCSbrBLSjxGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c72208d26122ec5937789ff2075b23eaf9b37fc09ffc0d6e870e005558055dcc","last_reissued_at":"2026-07-05T10:18:30.517813Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:18:30.517813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.11259","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":"2026-07-05T10:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9a+jUey0Oiv0t7KgZHkAh2lPYCtjWdb+IgllgQ/hIev6ZO/Wx5S/GX51n5oC0yu+MR443O25rIkaNVtprLBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T11:49:30.822622Z"},"content_sha256":"9bc529dbf800ff1107e894d8a28c734b4139dc66e137fe2bfabb7c4fbcbfd7ad","schema_version":"1.0","event_id":"sha256:9bc529dbf800ff1107e894d8a28c734b4139dc66e137fe2bfabb7c4fbcbfd7ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:Y4RARUTBELWFSN3YT7ZAOWZD5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbative approach to $f(R)$-gravitation in FLRW cosmology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Nguyen Anh Ky, Nguyen Thi Hong Van, Pham Van Ky","submitted_at":"2022-06-22T01:55:34Z","abstract_excerpt":"The $f(R)$ theory of gravitation developed perturbatively around the general theory of relativity with cosmological constant (the \\text{$\\Lambda$}CDM model) in a flat FLWR geometry is considered. As a result, a general explicit cosmological solution that can be used for any model with an arbitrary, but well-defined, $f(R)$ function (just satisfying given perturbation conditions) is derived. This perturbative solution shows how the Hubble parameter $H (t)$ depends on time (along with the cosmological constant and the matter density) to adapt to the evolution of the Universe. To illustrate, this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11259","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.11259/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qA2qrD3+wrMkR49PUvMNWb6oFTs/oUSzNnFFd79pGP32UcmKFHWMwYUf5SrHjUcdK0ciNIfgYUVboWrv3fgVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T11:49:30.823648Z"},"content_sha256":"60b8d91fecadbd723ff7c3124fd95e307436477af248c20dca879b3371c75101","schema_version":"1.0","event_id":"sha256:60b8d91fecadbd723ff7c3124fd95e307436477af248c20dca879b3371c75101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L/bundle.json","state_url":"https://pith.science/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L/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":"2026-08-10T11:49:30Z","links":{"resolver":"https://pith.science/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L","bundle":"https://pith.science/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L/bundle.json","state":"https://pith.science/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4RARUTBELWFSN3YT7ZAOWZD5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Y4RARUTBELWFSN3YT7ZAOWZD5L","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":"ef1074b87ddec6f75576963f9c728ebfb0b1b7a00817aa851bc733d9c7842761","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-06-22T01:55:34Z","title_canon_sha256":"13ec80a6ca8eea565b5c74358efb998caa89f74c7269707434efbf56fe7283f4"},"schema_version":"1.0","source":{"id":"2206.11259","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.11259","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"2206.11259v2","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.11259","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"Y4RARUTBELWF","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_16","alias_value":"Y4RARUTBELWFSN3Y","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_8","alias_value":"Y4RARUTB","created_at":"2026-07-05T10:18:30Z"}],"graph_snapshots":[{"event_id":"sha256:60b8d91fecadbd723ff7c3124fd95e307436477af248c20dca879b3371c75101","target":"graph","created_at":"2026-07-05T10:18:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.11259/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $f(R)$ theory of gravitation developed perturbatively around the general theory of relativity with cosmological constant (the \\text{$\\Lambda$}CDM model) in a flat FLWR geometry is considered. As a result, a general explicit cosmological solution that can be used for any model with an arbitrary, but well-defined, $f(R)$ function (just satisfying given perturbation conditions) is derived. This perturbative solution shows how the Hubble parameter $H (t)$ depends on time (along with the cosmological constant and the matter density) to adapt to the evolution of the Universe. To illustrate, this","authors_text":"Nguyen Anh Ky, Nguyen Thi Hong Van, Pham Van Ky","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-06-22T01:55:34Z","title":"Perturbative approach to $f(R)$-gravitation in FLRW cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11259","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":"sha256:9bc529dbf800ff1107e894d8a28c734b4139dc66e137fe2bfabb7c4fbcbfd7ad","target":"record","created_at":"2026-07-05T10:18:30Z","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":"ef1074b87ddec6f75576963f9c728ebfb0b1b7a00817aa851bc733d9c7842761","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-06-22T01:55:34Z","title_canon_sha256":"13ec80a6ca8eea565b5c74358efb998caa89f74c7269707434efbf56fe7283f4"},"schema_version":"1.0","source":{"id":"2206.11259","kind":"arxiv","version":2}},"canonical_sha256":"c72208d26122ec5937789ff2075b23eaf9b37fc09ffc0d6e870e005558055dcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c72208d26122ec5937789ff2075b23eaf9b37fc09ffc0d6e870e005558055dcc","first_computed_at":"2026-07-05T10:18:30.517813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:30.517813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pl8LJSMppy1Umb81bmIkc0cbml3lC4tSkyceNZaoFZ7dl+ZwWlK7BIuIMIb9ACfIGMrqgkQFpLCSbrBLSjxGBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:30.518232Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.11259","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bc529dbf800ff1107e894d8a28c734b4139dc66e137fe2bfabb7c4fbcbfd7ad","sha256:60b8d91fecadbd723ff7c3124fd95e307436477af248c20dca879b3371c75101"],"state_sha256":"5a1106eae399dd8de89b29b2423b26b710d8a3e9390d83be2b4ea16a8e166473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/lxJmP/wRVlFeMTPaKOO1tO/oB+w/eLKgnOQ8ERegDPtfkJzVPookrX2XMoUjfNdp/IpQ+nRxuFmTNGzbAOvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T11:49:30.830482Z","bundle_sha256":"f7bcaf6e30c93d850a65fdc50d960bb6632e03daa4dd9d99b7f357f732784d6b"}}