{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:U5H4U4GXI65YLCI6NQPKVEKUHX","short_pith_number":"pith:U5H4U4GX","schema_version":"1.0","canonical_sha256":"a74fca70d747bb85891e6c1eaa91543dcd11c383be238b6b196dd5ab47f626b1","source":{"kind":"arxiv","id":"gr-qc/0612180","version":2},"attestation_state":"computed","paper":{"title":"Conditions for the cosmological viability of f(R) dark energy models","license":"","headline":"","cross_cats":["astro-ph","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"David Polarski, Luca Amendola, Radouane Gannouji, Shinji Tsujikawa","submitted_at":"2006-12-28T14:17:09Z","abstract_excerpt":"We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f(R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r, m) plane, where m=Rf_{,RR}/f_{,R} and r=-Rf_{,R}/f with f_{,R}=df/dR. This allows us to classify the f(R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. The existence of a viable matter dominated epoch prior to a late-tim"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"gr-qc/0612180","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2006-12-28T14:17:09Z","cross_cats_sorted":["astro-ph","hep-ph","hep-th"],"title_canon_sha256":"6eddec7e2d024618d8f091eae6f329f542379292d7c74bc688591ba6395f240b","abstract_canon_sha256":"fb63f4727148ab7063cb31edf59eb14914be9ec56746d53a994e38cff8001e05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:21:59.712172Z","signature_b64":"xhzxvs8/fT+K3xMWa8ivoKK2GtJaF3dnztkzQRv4TZnZ5auzkkINQI9dS3+Qe6II4VqjNrsIkv4Dvh3YzhAhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a74fca70d747bb85891e6c1eaa91543dcd11c383be238b6b196dd5ab47f626b1","last_reissued_at":"2026-07-04T15:21:59.711768Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:21:59.711768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditions for the cosmological viability of f(R) dark energy models","license":"","headline":"","cross_cats":["astro-ph","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"David Polarski, Luca Amendola, Radouane Gannouji, Shinji Tsujikawa","submitted_at":"2006-12-28T14:17:09Z","abstract_excerpt":"We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f(R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r, m) plane, where m=Rf_{,RR}/f_{,R} and r=-Rf_{,R}/f with f_{,R}=df/dR. This allows us to classify the f(R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. The existence of a viable matter dominated epoch prior to a late-tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0612180","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/gr-qc/0612180/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0612180","created_at":"2026-07-04T15:21:59.711845+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0612180v2","created_at":"2026-07-04T15:21:59.711845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0612180","created_at":"2026-07-04T15:21:59.711845+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5H4U4GXI65Y","created_at":"2026-07-04T15:21:59.711845+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5H4U4GXI65YLCI6","created_at":"2026-07-04T15:21:59.711845+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5H4U4GX","created_at":"2026-07-04T15:21:59.711845+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2605.26173","citing_title":"Effect of $R^2$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"1906.08920","citing_title":"Cosmology in symmetric teleparallel gravity and its dynamical system","ref_index":43,"is_internal_anchor":true},{"citing_arxiv_id":"2511.19154","citing_title":"Dynamical system analysis of the cosmological phases in Palatini $k$-essence gravity","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX","json":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX.json","graph_json":"https://pith.science/api/pith-number/U5H4U4GXI65YLCI6NQPKVEKUHX/graph.json","events_json":"https://pith.science/api/pith-number/U5H4U4GXI65YLCI6NQPKVEKUHX/events.json","paper":"https://pith.science/paper/U5H4U4GX"},"agent_actions":{"view_html":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX","download_json":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX.json","view_paper":"https://pith.science/paper/U5H4U4GX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0612180&json=true","fetch_graph":"https://pith.science/api/pith-number/U5H4U4GXI65YLCI6NQPKVEKUHX/graph.json","fetch_events":"https://pith.science/api/pith-number/U5H4U4GXI65YLCI6NQPKVEKUHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX/action/storage_attestation","attest_author":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX/action/author_attestation","sign_citation":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX/action/citation_signature","submit_replication":"https://pith.science/pith/U5H4U4GXI65YLCI6NQPKVEKUHX/action/replication_record"}},"created_at":"2026-07-04T15:21:59.711845+00:00","updated_at":"2026-07-04T15:21:59.711845+00:00"}