{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ADEKLKIHCVM5VW66SVZVLKIF36","short_pith_number":"pith:ADEKLKIH","schema_version":"1.0","canonical_sha256":"00c8a5a9071559dadbde957355a905dfa446ea06b1845f378cf8bc52a8902f4e","source":{"kind":"arxiv","id":"1906.07683","version":3},"attestation_state":"computed","paper":{"title":"An Accurate Fitting Function For Scale-dependent Growth Rate in Hu-Sawicki $f(R)$ Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Elena Pierpaoli, Nareg Mirzatuny","submitted_at":"2019-06-18T16:55:26Z","abstract_excerpt":"We present a simple fitting formula for the scale-dependent growth rate of Hu-Sawicki model in $f(R)$ modified gravity. We compare the accuracy of the fitting function against numerical results and report achieving a sub-percent maximum error for all different studied cases. The validity of the fitting function is tested against a wide range of scales, $10^{-4} \\le k \\le 5 \\ [\\mathrm{Mpc}^{-1}]$ , for various redshift values in the range of $z \\in [0.0,\\ 3.0]$ and different $|f_R^0|$ values. This formula is useful in producing predictions for cosmological probes that are sensitive to growth ra"},"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":"1906.07683","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2019-06-18T16:55:26Z","cross_cats_sorted":[],"title_canon_sha256":"1ac4ef6c6477d01d4ac476add65148dfb52df8f791732d0ca4290c3b0898038a","abstract_canon_sha256":"0299fa0cdc155722a1393032bc1de45534d5148ff01620609244b80334fd13d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:15.963714Z","signature_b64":"+PTug/ItqFaeA1YJx/5X2k1DVI8iukXW/Na99naMK1Rstsl0hLmnt6ziJzzrwuvAthwA1XhApFGMDQptMoY+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00c8a5a9071559dadbde957355a905dfa446ea06b1845f378cf8bc52a8902f4e","last_reissued_at":"2026-07-05T00:30:15.963192Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:15.963192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Accurate Fitting Function For Scale-dependent Growth Rate in Hu-Sawicki $f(R)$ Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Elena Pierpaoli, Nareg Mirzatuny","submitted_at":"2019-06-18T16:55:26Z","abstract_excerpt":"We present a simple fitting formula for the scale-dependent growth rate of Hu-Sawicki model in $f(R)$ modified gravity. We compare the accuracy of the fitting function against numerical results and report achieving a sub-percent maximum error for all different studied cases. The validity of the fitting function is tested against a wide range of scales, $10^{-4} \\le k \\le 5 \\ [\\mathrm{Mpc}^{-1}]$ , for various redshift values in the range of $z \\in [0.0,\\ 3.0]$ and different $|f_R^0|$ values. This formula is useful in producing predictions for cosmological probes that are sensitive to growth ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07683","kind":"arxiv","version":3},"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/1906.07683/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":"1906.07683","created_at":"2026-07-05T00:30:15.963276+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.07683v3","created_at":"2026-07-05T00:30:15.963276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07683","created_at":"2026-07-05T00:30:15.963276+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADEKLKIHCVM5","created_at":"2026-07-05T00:30:15.963276+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADEKLKIHCVM5VW66","created_at":"2026-07-05T00:30:15.963276+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADEKLKIH","created_at":"2026-07-05T00:30:15.963276+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.09304","citing_title":"Fullshape power spectrum for the Symmetron modified gravity model","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36","json":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36.json","graph_json":"https://pith.science/api/pith-number/ADEKLKIHCVM5VW66SVZVLKIF36/graph.json","events_json":"https://pith.science/api/pith-number/ADEKLKIHCVM5VW66SVZVLKIF36/events.json","paper":"https://pith.science/paper/ADEKLKIH"},"agent_actions":{"view_html":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36","download_json":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36.json","view_paper":"https://pith.science/paper/ADEKLKIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.07683&json=true","fetch_graph":"https://pith.science/api/pith-number/ADEKLKIHCVM5VW66SVZVLKIF36/graph.json","fetch_events":"https://pith.science/api/pith-number/ADEKLKIHCVM5VW66SVZVLKIF36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36/action/storage_attestation","attest_author":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36/action/author_attestation","sign_citation":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36/action/citation_signature","submit_replication":"https://pith.science/pith/ADEKLKIHCVM5VW66SVZVLKIF36/action/replication_record"}},"created_at":"2026-07-05T00:30:15.963276+00:00","updated_at":"2026-07-05T00:30:15.963276+00:00"}