{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FKNOTHTTRYMJJ2GVRDJ5ZCWQPL","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":"f52663e177115c7bd43de45767844e9aefb66070ecc42a83bc78483fc6be34db","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-04-26T16:27:52Z","title_canon_sha256":"a002eb99290b8f6934de89a5e8bacad2dee5fff35d7eddfebbbf274cf8a80e22"},"schema_version":"1.0","source":{"id":"2104.12687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12687","created_at":"2026-07-05T03:16:14Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12687v2","created_at":"2026-07-05T03:16:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12687","created_at":"2026-07-05T03:16:14Z"},{"alias_kind":"pith_short_12","alias_value":"FKNOTHTTRYMJ","created_at":"2026-07-05T03:16:14Z"},{"alias_kind":"pith_short_16","alias_value":"FKNOTHTTRYMJJ2GV","created_at":"2026-07-05T03:16:14Z"},{"alias_kind":"pith_short_8","alias_value":"FKNOTHTT","created_at":"2026-07-05T03:16:14Z"}],"graph_snapshots":[{"event_id":"sha256:1cc523a279d131e95bd911a55836d332be92fb02ae070390391bf5be790adf65","target":"graph","created_at":"2026-07-05T03:16:14Z","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/2104.12687/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we investigate the dynamics of the interacting dark energy and dark matter in viable models of $f(R)$ gravity by using a standard framework of dynamical system analysis. A simple form of the interacting dark energy $Q=3\\alpha H\\rho_{m}$ is used to study three viable models of $f(R)$ gravity which are consistent with local gravity constraints and satisfying conditions for the cosmological viability. As a result, we find that the fixed points are slightly modified from those obtained in the standard non-interacting analysis of $f(R)$ gravity proposed so far in the literature. In ou","authors_text":"Bhuddhanubhap Silasan (Khon Kaen U.), Daris Samart (Khon Kaen U.), Phongpichit Channuie (Walailak U.)","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-04-26T16:27:52Z","title":"Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12687","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":"sha256:2a10eb935fec887c680a310621eac83536561b64c1af8293e3cc481b7f8973c0","target":"record","created_at":"2026-07-05T03:16:14Z","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":"f52663e177115c7bd43de45767844e9aefb66070ecc42a83bc78483fc6be34db","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-04-26T16:27:52Z","title_canon_sha256":"a002eb99290b8f6934de89a5e8bacad2dee5fff35d7eddfebbbf274cf8a80e22"},"schema_version":"1.0","source":{"id":"2104.12687","kind":"arxiv","version":2}},"canonical_sha256":"2a9ae99e738e1894e8d588d3dc8ad07affb7b532681f905ae0539eb315da678a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a9ae99e738e1894e8d588d3dc8ad07affb7b532681f905ae0539eb315da678a","first_computed_at":"2026-07-05T03:16:14.184757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:16:14.184757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sT8EY+SrE2Pg0t6+MwQdaYS8qnTxa6wn8r0j81983p91o+bYRi1ug9rRt8YSLd4xcgBMGNC5ZNJKzNZuCu9DDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:16:14.185295Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.12687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a10eb935fec887c680a310621eac83536561b64c1af8293e3cc481b7f8973c0","sha256:1cc523a279d131e95bd911a55836d332be92fb02ae070390391bf5be790adf65"],"state_sha256":"e96424d2e478bc66e769b447d21b826711d8b3c5893033604b9a660957303f24"}