{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UDNPTZU46WGV4HJNZYCSRAUT2U","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":"890640dcf7c32955b8f7e56489d627ce1cef46ebc932abe7ae6c7c12b2365491","cross_cats_sorted":["astro-ph.CO","math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-19T19:57:36Z","title_canon_sha256":"444dde00a166e10a66bd6480dc6c45d6e4bde283839ee960c359794ebaeeabea"},"schema_version":"1.0","source":{"id":"1607.05715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05715","created_at":"2026-05-18T01:05:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05715v2","created_at":"2026-05-18T01:05:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05715","created_at":"2026-05-18T01:05:42Z"},{"alias_kind":"pith_short_12","alias_value":"UDNPTZU46WGV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UDNPTZU46WGV4HJN","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UDNPTZU4","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:6d288b38a02d44bdb4c2ba089596593a615743ae6ea1918bf018dd86f5bf00a4","target":"graph","created_at":"2026-05-18T01:05:42Z","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 discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, $f(R) = R + \\alpha R^2$, $\\alpha > 0$, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniqu","authors_text":"Artur Alho, Claes Uggla, Sante Carloni","cross_cats":["astro-ph.CO","math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-19T19:57:36Z","title":"On dynamical systems approaches and methods in $f(R)$ cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05715","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:a85a60a1ae2d9fd9320d352a14a72f9729d07d1c93e4bf6943056f6d26e92039","target":"record","created_at":"2026-05-18T01:05:42Z","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":"890640dcf7c32955b8f7e56489d627ce1cef46ebc932abe7ae6c7c12b2365491","cross_cats_sorted":["astro-ph.CO","math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-07-19T19:57:36Z","title_canon_sha256":"444dde00a166e10a66bd6480dc6c45d6e4bde283839ee960c359794ebaeeabea"},"schema_version":"1.0","source":{"id":"1607.05715","kind":"arxiv","version":2}},"canonical_sha256":"a0daf9e69cf58d5e1d2dce05288293d525b29cc526cab057e6f8db9ee8a33fcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0daf9e69cf58d5e1d2dce05288293d525b29cc526cab057e6f8db9ee8a33fcf","first_computed_at":"2026-05-18T01:05:42.218217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:42.218217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RBigi7o1Bq/9ssi4BrFnT/TbJGAxyIqiS7Hf1OUkX9JZYTDlgG+OR2vDWED/rJGDeZPFDNlU9/FAcfFDd6r+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:42.218697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a85a60a1ae2d9fd9320d352a14a72f9729d07d1c93e4bf6943056f6d26e92039","sha256:6d288b38a02d44bdb4c2ba089596593a615743ae6ea1918bf018dd86f5bf00a4"],"state_sha256":"8317e7df17557e7a93829b8f2b9aabd06b085de36fba2bd0ee468e64ede1b020"}