{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XIB2GB26OUCRWIW3JSGQS6GLQL","short_pith_number":"pith:XIB2GB26","canonical_record":{"source":{"id":"1111.0171","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-01T11:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"cafa0200f2521ec341f875a0f1c91e3121ab4b07680774824f9b2930b7cbed59","abstract_canon_sha256":"7817dac4845f32e6c30ab6dd37b1d6f95385e2ad2d8611c45a984a25ae5c8b7f"},"schema_version":"1.0"},"canonical_sha256":"ba03a3075e75051b22db4c8d0978cb82ff31df0f7a3481b20d568b28bdbe6cf0","source":{"kind":"arxiv","id":"1111.0171","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0171","created_at":"2026-05-18T01:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0171v3","created_at":"2026-05-18T01:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0171","created_at":"2026-05-18T01:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"XIB2GB26OUCR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XIB2GB26OUCRWIW3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XIB2GB26","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XIB2GB26OUCRWIW3JSGQS6GLQL","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0171","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-01T11:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"cafa0200f2521ec341f875a0f1c91e3121ab4b07680774824f9b2930b7cbed59","abstract_canon_sha256":"7817dac4845f32e6c30ab6dd37b1d6f95385e2ad2d8611c45a984a25ae5c8b7f"},"schema_version":"1.0"},"canonical_sha256":"ba03a3075e75051b22db4c8d0978cb82ff31df0f7a3481b20d568b28bdbe6cf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:48.988873Z","signature_b64":"K9d9IVnO0aIOnCc9QOIcDKJqOX0Qfe5RpZQTM92wjwbzyZ0CmUnW0hkXfMnVgfdjDvq1F/QMCFS0A7u5TNIpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba03a3075e75051b22db4c8d0978cb82ff31df0f7a3481b20d568b28bdbe6cf0","last_reissued_at":"2026-05-18T01:59:48.988167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:48.988167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0171","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GArz2m1F8T8cCV4AWfEpRxj7SyfRoXUmnoOZPnnjdz+JjsODgDZBzAlF5lqABqNXSjxfThWqfcSmmQz8fPHbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:21:15.033246Z"},"content_sha256":"b7bb0ee9a1f1b59856c364e08eb2d03bbe9c740c3397f9f3e55a1a968d20818a","schema_version":"1.0","event_id":"sha256:b7bb0ee9a1f1b59856c364e08eb2d03bbe9c740c3397f9f3e55a1a968d20818a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XIB2GB26OUCRWIW3JSGQS6GLQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosmological dynamics of fourth order gravity: A compact view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Mohamed Abdelwahab, Peter K. S. Dunsby, Rituparno Goswami","submitted_at":"2011-11-01T11:16:04Z","abstract_excerpt":"We construct a compact phase space for flat FLRW spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behaviour of the phase space of Universes with a non-negative Ricci scalar in R + {\\alpha}R^n gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature fluid dominated phase mimicking standard radiation, then pass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0171","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":""},"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":"2026-05-18T01:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MfbPeBeLxSH035vUkhYJFlvVWgsS498VNpEKdWrSyWwOn0HJCa3X+rwz/RB4eqVsjMZwmqh4Fr4G27LAVHjfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:21:15.033978Z"},"content_sha256":"2b7675bf8a41fe66d6eb05bf1c87e7226814bf9f86da4c4ceeb2929acdf473f6","schema_version":"1.0","event_id":"sha256:2b7675bf8a41fe66d6eb05bf1c87e7226814bf9f86da4c4ceeb2929acdf473f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XIB2GB26OUCRWIW3JSGQS6GLQL/bundle.json","state_url":"https://pith.science/pith/XIB2GB26OUCRWIW3JSGQS6GLQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XIB2GB26OUCRWIW3JSGQS6GLQL/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":"2026-05-31T19:21:15Z","links":{"resolver":"https://pith.science/pith/XIB2GB26OUCRWIW3JSGQS6GLQL","bundle":"https://pith.science/pith/XIB2GB26OUCRWIW3JSGQS6GLQL/bundle.json","state":"https://pith.science/pith/XIB2GB26OUCRWIW3JSGQS6GLQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XIB2GB26OUCRWIW3JSGQS6GLQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XIB2GB26OUCRWIW3JSGQS6GLQL","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":"7817dac4845f32e6c30ab6dd37b1d6f95385e2ad2d8611c45a984a25ae5c8b7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-01T11:16:04Z","title_canon_sha256":"cafa0200f2521ec341f875a0f1c91e3121ab4b07680774824f9b2930b7cbed59"},"schema_version":"1.0","source":{"id":"1111.0171","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0171","created_at":"2026-05-18T01:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0171v3","created_at":"2026-05-18T01:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0171","created_at":"2026-05-18T01:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"XIB2GB26OUCR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XIB2GB26OUCRWIW3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XIB2GB26","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:2b7675bf8a41fe66d6eb05bf1c87e7226814bf9f86da4c4ceeb2929acdf473f6","target":"graph","created_at":"2026-05-18T01:59:48Z","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 construct a compact phase space for flat FLRW spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behaviour of the phase space of Universes with a non-negative Ricci scalar in R + {\\alpha}R^n gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature fluid dominated phase mimicking standard radiation, then pass","authors_text":"Mohamed Abdelwahab, Peter K. S. Dunsby, Rituparno Goswami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-01T11:16:04Z","title":"Cosmological dynamics of fourth order gravity: A compact view"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0171","kind":"arxiv","version":3},"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:b7bb0ee9a1f1b59856c364e08eb2d03bbe9c740c3397f9f3e55a1a968d20818a","target":"record","created_at":"2026-05-18T01:59:48Z","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":"7817dac4845f32e6c30ab6dd37b1d6f95385e2ad2d8611c45a984a25ae5c8b7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-01T11:16:04Z","title_canon_sha256":"cafa0200f2521ec341f875a0f1c91e3121ab4b07680774824f9b2930b7cbed59"},"schema_version":"1.0","source":{"id":"1111.0171","kind":"arxiv","version":3}},"canonical_sha256":"ba03a3075e75051b22db4c8d0978cb82ff31df0f7a3481b20d568b28bdbe6cf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba03a3075e75051b22db4c8d0978cb82ff31df0f7a3481b20d568b28bdbe6cf0","first_computed_at":"2026-05-18T01:59:48.988167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:48.988167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K9d9IVnO0aIOnCc9QOIcDKJqOX0Qfe5RpZQTM92wjwbzyZ0CmUnW0hkXfMnVgfdjDvq1F/QMCFS0A7u5TNIpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:48.988873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0171","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7bb0ee9a1f1b59856c364e08eb2d03bbe9c740c3397f9f3e55a1a968d20818a","sha256:2b7675bf8a41fe66d6eb05bf1c87e7226814bf9f86da4c4ceeb2929acdf473f6"],"state_sha256":"4b455109d69502a15d0e035cc723b8f6484340ccad4bbd5ffb8a15f60c6101ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hu1ZVFoj42I+VwfKf9Xu6xw1mhLevJz4T+Pjk/gXvUph3wzSjhCzKpafWeCsdDH3Rmo73SSsZO5pihXahrydAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:21:15.037560Z","bundle_sha256":"64f7cd50626bec4f37ac66b4d993c006996878ebdc7b63752513db2fcc5d9423"}}