{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AXMH2GM5W35XMYHXCD4ROHCU3E","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":"7dcda7da61a51cfa1b91da7e1526ad272799d07facc8ea611cdfe7ba241f906e","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-12-08T08:52:35Z","title_canon_sha256":"9cdebf2ee47cf201533c5288de7c587d6bf7bf7d4ceb371a77c4348b45502e44"},"schema_version":"1.0","source":{"id":"1212.1769","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1769","created_at":"2026-05-18T03:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1769v2","created_at":"2026-05-18T03:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1769","created_at":"2026-05-18T03:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"AXMH2GM5W35X","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AXMH2GM5W35XMYHX","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AXMH2GM5","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:dd3559fff3ced704c33c99d631e523a4da26f284168034af91d5f9787e7ec2bc","target":"graph","created_at":"2026-05-18T03:21:21Z","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 study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we disc","authors_text":"D. Singleton, H.-J. Schmidt","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-12-08T08:52:35Z","title":"Isotropic universe with almost scale-invariant fourth-order gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1769","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:ae8087b1463c246eea9579ecef2f28a31a9f725611e4e7670c27411508bad4e2","target":"record","created_at":"2026-05-18T03:21:21Z","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":"7dcda7da61a51cfa1b91da7e1526ad272799d07facc8ea611cdfe7ba241f906e","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-12-08T08:52:35Z","title_canon_sha256":"9cdebf2ee47cf201533c5288de7c587d6bf7bf7d4ceb371a77c4348b45502e44"},"schema_version":"1.0","source":{"id":"1212.1769","kind":"arxiv","version":2}},"canonical_sha256":"05d87d199db6fb7660f710f9171c54d9002b68b6fd1e3fe75971b46fd3510b13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05d87d199db6fb7660f710f9171c54d9002b68b6fd1e3fe75971b46fd3510b13","first_computed_at":"2026-05-18T03:21:21.565460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:21.565460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pg4HCv5Hjgy6uf2vkxdQg1SP6n/zZsGnxMHvaycqNH0P4csQi0amRwkOdmCpSzC2jpJfCZmaJ0BPZsWy+6WyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:21.566046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1769","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae8087b1463c246eea9579ecef2f28a31a9f725611e4e7670c27411508bad4e2","sha256:dd3559fff3ced704c33c99d631e523a4da26f284168034af91d5f9787e7ec2bc"],"state_sha256":"0af00bf543c5b0dc2a98fd3cfc1488cdb2b9cfacd580017b1ba389d8baff9ddf"}