{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UTMI5MC7F5SCJBEZTFKQNGEJXJ","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":"87f81ce318bc3159ae4b04ddec15f59276b14e26d09e6c7b30f0cb560560014f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-06-14T02:38:58Z","title_canon_sha256":"f205be7abc75277eb0097434ff31dec023861b0bcfa34269990812a1c3e3e8d8"},"schema_version":"1.0","source":{"id":"1906.05989","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05989","created_at":"2026-05-17T23:42:41Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05989v2","created_at":"2026-05-17T23:42:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05989","created_at":"2026-05-17T23:42:41Z"},{"alias_kind":"pith_short_12","alias_value":"UTMI5MC7F5SC","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UTMI5MC7F5SCJBEZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UTMI5MC7","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:74157dc690080385423567cef7b8ed60386f56c185474adc72970e6c92e18cdb","target":"graph","created_at":"2026-05-17T23:42:41Z","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":"Generalized Noether's theory is a useful method for researching the modified gravity theories about the conserved quantities and symmetries. A generally Gauss-Bonnet gravity $f(R,\\mathcal{G})$ theory was proposed as an alternative gravity model. Through the generalized Noether symmetry, polynomial and product forms of the $f(R,\\mathcal{G})$ theory with corresponding conserved quantities and symmetries are researched. Then suitable general forms of the polynomial form $f(R,\\mathcal{G}) \\!=\\! k_1 R^n + (6)^{\\frac{n}{2}}(-1)^{n+1} k_1 \\mathcal{G}^{\\frac{n}{2}}$ and the product form $f(R,\\mathcal{","authors_text":"Han Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-06-14T02:38:58Z","title":"Generalized Noether Theorem for Gauss-Bonnet Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05989","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":"sha256:80074633702f8bdd7f17a0397fbcbf9a2634cb253a5b0c1e871d1b73ce747ac2","target":"record","created_at":"2026-05-17T23:42:41Z","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":"87f81ce318bc3159ae4b04ddec15f59276b14e26d09e6c7b30f0cb560560014f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-06-14T02:38:58Z","title_canon_sha256":"f205be7abc75277eb0097434ff31dec023861b0bcfa34269990812a1c3e3e8d8"},"schema_version":"1.0","source":{"id":"1906.05989","kind":"arxiv","version":2}},"canonical_sha256":"a4d88eb05f2f642484999955069889ba518f400fd9bfa961df647606aa95384e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4d88eb05f2f642484999955069889ba518f400fd9bfa961df647606aa95384e","first_computed_at":"2026-05-17T23:42:41.358192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:41.358192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSc1+Ybwao6rCIuz6jlOIA8kcdkAZImGbfppz9OtQaaUw9SpWklaWRxj8K83L/EOz9x3seOpQ5HoLK/ww25LAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:41.358883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.05989","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80074633702f8bdd7f17a0397fbcbf9a2634cb253a5b0c1e871d1b73ce747ac2","sha256:74157dc690080385423567cef7b8ed60386f56c185474adc72970e6c92e18cdb"],"state_sha256":"8dd148c6a768e26b9048043637729796bebeaf229f81b3a7762de9d4463e3686"}