{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DZRWTSODSMJA6K34WOAOQJR2GZ","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":"a56345013b18d95824a47c08ac1d16009c67fa8ffc7ce857aac1e8059d225b7e","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-04-20T18:20:11Z","title_canon_sha256":"ed17d2fcba068a9812d2d2dc1033a689766007e6c46bc99cdb3862a7c15ee79e"},"schema_version":"1.0","source":{"id":"2104.10192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.10192","created_at":"2026-07-05T03:25:54Z"},{"alias_kind":"arxiv_version","alias_value":"2104.10192v2","created_at":"2026-07-05T03:25:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.10192","created_at":"2026-07-05T03:25:54Z"},{"alias_kind":"pith_short_12","alias_value":"DZRWTSODSMJA","created_at":"2026-07-05T03:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"DZRWTSODSMJA6K34","created_at":"2026-07-05T03:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"DZRWTSOD","created_at":"2026-07-05T03:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:1c69bd0f8582994c63a9691a78423c265110424f1ff2dd0fdcc6f2d550e99428","target":"graph","created_at":"2026-07-05T03:25:54Z","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/2104.10192/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analytically derive the covariant form of the Riemann (curvature) tensor for homogeneous Metric-Affine Cosmologies. That is, we present, in a Cosmological setting, the most general covariant form of the full Riemann tensor including also its non-Riemannian pieces which are associated to spacetime torsion and non-metricity. Having done so we also compute a list of the curvature tensor by-products such as Ricci tensor, homothetic curvature, Ricci scalar, Einstein tensor etc. Finally we derive the generalized Metric-Affine version of the usual Gauss-Bonnet density in this background and demons","authors_text":"Damianos Iosifidis","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-04-20T18:20:11Z","title":"Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.10192","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":"sha256:709891546c861296bbd9f9f0274104dbcbfee7bacdc6989498e9c2c8c9f78f4c","target":"record","created_at":"2026-07-05T03:25:54Z","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":"a56345013b18d95824a47c08ac1d16009c67fa8ffc7ce857aac1e8059d225b7e","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-04-20T18:20:11Z","title_canon_sha256":"ed17d2fcba068a9812d2d2dc1033a689766007e6c46bc99cdb3862a7c15ee79e"},"schema_version":"1.0","source":{"id":"2104.10192","kind":"arxiv","version":2}},"canonical_sha256":"1e6369c9c393120f2b7cb380e8263a365a05dc7c6b52663822bf86736dbb1a5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e6369c9c393120f2b7cb380e8263a365a05dc7c6b52663822bf86736dbb1a5f","first_computed_at":"2026-07-05T03:25:54.192306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:25:54.192306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gjy3RQBKXu8RjMDhKSIef1yK8z1t/DGmQXSwCUUecn18qgHskQZ/v6/jB6i7ZUTr0iXr9TN7F6tiUs9zhabHDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:25:54.192749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.10192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:709891546c861296bbd9f9f0274104dbcbfee7bacdc6989498e9c2c8c9f78f4c","sha256:1c69bd0f8582994c63a9691a78423c265110424f1ff2dd0fdcc6f2d550e99428"],"state_sha256":"86a10ec641eaaf956a94aec629e784f453a574a4ee4a3e11ae70ddfd1efc7e93"}