{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:FHALWUPUB2VXKM2HTWH6DED7LB","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":"a98c6b215f55e26bf4879281485f834702ac3e25607cbcece59b18bc58d6973d","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"1993-12-15T23:11:17Z","title_canon_sha256":"d56b91eec481b8637a026ea0f06f8471fba61346157975dbebfc85dd48ba4e1e"},"schema_version":"1.0","source":{"id":"gr-qc/9312025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9312025","created_at":"2026-05-18T04:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9312025v1","created_at":"2026-05-18T04:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9312025","created_at":"2026-05-18T04:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"FHALWUPUB2VX","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"FHALWUPUB2VXKM2H","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"FHALWUPU","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:2c0d2a66a066debdc34469fa1da344e3a1c3e619928385610b16aefde349af5e","target":"graph","created_at":"2026-05-18T04:37:57Z","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":"The evolution of a universe with Brans-Dicke gravity and nonzero curvature is investigated here. We present the equations of motion and their solutions during the radiation dominated era. In a Friedman-Robertson-Walker cosmology we show explicitly that the three possible values of curvature $\\kappa=+1,0,-1$ divide the evolution of the Brans-Dicke universe into dynamically distinct classes just as for the standard model. Subsequently we discuss the flatness problem which exists in Brans-Dicke gravity as it does in the standard model. In addition, we demonstrate a flatness problem in MAD Brans-D","authors_text":"Janna Levin, Katherine Freese","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1993-12-15T23:11:17Z","title":"Curvature and Flatness in a Brans-Dicke Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9312025","kind":"arxiv","version":1},"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":"sha256:50a4ce30aa77474888eff7c3be66b2b1bb0e3dfc4f51813c650a4237e00fbf14","target":"record","created_at":"2026-05-18T04:37:57Z","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":"a98c6b215f55e26bf4879281485f834702ac3e25607cbcece59b18bc58d6973d","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"1993-12-15T23:11:17Z","title_canon_sha256":"d56b91eec481b8637a026ea0f06f8471fba61346157975dbebfc85dd48ba4e1e"},"schema_version":"1.0","source":{"id":"gr-qc/9312025","kind":"arxiv","version":1}},"canonical_sha256":"29c0bb51f40eab7533479d8fe1907f586da81f81f2c869593db06496de4fd184","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29c0bb51f40eab7533479d8fe1907f586da81f81f2c869593db06496de4fd184","first_computed_at":"2026-05-18T04:37:57.357051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:57.357051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4pwm0Ef6CCvYZ3nyegOac+5rXjzypsOATLcFwkJjnRDDsLR1irB7xVZe678LYHGyrzBL7mPFoyGKqtzpuAoEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:57.357460Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9312025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50a4ce30aa77474888eff7c3be66b2b1bb0e3dfc4f51813c650a4237e00fbf14","sha256:2c0d2a66a066debdc34469fa1da344e3a1c3e619928385610b16aefde349af5e"],"state_sha256":"ff336bd7b64dcfe17b2f0259b83fb2fe3c964f5f7e9593b96467304138f9aaca"}