{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EATLHVGUEALUCH7H7EKXACGKP2","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":"0cc33523bbb5895ae660781cff5086aeb7978c6ee494ed81de198b8550f3b8cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-23T12:15:26Z","title_canon_sha256":"5ff13e1b71b57f7e9b663414d046cf28f7d1e6f65f2386b2e7d4427e95452dbf"},"schema_version":"1.0","source":{"id":"1611.07761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07761","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07761v1","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07761","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"EATLHVGUEALU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EATLHVGUEALUCH7H","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EATLHVGU","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:e258262a8b471cf26e902f79450bc4c6101de4a963c55ca655569cf7c06348ef","target":"graph","created_at":"2026-05-18T00:56:59Z","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 prove that the Euclidean plane is the only Riemannian plane with total curvature and free of conjugate points that satisfies Playfair's version of the parallel postulate.","authors_text":"Jian Ge, Luis Guijarro, Pedro Sol\\'orzano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-23T12:15:26Z","title":"Riemannian Rigidity of the Parallel Postulate in Total Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07761","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:a3159f4d26fbead7c053835cc7a2a4a4d49824d7987ee0b7b7e2950d9748f0b8","target":"record","created_at":"2026-05-18T00:56:59Z","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":"0cc33523bbb5895ae660781cff5086aeb7978c6ee494ed81de198b8550f3b8cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-23T12:15:26Z","title_canon_sha256":"5ff13e1b71b57f7e9b663414d046cf28f7d1e6f65f2386b2e7d4427e95452dbf"},"schema_version":"1.0","source":{"id":"1611.07761","kind":"arxiv","version":1}},"canonical_sha256":"2026b3d4d42017411fe7f9157008ca7e9c740a587f91947c5ea311b06712d944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2026b3d4d42017411fe7f9157008ca7e9c740a587f91947c5ea311b06712d944","first_computed_at":"2026-05-18T00:56:59.868369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:59.868369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uv00ipePTWA6gJQrfPZJpdD/NWZKI39g/dMZlLv6B27rOZQvY+5IbVLpa2IOTmZa4okF67uw3d3BlMvKF9MRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:59.868833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3159f4d26fbead7c053835cc7a2a4a4d49824d7987ee0b7b7e2950d9748f0b8","sha256:e258262a8b471cf26e902f79450bc4c6101de4a963c55ca655569cf7c06348ef"],"state_sha256":"2341036090ffaae5af512eb417d435dc973049b40894f0f3abe8b0eea7746306"}