{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GGFFEGB2K4K7G6TA4IBEHODHVE","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":"5fd0a1a87d89eca3242b077491058ac755787cfa85a23c5aab00fa0fea8f2c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T09:27:12Z","title_canon_sha256":"be46fe12aab6391ec991baf099c53eb69941adbfa72bad6355e469d4562861e0"},"schema_version":"1.0","source":{"id":"1009.4789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4789","created_at":"2026-05-18T02:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4789v1","created_at":"2026-05-18T02:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4789","created_at":"2026-05-18T02:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"GGFFEGB2K4K7","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GGFFEGB2K4K7G6TA","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GGFFEGB2","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:16242a11e829d1f96fa7a5dd6b2e4e9d89d315a79b38e02add3fcacf1b7555e2","target":"graph","created_at":"2026-05-18T02:05:17Z","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":"Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of 3-dimensional sphere and some partial results are obtained in the general case. The Carnot-Carath\\'eodory distance is calculated. We also present some motivations related to quantum mechanics.","authors_text":"Alexander Vasil'ev, Der-Chen Chang, Irina Markina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T09:27:12Z","title":"Hopf fibration: geodesics and distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4789","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":"sha256:27e3dd6437dc1df625a7f2cb5a780ad3b24e06bb0af6b4139f61d99dfb85d5b5","target":"record","created_at":"2026-05-18T02:05:17Z","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":"5fd0a1a87d89eca3242b077491058ac755787cfa85a23c5aab00fa0fea8f2c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T09:27:12Z","title_canon_sha256":"be46fe12aab6391ec991baf099c53eb69941adbfa72bad6355e469d4562861e0"},"schema_version":"1.0","source":{"id":"1009.4789","kind":"arxiv","version":1}},"canonical_sha256":"318a52183a5715f37a60e20243b867a9393eea57578211ed3ae2c8eef3e58876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"318a52183a5715f37a60e20243b867a9393eea57578211ed3ae2c8eef3e58876","first_computed_at":"2026-05-18T02:05:17.764681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:17.764681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rB8j/r7UayqB7DoK7xbG9u6hma87yAWZ4mxXLRiFvDdx5eDXJ2G64FMi8bNdjRdsLwzG1nxJ2dHxTqTfQeA5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:17.765417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27e3dd6437dc1df625a7f2cb5a780ad3b24e06bb0af6b4139f61d99dfb85d5b5","sha256:16242a11e829d1f96fa7a5dd6b2e4e9d89d315a79b38e02add3fcacf1b7555e2"],"state_sha256":"93462b0dae783c444dbe6f13d00382040db8ee2a1cc6919b084386832e72d70f"}