{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KTNV6RCBHBAEXFHJVVM4ZAKJ42","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":"bcd455b31fd6b765cbaecfeed931ca71466262eff831754c8659331abc62b956","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2012-11-26T21:38:52Z","title_canon_sha256":"f2ff7903044489052036c4063e8c6274c788ed3528f523154ab6c4cd430e0c79"},"schema_version":"1.0","source":{"id":"1211.6141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6141","created_at":"2026-05-18T01:09:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6141v1","created_at":"2026-05-18T01:09:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6141","created_at":"2026-05-18T01:09:26Z"},{"alias_kind":"pith_short_12","alias_value":"KTNV6RCBHBAE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KTNV6RCBHBAEXFHJ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KTNV6RCB","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:c0ba21d78bb8f8c10dd8dd2fb9a3b4bb4e22de24eee95508b4636d4504162f7b","target":"graph","created_at":"2026-05-18T01:09:26Z","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":"In this paper, we define Mannheim partner curves in a three dimensional Lie group G with a bi-invariant metric. And then the main result in this paper is given as (Theorem 3.3): A curve {\\alpha} with the Frenet apparatus {T,N,B,{\\kappa},{\\tau}} in G is a Mannheim partner curve if and only if {\\lambda}{\\kappa}(1+H2)=1, where {\\lambda} is constant and H is the harmonic curvature function of the curve {\\alpha}.","authors_text":"\\.Ismail G\\\"ok, Nejat Ekmekci, O. Zeki Okuyucu, Yusuf Yayl{\\i}","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2012-11-26T21:38:52Z","title":"On Mannheim Partner Curves in three Dimensional Lie Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6141","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":"sha256:99837484a4c47914019cdabe60fc1718c5127511132718ea98f58d62580b23cd","target":"record","created_at":"2026-05-18T01:09:26Z","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":"bcd455b31fd6b765cbaecfeed931ca71466262eff831754c8659331abc62b956","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.DG","submitted_at":"2012-11-26T21:38:52Z","title_canon_sha256":"f2ff7903044489052036c4063e8c6274c788ed3528f523154ab6c4cd430e0c79"},"schema_version":"1.0","source":{"id":"1211.6141","kind":"arxiv","version":1}},"canonical_sha256":"54db5f444138404b94e9ad59cc8149e6891fb39ab24595d6397867e53ac39c59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54db5f444138404b94e9ad59cc8149e6891fb39ab24595d6397867e53ac39c59","first_computed_at":"2026-05-18T01:09:26.185182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:26.185182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8CtUjVupGrYEVlKs8t4P3KYiR8lHEaGmGv3HE6FDpW7Epg239en+voFG+/pB2H9MTbKc1bbd1MJJprIlU2HEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:26.185687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99837484a4c47914019cdabe60fc1718c5127511132718ea98f58d62580b23cd","sha256:c0ba21d78bb8f8c10dd8dd2fb9a3b4bb4e22de24eee95508b4636d4504162f7b"],"state_sha256":"558e63b72bc1d9068a8d3e1d3f4844e52944ae23cb3857fd82384f2d5c2ab069"}