{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YRWWSPNCMFW7X3AMFL2ZIY5NIV","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":"694b4d4b344187cc5639a1f022a2b4f4f0feaff99ccde90bc01772c84862ae9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-21T08:42:49Z","title_canon_sha256":"43cd48e5213933ee7db716c092af8c08d1355320f65367e28e6a031b21a2fbaf"},"schema_version":"1.0","source":{"id":"1211.4960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4960","created_at":"2026-05-18T03:40:15Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4960v1","created_at":"2026-05-18T03:40:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4960","created_at":"2026-05-18T03:40:15Z"},{"alias_kind":"pith_short_12","alias_value":"YRWWSPNCMFW7","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YRWWSPNCMFW7X3AM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YRWWSPNC","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:71c0b5b256bbd5e89ac7db03fe134131dd9a2a385a5fcfc28282186d59dda685","target":"graph","created_at":"2026-05-18T03:40:15Z","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 f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Also, we give the definition of harmonic curvature functions related to f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Moreover, we give characterizations for f-eikonal helix curves and f-eikonal V_{n}-slant helix curves by making use of the harmonic curvature functions.","authors_text":"Ali \\c{S}enol, Evren Ziplar, Yusuf Yayli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-21T08:42:49Z","title":"On f-Eikonal Helices And f-Eikonal Slant Helices In Riemannian Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4960","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:c13daf54ef92f2e795543261b25ebd5ae0cce98d8dad8bd801242f24c244302f","target":"record","created_at":"2026-05-18T03:40:15Z","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":"694b4d4b344187cc5639a1f022a2b4f4f0feaff99ccde90bc01772c84862ae9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-21T08:42:49Z","title_canon_sha256":"43cd48e5213933ee7db716c092af8c08d1355320f65367e28e6a031b21a2fbaf"},"schema_version":"1.0","source":{"id":"1211.4960","kind":"arxiv","version":1}},"canonical_sha256":"c46d693da2616dfbec0c2af59463ad4556f3ececbd452d1cf0b78f2809882e0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c46d693da2616dfbec0c2af59463ad4556f3ececbd452d1cf0b78f2809882e0d","first_computed_at":"2026-05-18T03:40:15.410521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:15.410521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EpNhw1RP44NYOGw7faqpRYbYowIoXcTKb1NFAGX/6XzxlzEBKH1VMufetShZUQp5zdh/rvP2/BZVTyNDc5LICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:15.411237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c13daf54ef92f2e795543261b25ebd5ae0cce98d8dad8bd801242f24c244302f","sha256:71c0b5b256bbd5e89ac7db03fe134131dd9a2a385a5fcfc28282186d59dda685"],"state_sha256":"1a754070045d48556d75ab2f004965d99f4c44cf1f24c50e1fc78a1b5706499d"}