{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HCJMTAMLF4DTD3L7OSUA3ZKKSH","short_pith_number":"pith:HCJMTAML","canonical_record":{"source":{"id":"1410.5577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T09:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"c70731874a98c8a580787182c3c9cb15be8c504e32f622f7ee3bc01a6595d71e","abstract_canon_sha256":"532784c3bee6fbd34040ee3f29249025920474a677e3fae67e9a58a4ecd4d908"},"schema_version":"1.0"},"canonical_sha256":"3892c9818b2f0731ed7f74a80de54a91defb1657c892afa5da89eb5eaa869bec","source":{"kind":"arxiv","id":"1410.5577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5577","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5577v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5577","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"HCJMTAMLF4DT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCJMTAMLF4DTD3L7","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCJMTAML","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HCJMTAMLF4DTD3L7OSUA3ZKKSH","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T09:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"c70731874a98c8a580787182c3c9cb15be8c504e32f622f7ee3bc01a6595d71e","abstract_canon_sha256":"532784c3bee6fbd34040ee3f29249025920474a677e3fae67e9a58a4ecd4d908"},"schema_version":"1.0"},"canonical_sha256":"3892c9818b2f0731ed7f74a80de54a91defb1657c892afa5da89eb5eaa869bec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:39.522851Z","signature_b64":"CgXtTN38zO8VLkdNQs1xE9qiFJa248SrsO3mL+iwDbYWLazobVwBQKGrzNzwOeTYZCQkjOuOFsVqFRn1nauxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3892c9818b2f0731ed7f74a80de54a91defb1657c892afa5da89eb5eaa869bec","last_reissued_at":"2026-05-18T02:39:39.522416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:39.522416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5577","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBm6URiwhqYGo4iugM4jfnlTCU+qVTJReP7Hr651yrodeE8DA3WxZ7uh8JUDkkp03J+KuCkbIHfaGG6VmOazDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:30:24.074403Z"},"content_sha256":"24208804e04a4957d9b43dbf5879581c3b216653c3ce75f86a817a004ec74a08","schema_version":"1.0","event_id":"sha256:24208804e04a4957d9b43dbf5879581c3b216653c3ce75f86a817a004ec74a08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HCJMTAMLF4DTD3L7OSUA3ZKKSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Characterization of Constant-Ratio Curves in Euclidean 3-Space E^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gunay Ozturk, Kadri Arslan, Selin Gurpinar","submitted_at":"2014-10-21T09:00:25Z","abstract_excerpt":"A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some results of T-constant and N-constant type twisted curves in E^3. Finally, we give some examples of equiangular spirals which are constant ratio curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5577","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HpJRphqmyQ+wBTeP6Z/AxejPSvcOLSZOTYpAMQs9HCnajHBT27fGrFOdEM4BvTJ2Bwcr+dGNDeU390bALEUKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:30:24.074748Z"},"content_sha256":"2fb50d529632e753cc803bb738286e1199b46b2d8d2c0f20cb22ec7b4bf95c5f","schema_version":"1.0","event_id":"sha256:2fb50d529632e753cc803bb738286e1199b46b2d8d2c0f20cb22ec7b4bf95c5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH/bundle.json","state_url":"https://pith.science/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T07:30:24Z","links":{"resolver":"https://pith.science/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH","bundle":"https://pith.science/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH/bundle.json","state":"https://pith.science/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCJMTAMLF4DTD3L7OSUA3ZKKSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HCJMTAMLF4DTD3L7OSUA3ZKKSH","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":"532784c3bee6fbd34040ee3f29249025920474a677e3fae67e9a58a4ecd4d908","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T09:00:25Z","title_canon_sha256":"c70731874a98c8a580787182c3c9cb15be8c504e32f622f7ee3bc01a6595d71e"},"schema_version":"1.0","source":{"id":"1410.5577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5577","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5577v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5577","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"HCJMTAMLF4DT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCJMTAMLF4DTD3L7","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCJMTAML","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:2fb50d529632e753cc803bb738286e1199b46b2d8d2c0f20cb22ec7b4bf95c5f","target":"graph","created_at":"2026-05-18T02:39:39Z","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":"A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some results of T-constant and N-constant type twisted curves in E^3. Finally, we give some examples of equiangular spirals which are constant ratio curves.","authors_text":"Gunay Ozturk, Kadri Arslan, Selin Gurpinar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T09:00:25Z","title":"A Characterization of Constant-Ratio Curves in Euclidean 3-Space E^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5577","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":"sha256:24208804e04a4957d9b43dbf5879581c3b216653c3ce75f86a817a004ec74a08","target":"record","created_at":"2026-05-18T02:39:39Z","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":"532784c3bee6fbd34040ee3f29249025920474a677e3fae67e9a58a4ecd4d908","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T09:00:25Z","title_canon_sha256":"c70731874a98c8a580787182c3c9cb15be8c504e32f622f7ee3bc01a6595d71e"},"schema_version":"1.0","source":{"id":"1410.5577","kind":"arxiv","version":1}},"canonical_sha256":"3892c9818b2f0731ed7f74a80de54a91defb1657c892afa5da89eb5eaa869bec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3892c9818b2f0731ed7f74a80de54a91defb1657c892afa5da89eb5eaa869bec","first_computed_at":"2026-05-18T02:39:39.522416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.522416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CgXtTN38zO8VLkdNQs1xE9qiFJa248SrsO3mL+iwDbYWLazobVwBQKGrzNzwOeTYZCQkjOuOFsVqFRn1nauxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.522851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24208804e04a4957d9b43dbf5879581c3b216653c3ce75f86a817a004ec74a08","sha256:2fb50d529632e753cc803bb738286e1199b46b2d8d2c0f20cb22ec7b4bf95c5f"],"state_sha256":"b84d9e2b52d4c4e95e895168e44a7993754d00ab5e1ef65578d6f4aba0477dc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISrAAwJmJ/Ik3Fhpwwrx68T7rUR2mv8lFGpDPkgAWNnEjxi/Nlj6bazubLA8Flk+COZvcoQ3B7Isdw3giMXDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:30:24.076688Z","bundle_sha256":"65a1f53e35bf8ec1023d030644cd6dc68d0f59eef5077073dd7c27b6866849b6"}}