{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4A7HGJ2JPEFXO7774WYE7HBKQX","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":"e19e34dc3eeab06baa1ab1e5d43eeb01dd341af53183c776c30aeda85316c33d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-10-16T21:34:28Z","title_canon_sha256":"3fca7f20fe225882805c067b9b122bb668042a76ec46491b34b13c6da78d819d"},"schema_version":"1.0","source":{"id":"1210.4185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4185","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4185v1","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4185","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"4A7HGJ2JPEFX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4A7HGJ2JPEFXO777","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4A7HGJ2J","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:3daf0ae365e294ac38b723cccba4a4618bbcc49ab1da5057d109e54a8200212d","target":"graph","created_at":"2026-05-18T03:43:06Z","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, the spinor formulation of Darboux frame on an oriented surface is given. Also, the relation between the spinor formulation of Frenet frame and Darboux frame are obtained.","authors_text":"\\.Il\\.Im K\\.I\\c{S}\\.I, Murat Tosun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-10-16T21:34:28Z","title":"Spinor Darboux Equations of Curves in Euclidean 3-Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4185","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":"sha256:3a3776fc034ac89b7352b77232973034f64a77318453c67f42fedb839e7ea90b","target":"record","created_at":"2026-05-18T03:43:06Z","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":"e19e34dc3eeab06baa1ab1e5d43eeb01dd341af53183c776c30aeda85316c33d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-10-16T21:34:28Z","title_canon_sha256":"3fca7f20fe225882805c067b9b122bb668042a76ec46491b34b13c6da78d819d"},"schema_version":"1.0","source":{"id":"1210.4185","kind":"arxiv","version":1}},"canonical_sha256":"e03e732749790b777fffe5b04f9c2a85c957d84e926a13a7ebe82cf2a3109267","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e03e732749790b777fffe5b04f9c2a85c957d84e926a13a7ebe82cf2a3109267","first_computed_at":"2026-05-18T03:43:06.685439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:06.685439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CgqJdWinrjqBXjeH1OvFaew6hXDu5wutIJWFkzpaarBfqLQjz7qOM3DDENMNLXqMC90uMXZG4Qww2MKfBvQVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:06.686737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a3776fc034ac89b7352b77232973034f64a77318453c67f42fedb839e7ea90b","sha256:3daf0ae365e294ac38b723cccba4a4618bbcc49ab1da5057d109e54a8200212d"],"state_sha256":"6567ad03f6e315203fe6a2c7753f8a5e347426bb87e09595be4a527907c732f2"}