{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ST6OGMGWW7WNFCQ6VY5LN5BDKB","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":"1e5a3d75a8b871ec19e608d55a18a4c5547b61bf80a2f4c4823ae75551697c28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-10T11:56:15Z","title_canon_sha256":"75ce05aa0de3287cdad988eebd13dcc4a71b6f3f4925b26489496c18899f19e4"},"schema_version":"1.0","source":{"id":"1205.2239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2239","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2239v1","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2239","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"ST6OGMGWW7WN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"ST6OGMGWW7WNFCQ6","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"ST6OGMGW","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:c6f85223fb813cd82f972e648f5d5fc9c741e04b577a0699ea8f053a38e1754a","target":"graph","created_at":"2026-05-18T01:37:06Z","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 study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and null helices form the families of null similar curves with variable transformation.","authors_text":"Mehmet \\\"Onder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-10T11:56:15Z","title":"Null Similar Curves with Variable Transformations in Minkowski 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2239","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":"sha256:18d33568c2e66bdf9ff9ed5ed5a33380e5157edcb7f9067e96a033a791196310","target":"record","created_at":"2026-05-18T01:37:06Z","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":"1e5a3d75a8b871ec19e608d55a18a4c5547b61bf80a2f4c4823ae75551697c28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-10T11:56:15Z","title_canon_sha256":"75ce05aa0de3287cdad988eebd13dcc4a71b6f3f4925b26489496c18899f19e4"},"schema_version":"1.0","source":{"id":"1205.2239","kind":"arxiv","version":1}},"canonical_sha256":"94fce330d6b7ecd28a1eae3ab6f423507cbb1802496d96cbbacb0fbaa180b14f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94fce330d6b7ecd28a1eae3ab6f423507cbb1802496d96cbbacb0fbaa180b14f","first_computed_at":"2026-05-18T01:37:06.003067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:06.003067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A4tBQyLTyr+saEwzJlCtLxXDD4bKOCdQ8jb7FjFDx+FD6Y1PDhMeh234u6Ho6IY575keT0cQsyQud87ziH/eCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:06.003589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18d33568c2e66bdf9ff9ed5ed5a33380e5157edcb7f9067e96a033a791196310","sha256:c6f85223fb813cd82f972e648f5d5fc9c741e04b577a0699ea8f053a38e1754a"],"state_sha256":"c9c99b512aa0c4c57499724be04372f26ff6a264d61190739c114d8bca7c1752"}