{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:E7ADNKPFDWG2QWNVT36FC2MXKT","short_pith_number":"pith:E7ADNKPF","canonical_record":{"source":{"id":"1204.2988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T13:30:41Z","cross_cats_sorted":[],"title_canon_sha256":"b63b8aec66f57c392a13d334e5a45c2247d36171412aa9d7c19c37b2c14caf0d","abstract_canon_sha256":"2a682f130538026bcecd1d37a83fd466c14171017f6a9adb4e5a926637a9cbd5"},"schema_version":"1.0"},"canonical_sha256":"27c036a9e51d8da859b59efc51699754c99dcf2e3232fdf383e186ae3c339ced","source":{"kind":"arxiv","id":"1204.2988","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2988","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2988v1","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2988","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"E7ADNKPFDWG2","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E7ADNKPFDWG2QWNV","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E7ADNKPF","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:E7ADNKPFDWG2QWNVT36FC2MXKT","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T13:30:41Z","cross_cats_sorted":[],"title_canon_sha256":"b63b8aec66f57c392a13d334e5a45c2247d36171412aa9d7c19c37b2c14caf0d","abstract_canon_sha256":"2a682f130538026bcecd1d37a83fd466c14171017f6a9adb4e5a926637a9cbd5"},"schema_version":"1.0"},"canonical_sha256":"27c036a9e51d8da859b59efc51699754c99dcf2e3232fdf383e186ae3c339ced","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:24.449976Z","signature_b64":"Kch5gGUzZ2GBukzpI0JY0G+qZdBL4xb5XqYySZoqsA2AQZ3mVh5W+Xgb7nJKK0tYvMaz66hoamngU3BoobHeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27c036a9e51d8da859b59efc51699754c99dcf2e3232fdf383e186ae3c339ced","last_reissued_at":"2026-05-18T01:15:24.449303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:24.449303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2988","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":"2026-05-18T01:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGwag5dXsO0GER4SG9ZeA26KoOV0UHTEgGV4ZCnXKCAVPbg6iqgQg18vb/9C3cKVLMcbPmfthkK8O64STMupDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:05:27.050571Z"},"content_sha256":"7a59e6ee6a01e7282cfa80a6a403e71b61d590f5b71d5531135317e4355c691f","schema_version":"1.0","event_id":"sha256:7a59e6ee6a01e7282cfa80a6a403e71b61d590f5b71d5531135317e4355c691f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:E7ADNKPFDWG2QWNVT36FC2MXKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Murat Kemal Karacan, Serpil \\\"Unal, Y{\\i}lmaz Tun\\c{c}er","submitted_at":"2012-04-13T13:30:41Z","abstract_excerpt":"In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2988","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":"2026-05-18T01:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BXlCu+SC9P6UJGjRR2FMy9Sb1EeAEsk7kn3aEHyKDqmbmgI61wUHlOtIANsu/M9+6ItkQ0ZOBVmGWBKb1avBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:05:27.050911Z"},"content_sha256":"f5acd97857293f4f3d4ff07f02a49a50865fe03eeaa686e0f1b2b8d424da21cb","schema_version":"1.0","event_id":"sha256:f5acd97857293f4f3d4ff07f02a49a50865fe03eeaa686e0f1b2b8d424da21cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7ADNKPFDWG2QWNVT36FC2MXKT/bundle.json","state_url":"https://pith.science/pith/E7ADNKPFDWG2QWNVT36FC2MXKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7ADNKPFDWG2QWNVT36FC2MXKT/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":"2026-06-23T22:05:27Z","links":{"resolver":"https://pith.science/pith/E7ADNKPFDWG2QWNVT36FC2MXKT","bundle":"https://pith.science/pith/E7ADNKPFDWG2QWNVT36FC2MXKT/bundle.json","state":"https://pith.science/pith/E7ADNKPFDWG2QWNVT36FC2MXKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7ADNKPFDWG2QWNVT36FC2MXKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E7ADNKPFDWG2QWNVT36FC2MXKT","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":"2a682f130538026bcecd1d37a83fd466c14171017f6a9adb4e5a926637a9cbd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T13:30:41Z","title_canon_sha256":"b63b8aec66f57c392a13d334e5a45c2247d36171412aa9d7c19c37b2c14caf0d"},"schema_version":"1.0","source":{"id":"1204.2988","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2988","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2988v1","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2988","created_at":"2026-05-18T01:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"E7ADNKPFDWG2","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E7ADNKPFDWG2QWNV","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E7ADNKPF","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f5acd97857293f4f3d4ff07f02a49a50865fe03eeaa686e0f1b2b8d424da21cb","target":"graph","created_at":"2026-05-18T01:15:24Z","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 work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.","authors_text":"Murat Kemal Karacan, Serpil \\\"Unal, Y{\\i}lmaz Tun\\c{c}er","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T13:30:41Z","title":"Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2988","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":"sha256:7a59e6ee6a01e7282cfa80a6a403e71b61d590f5b71d5531135317e4355c691f","target":"record","created_at":"2026-05-18T01:15:24Z","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":"2a682f130538026bcecd1d37a83fd466c14171017f6a9adb4e5a926637a9cbd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T13:30:41Z","title_canon_sha256":"b63b8aec66f57c392a13d334e5a45c2247d36171412aa9d7c19c37b2c14caf0d"},"schema_version":"1.0","source":{"id":"1204.2988","kind":"arxiv","version":1}},"canonical_sha256":"27c036a9e51d8da859b59efc51699754c99dcf2e3232fdf383e186ae3c339ced","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27c036a9e51d8da859b59efc51699754c99dcf2e3232fdf383e186ae3c339ced","first_computed_at":"2026-05-18T01:15:24.449303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:24.449303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kch5gGUzZ2GBukzpI0JY0G+qZdBL4xb5XqYySZoqsA2AQZ3mVh5W+Xgb7nJKK0tYvMaz66hoamngU3BoobHeDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:24.449976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2988","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a59e6ee6a01e7282cfa80a6a403e71b61d590f5b71d5531135317e4355c691f","sha256:f5acd97857293f4f3d4ff07f02a49a50865fe03eeaa686e0f1b2b8d424da21cb"],"state_sha256":"6dcf3ca38d626d96b16cb625509281161d8c0f8e44d748251b014d923b54069f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JgvhJkukqo6sDkC6YIM58jEvh1PnfcC3PPP8YaO7LJeKSoghCdoAeLvqm10TaGZSIUjNqqHpU6CLW0utuj0cAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:05:27.052837Z","bundle_sha256":"c7109c7a2a0a2eee2844c2d426659467efcf00407959efebf72ecf685ddc44ee"}}