{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HKYZCZS7UKJ7YZPQCIMZRZXU3F","short_pith_number":"pith:HKYZCZS7","canonical_record":{"source":{"id":"1809.10876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-28T06:42:03Z","cross_cats_sorted":[],"title_canon_sha256":"758b8532fb0271745d1e87a5cc3c887471947b8fd6ee9685f30d771e7b12238b","abstract_canon_sha256":"d29ba0463d1a40e3340c664f7e14d65e15efc29a86f5c92ffbc2c0200caa94eb"},"schema_version":"1.0"},"canonical_sha256":"3ab191665fa293fc65f0121998e6f4d96d89b805fc98f096d74478f2aefb30b7","source":{"kind":"arxiv","id":"1809.10876","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10876","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10876v1","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10876","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"HKYZCZS7UKJ7","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HKYZCZS7UKJ7YZPQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HKYZCZS7","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HKYZCZS7UKJ7YZPQCIMZRZXU3F","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-28T06:42:03Z","cross_cats_sorted":[],"title_canon_sha256":"758b8532fb0271745d1e87a5cc3c887471947b8fd6ee9685f30d771e7b12238b","abstract_canon_sha256":"d29ba0463d1a40e3340c664f7e14d65e15efc29a86f5c92ffbc2c0200caa94eb"},"schema_version":"1.0"},"canonical_sha256":"3ab191665fa293fc65f0121998e6f4d96d89b805fc98f096d74478f2aefb30b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:34.756807Z","signature_b64":"Q2SFOpDqeVCE/ozVMae+xF2oZBGjwdiH5wW55+OD9VRpqU2yRPiVKAMpRigiPEgizTsq8KlekB443H/P6gZcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ab191665fa293fc65f0121998e6f4d96d89b805fc98f096d74478f2aefb30b7","last_reissued_at":"2026-05-18T00:04:34.756335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:34.756335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10876","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":"2026-05-18T00:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OAJ3NV5zLr4LI0GXnk7VJrO01vyml7yieyuTrLAouZtUZ7MVZdC4jr5ZaSRmeFrZxaE+wO9099a4z8AUuQvvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:30:10.465184Z"},"content_sha256":"0325e45a5b29246a8ef123e8e42caae24f236c3dd3251f80d556a2e3039b4777","schema_version":"1.0","event_id":"sha256:0325e45a5b29246a8ef123e8e42caae24f236c3dd3251f80d556a2e3039b4777"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HKYZCZS7UKJ7YZPQCIMZRZXU3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mannheim curves with modified orthogonal frame in Euclidean 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bahaddin Bukcu, Hasan Es, Mohamd Saleem Lone, Murat Kemal Karacan","submitted_at":"2018-09-28T06:42:03Z","abstract_excerpt":"In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10876","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":"2026-05-18T00:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RS3yW00uqb4/5nINAmwYNDkncuapVj2O1luXGkL3Ty8HbXJcwrD6PmDq/kVF8EHQjHrSHZ0CYLHC7J3wybsHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:30:10.465787Z"},"content_sha256":"cda7a77fae3290e6ef52ca9d44f562cc2df9ff010431135b716dc5da08622f13","schema_version":"1.0","event_id":"sha256:cda7a77fae3290e6ef52ca9d44f562cc2df9ff010431135b716dc5da08622f13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F/bundle.json","state_url":"https://pith.science/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F/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":"2026-06-23T10:30:10Z","links":{"resolver":"https://pith.science/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F","bundle":"https://pith.science/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F/bundle.json","state":"https://pith.science/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKYZCZS7UKJ7YZPQCIMZRZXU3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HKYZCZS7UKJ7YZPQCIMZRZXU3F","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":"d29ba0463d1a40e3340c664f7e14d65e15efc29a86f5c92ffbc2c0200caa94eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-28T06:42:03Z","title_canon_sha256":"758b8532fb0271745d1e87a5cc3c887471947b8fd6ee9685f30d771e7b12238b"},"schema_version":"1.0","source":{"id":"1809.10876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10876","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10876v1","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10876","created_at":"2026-05-18T00:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"HKYZCZS7UKJ7","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HKYZCZS7UKJ7YZPQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HKYZCZS7","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:cda7a77fae3290e6ef52ca9d44f562cc2df9ff010431135b716dc5da08622f13","target":"graph","created_at":"2026-05-18T00:04:34Z","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 investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.","authors_text":"Bahaddin Bukcu, Hasan Es, Mohamd Saleem Lone, Murat Kemal Karacan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-28T06:42:03Z","title":"Mannheim curves with modified orthogonal frame in Euclidean 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10876","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":"sha256:0325e45a5b29246a8ef123e8e42caae24f236c3dd3251f80d556a2e3039b4777","target":"record","created_at":"2026-05-18T00:04:34Z","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":"d29ba0463d1a40e3340c664f7e14d65e15efc29a86f5c92ffbc2c0200caa94eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-28T06:42:03Z","title_canon_sha256":"758b8532fb0271745d1e87a5cc3c887471947b8fd6ee9685f30d771e7b12238b"},"schema_version":"1.0","source":{"id":"1809.10876","kind":"arxiv","version":1}},"canonical_sha256":"3ab191665fa293fc65f0121998e6f4d96d89b805fc98f096d74478f2aefb30b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ab191665fa293fc65f0121998e6f4d96d89b805fc98f096d74478f2aefb30b7","first_computed_at":"2026-05-18T00:04:34.756335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:34.756335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q2SFOpDqeVCE/ozVMae+xF2oZBGjwdiH5wW55+OD9VRpqU2yRPiVKAMpRigiPEgizTsq8KlekB443H/P6gZcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:34.756807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0325e45a5b29246a8ef123e8e42caae24f236c3dd3251f80d556a2e3039b4777","sha256:cda7a77fae3290e6ef52ca9d44f562cc2df9ff010431135b716dc5da08622f13"],"state_sha256":"205be7ab6fd8de2372c556e9637dcda776417e7348ce437509a24f6a5a9f5306"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t/5gXmAB79s0sNPgrogwMIBnZ3c6ypYmmjHTYEwsx/F3v6mge4wa35jLH38jCzRtSZSEvg0TcSTpQyiGbmSdCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:30:10.468776Z","bundle_sha256":"d4bbf2cc4e88cda6cc2ba2290ddf30b26bfce63d9015faa843a0552e4680dd6b"}}