{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JR2JZY6QNGCZ7WLEBIMEMOM4QM","short_pith_number":"pith:JR2JZY6Q","canonical_record":{"source":{"id":"1508.03294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-13T18:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"a01ccee6176b43757127f7102bd7386351c4601d6e842dcabf6c42374951783a","abstract_canon_sha256":"ea86760ea8d15bd83b25add518614e7ff9cf2f63961c38bd2213b792386d08ad"},"schema_version":"1.0"},"canonical_sha256":"4c749ce3d069859fd9640a1846399c8306d712dc729d40ed537db5677eb0eb1b","source":{"kind":"arxiv","id":"1508.03294","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03294","created_at":"2026-05-18T01:35:21Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03294v1","created_at":"2026-05-18T01:35:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03294","created_at":"2026-05-18T01:35:21Z"},{"alias_kind":"pith_short_12","alias_value":"JR2JZY6QNGCZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JR2JZY6QNGCZ7WLE","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JR2JZY6Q","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JR2JZY6QNGCZ7WLEBIMEMOM4QM","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-13T18:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"a01ccee6176b43757127f7102bd7386351c4601d6e842dcabf6c42374951783a","abstract_canon_sha256":"ea86760ea8d15bd83b25add518614e7ff9cf2f63961c38bd2213b792386d08ad"},"schema_version":"1.0"},"canonical_sha256":"4c749ce3d069859fd9640a1846399c8306d712dc729d40ed537db5677eb0eb1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:21.224050Z","signature_b64":"o9kbeHzLmVI3C3Ug5lxEM4xMzHRsLGbe48fNmi9aH8pVvOit8Xf3XwmDP5gj8lpOagatTec0K2ePuFPoYsNTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c749ce3d069859fd9640a1846399c8306d712dc729d40ed537db5677eb0eb1b","last_reissued_at":"2026-05-18T01:35:21.222827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:21.222827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03294","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":"2026-05-18T01:35:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XnffhTSqKqo9yEz983YbSPdQN7KPrmF6qKDrNnijPiL1FT72FewbopjitSsTqCRqekTtZA6BB5qWe86U9h4aBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:19:39.131212Z"},"content_sha256":"7cf7d9bf974eb7d227863a58b69115be0b8f9fa6017e068d83a71fe63af8df41","schema_version":"1.0","event_id":"sha256:7cf7d9bf974eb7d227863a58b69115be0b8f9fa6017e068d83a71fe63af8df41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JR2JZY6QNGCZ7WLEBIMEMOM4QM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On rotational surfaces in pseudo-Euclidean space $\\mathbb{E}^4_t$ with pointwise 1-type Gauss map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Burcu Bekta\\c{s}, Elif \\\"Ozkara Canfes, U\\u{g}ur Dursun","submitted_at":"2015-08-13T18:27:52Z","abstract_excerpt":"In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space $\\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\\mathbb{E}^4_1$ with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain rotational surfaces in $\\mathbb{E}^4_2$ with zero mean curvature and having pointwise 1--type Gauss map of second kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03294","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":"2026-05-18T01:35:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJiU4X+SWTucrMNTez19bxLdNNt5A/W9h0292K0CFPDfLTmO/9acGTYSqgq17VEojMHStP76vhOFOPl93UDWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:19:39.131570Z"},"content_sha256":"0aafbea6276cdefabf479a0eee46465e0b016d43edce7211adc4416b6318290d","schema_version":"1.0","event_id":"sha256:0aafbea6276cdefabf479a0eee46465e0b016d43edce7211adc4416b6318290d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM/bundle.json","state_url":"https://pith.science/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM/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":"2026-06-25T08:19:39Z","links":{"resolver":"https://pith.science/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM","bundle":"https://pith.science/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM/bundle.json","state":"https://pith.science/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JR2JZY6QNGCZ7WLEBIMEMOM4QM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JR2JZY6QNGCZ7WLEBIMEMOM4QM","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":"ea86760ea8d15bd83b25add518614e7ff9cf2f63961c38bd2213b792386d08ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-13T18:27:52Z","title_canon_sha256":"a01ccee6176b43757127f7102bd7386351c4601d6e842dcabf6c42374951783a"},"schema_version":"1.0","source":{"id":"1508.03294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03294","created_at":"2026-05-18T01:35:21Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03294v1","created_at":"2026-05-18T01:35:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03294","created_at":"2026-05-18T01:35:21Z"},{"alias_kind":"pith_short_12","alias_value":"JR2JZY6QNGCZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JR2JZY6QNGCZ7WLE","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JR2JZY6Q","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:0aafbea6276cdefabf479a0eee46465e0b016d43edce7211adc4416b6318290d","target":"graph","created_at":"2026-05-18T01:35:21Z","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 study some classes of rotational surfaces in the pseudo-Euclidean space $\\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\\mathbb{E}^4_1$ with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain rotational surfaces in $\\mathbb{E}^4_2$ with zero mean curvature and having pointwise 1--type Gauss map of second kind.","authors_text":"Burcu Bekta\\c{s}, Elif \\\"Ozkara Canfes, U\\u{g}ur Dursun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-13T18:27:52Z","title":"On rotational surfaces in pseudo-Euclidean space $\\mathbb{E}^4_t$ with pointwise 1-type Gauss map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03294","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":"sha256:7cf7d9bf974eb7d227863a58b69115be0b8f9fa6017e068d83a71fe63af8df41","target":"record","created_at":"2026-05-18T01:35:21Z","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":"ea86760ea8d15bd83b25add518614e7ff9cf2f63961c38bd2213b792386d08ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-13T18:27:52Z","title_canon_sha256":"a01ccee6176b43757127f7102bd7386351c4601d6e842dcabf6c42374951783a"},"schema_version":"1.0","source":{"id":"1508.03294","kind":"arxiv","version":1}},"canonical_sha256":"4c749ce3d069859fd9640a1846399c8306d712dc729d40ed537db5677eb0eb1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c749ce3d069859fd9640a1846399c8306d712dc729d40ed537db5677eb0eb1b","first_computed_at":"2026-05-18T01:35:21.222827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:21.222827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o9kbeHzLmVI3C3Ug5lxEM4xMzHRsLGbe48fNmi9aH8pVvOit8Xf3XwmDP5gj8lpOagatTec0K2ePuFPoYsNTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:21.224050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cf7d9bf974eb7d227863a58b69115be0b8f9fa6017e068d83a71fe63af8df41","sha256:0aafbea6276cdefabf479a0eee46465e0b016d43edce7211adc4416b6318290d"],"state_sha256":"5472e2a3b2e00cadb2cdf7d524f874fded3397e1ad48e27ec54f3716e0279eca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1XKc8GxZZk5UaFHnQDmXXP3BbcQtjxan7LIVZoOszKaDVA1l1T1n7glVh4TDaX1hh6fruTgVyj0nsyfGF0QCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:19:39.133507Z","bundle_sha256":"3e3591156dab008d5b3d773d08bd7a0fa30622c6705e6466d35ae36853a2cb26"}}