{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RSMBGBDZR6HQAMA5DG2IPJ2MYV","short_pith_number":"pith:RSMBGBDZ","canonical_record":{"source":{"id":"1901.07883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-01-21T12:41:39Z","cross_cats_sorted":[],"title_canon_sha256":"da2ef46a2443128a1050bb411abe901714fd52a6ad7eeb32cb25c4796c1dd251","abstract_canon_sha256":"27a96b432369fc958bcb95fb58e60d8eb6a05cc413562c82f9f099b1e4a29f24"},"schema_version":"1.0"},"canonical_sha256":"8c981304798f8f00301d19b487a74cc55a9ae1427e532d5124fe1388a78bfd0b","source":{"kind":"arxiv","id":"1901.07883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07883","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07883v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07883","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"RSMBGBDZR6HQ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RSMBGBDZR6HQAMA5","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RSMBGBDZ","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RSMBGBDZR6HQAMA5DG2IPJ2MYV","target":"record","payload":{"canonical_record":{"source":{"id":"1901.07883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-01-21T12:41:39Z","cross_cats_sorted":[],"title_canon_sha256":"da2ef46a2443128a1050bb411abe901714fd52a6ad7eeb32cb25c4796c1dd251","abstract_canon_sha256":"27a96b432369fc958bcb95fb58e60d8eb6a05cc413562c82f9f099b1e4a29f24"},"schema_version":"1.0"},"canonical_sha256":"8c981304798f8f00301d19b487a74cc55a9ae1427e532d5124fe1388a78bfd0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:39.541613Z","signature_b64":"tUOc6tRBMEU5h4rFCTzGIW3PMFAnv2lN/HXlFThTto6MR5oZ3Zyc+XKuqAle0wEcSywyB8h+JC/AfZpKNByKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c981304798f8f00301d19b487a74cc55a9ae1427e532d5124fe1388a78bfd0b","last_reissued_at":"2026-05-17T23:55:39.541175Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:39.541175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.07883","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":"2026-05-17T23:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PQXs/Gl3NXGbYaykpPmSO+y1uOAXL/AbgzaxBoE+E10sIcuQoXQrISw2Ez9lZazKzHqyYo26PvyjN/KJvli8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:30:35.302877Z"},"content_sha256":"b09a8316eb097c0c3b36578cecb658804472ed6656eb68eff190139b7e711ed1","schema_version":"1.0","event_id":"sha256:b09a8316eb097c0c3b36578cecb658804472ed6656eb68eff190139b7e711ed1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RSMBGBDZR6HQAMA5DG2IPJ2MYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weingarten map of the hypersurface in 4-dimensional Euclidean space and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Salim Y\\\"uce","submitted_at":"2019-01-21T12:41:39Z","abstract_excerpt":"In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space $E^4$, a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface $M^3$ in $E^4$ is obtained. By taking this efficient method, it is possible to study of the hypersurface theory in $E^4$ which is analog the surface theory in $E^3$. Furthermore, the Gaussian curvature, mean curvature, fundamental forms and Dupin indicatrix of $M^3$ is introduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07883","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":"2026-05-17T23:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QljpUn/dngVZWRmaGdUymdt9EA3SE/k6iZcALG7Etc3C4skYIq5uU0etfzqWsKljk99XvGW3D95O7+7nRPi9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:30:35.303232Z"},"content_sha256":"fefd02b7693fbb3f9ddaf5318c57e7316b9d6115e123a59e7dfd5ff3b4fd3bc6","schema_version":"1.0","event_id":"sha256:fefd02b7693fbb3f9ddaf5318c57e7316b9d6115e123a59e7dfd5ff3b4fd3bc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV/bundle.json","state_url":"https://pith.science/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV/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":"2026-07-04T18:30:35Z","links":{"resolver":"https://pith.science/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV","bundle":"https://pith.science/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV/bundle.json","state":"https://pith.science/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RSMBGBDZR6HQAMA5DG2IPJ2MYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RSMBGBDZR6HQAMA5DG2IPJ2MYV","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":"27a96b432369fc958bcb95fb58e60d8eb6a05cc413562c82f9f099b1e4a29f24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-01-21T12:41:39Z","title_canon_sha256":"da2ef46a2443128a1050bb411abe901714fd52a6ad7eeb32cb25c4796c1dd251"},"schema_version":"1.0","source":{"id":"1901.07883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07883","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07883v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07883","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"RSMBGBDZR6HQ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RSMBGBDZR6HQAMA5","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RSMBGBDZ","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:fefd02b7693fbb3f9ddaf5318c57e7316b9d6115e123a59e7dfd5ff3b4fd3bc6","target":"graph","created_at":"2026-05-17T23:55:39Z","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, by taking into account the beginning of the hypersurface theory in Euclidean space $E^4$, a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface $M^3$ in $E^4$ is obtained. By taking this efficient method, it is possible to study of the hypersurface theory in $E^4$ which is analog the surface theory in $E^3$. Furthermore, the Gaussian curvature, mean curvature, fundamental forms and Dupin indicatrix of $M^3$ is introduced.","authors_text":"Salim Y\\\"uce","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-01-21T12:41:39Z","title":"Weingarten map of the hypersurface in 4-dimensional Euclidean space and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07883","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:b09a8316eb097c0c3b36578cecb658804472ed6656eb68eff190139b7e711ed1","target":"record","created_at":"2026-05-17T23:55:39Z","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":"27a96b432369fc958bcb95fb58e60d8eb6a05cc413562c82f9f099b1e4a29f24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-01-21T12:41:39Z","title_canon_sha256":"da2ef46a2443128a1050bb411abe901714fd52a6ad7eeb32cb25c4796c1dd251"},"schema_version":"1.0","source":{"id":"1901.07883","kind":"arxiv","version":1}},"canonical_sha256":"8c981304798f8f00301d19b487a74cc55a9ae1427e532d5124fe1388a78bfd0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c981304798f8f00301d19b487a74cc55a9ae1427e532d5124fe1388a78bfd0b","first_computed_at":"2026-05-17T23:55:39.541175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:39.541175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tUOc6tRBMEU5h4rFCTzGIW3PMFAnv2lN/HXlFThTto6MR5oZ3Zyc+XKuqAle0wEcSywyB8h+JC/AfZpKNByKBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:39.541613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b09a8316eb097c0c3b36578cecb658804472ed6656eb68eff190139b7e711ed1","sha256:fefd02b7693fbb3f9ddaf5318c57e7316b9d6115e123a59e7dfd5ff3b4fd3bc6"],"state_sha256":"0bcabb2310b0922d9d8cda12eebe0f8d2dea9961e18bab8f68c59f1903276501"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XJSMvgzhHkpnhJsK6B6+vG6NHupN1qxqMSUW/4Ll2KZbus4M8CEuk5lZ0mJ/5rOir/c637OLuvJs9cTa++q0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:30:35.305444Z","bundle_sha256":"54ec267e68c2ee738657b76b9b65ff3db29ceec93ec783b27202e9698d1ac9e1"}}