{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CTGW7BWW3ZHHCP3JY622YD2LIB","short_pith_number":"pith:CTGW7BWW","canonical_record":{"source":{"id":"1301.4742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-21T03:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"636d03303d899a0f36dc8fe8653cd271c25ba1e1d5b3f813deb1dd97056546ed","abstract_canon_sha256":"c1167864654a5269fef37b85f0d0f64b9386bf2474fd24bf445c77f982eccb6d"},"schema_version":"1.0"},"canonical_sha256":"14cd6f86d6de4e713f69c7b5ac0f4b405474df0efaee2942c7a6babd1c047099","source":{"kind":"arxiv","id":"1301.4742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4742","created_at":"2026-05-18T03:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4742v2","created_at":"2026-05-18T03:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4742","created_at":"2026-05-18T03:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"CTGW7BWW3ZHH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CTGW7BWW3ZHHCP3J","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CTGW7BWW","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CTGW7BWW3ZHHCP3JY622YD2LIB","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-21T03:21:52Z","cross_cats_sorted":[],"title_canon_sha256":"636d03303d899a0f36dc8fe8653cd271c25ba1e1d5b3f813deb1dd97056546ed","abstract_canon_sha256":"c1167864654a5269fef37b85f0d0f64b9386bf2474fd24bf445c77f982eccb6d"},"schema_version":"1.0"},"canonical_sha256":"14cd6f86d6de4e713f69c7b5ac0f4b405474df0efaee2942c7a6babd1c047099","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:53.446564Z","signature_b64":"DRD57Zga+o+eju6+T3t7PlYq0RU/rqDusgVcfNUhEw5i/tXLlwe5PV7IZCiVqnaBAuPYlj+mQXZwFpNhr4IhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14cd6f86d6de4e713f69c7b5ac0f4b405474df0efaee2942c7a6babd1c047099","last_reissued_at":"2026-05-18T03:35:53.445775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:53.445775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4742","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xklRtWFlGq15367Xr7K8Qb8N/iqmwFvTcVp3tJC84EuGA9xnf7jceqTNSMkhx/ZqcZP7zqQKuS1wSscrb0hXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:39:06.762581Z"},"content_sha256":"8bb402791426d09d0e6e26ceb4cd7ef7abed6f7f2580bee038c1cbb21da09655","schema_version":"1.0","event_id":"sha256:8bb402791426d09d0e6e26ceb4cd7ef7abed6f7f2580bee038c1cbb21da09655"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CTGW7BWW3ZHHCP3JY622YD2LIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wintgen ideal submanifolds with a low-dimensional integrable distribution (I)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Changping Wang, Tongzhu Li, Xiang Ma","submitted_at":"2013-01-21T03:21:52Z","abstract_excerpt":"A submanifold in space forms satisfies the well-known DDVV inequality due to De Smet, Dillen, Verstraelen and Vrancken. The submanifold attaining equality in the DDVV inequality at every point is called Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are studied in this paper using the framework of M\\\"{o}bius geometry. We classify Wintgen ideal submanfiolds of dimension $m>2$ and arbitrary codimension when a canonically defined 2-dimensional distribution $\\mathbb{D}$ is integrable. Such examples come from cones, cylinders, or rotational submanifolds over s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4742","kind":"arxiv","version":2},"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":"2026-05-18T03:35:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Glr9T/rsUxJw9jiEGrLSnhXiORXn/fj1kTFcQpvnN/RAWe2gKZSUW08vikNigFZ5HZg7oGPX1limqFFjbF/eAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:39:06.763208Z"},"content_sha256":"1bef2ad6f5973cf7597d54848ea89ca4732124f14493d32e9552de442e7ce8af","schema_version":"1.0","event_id":"sha256:1bef2ad6f5973cf7597d54848ea89ca4732124f14493d32e9552de442e7ce8af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CTGW7BWW3ZHHCP3JY622YD2LIB/bundle.json","state_url":"https://pith.science/pith/CTGW7BWW3ZHHCP3JY622YD2LIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CTGW7BWW3ZHHCP3JY622YD2LIB/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":"2026-05-27T17:39:06Z","links":{"resolver":"https://pith.science/pith/CTGW7BWW3ZHHCP3JY622YD2LIB","bundle":"https://pith.science/pith/CTGW7BWW3ZHHCP3JY622YD2LIB/bundle.json","state":"https://pith.science/pith/CTGW7BWW3ZHHCP3JY622YD2LIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CTGW7BWW3ZHHCP3JY622YD2LIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CTGW7BWW3ZHHCP3JY622YD2LIB","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":"c1167864654a5269fef37b85f0d0f64b9386bf2474fd24bf445c77f982eccb6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-21T03:21:52Z","title_canon_sha256":"636d03303d899a0f36dc8fe8653cd271c25ba1e1d5b3f813deb1dd97056546ed"},"schema_version":"1.0","source":{"id":"1301.4742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4742","created_at":"2026-05-18T03:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4742v2","created_at":"2026-05-18T03:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4742","created_at":"2026-05-18T03:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"CTGW7BWW3ZHH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CTGW7BWW3ZHHCP3J","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CTGW7BWW","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:1bef2ad6f5973cf7597d54848ea89ca4732124f14493d32e9552de442e7ce8af","target":"graph","created_at":"2026-05-18T03:35:53Z","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":"A submanifold in space forms satisfies the well-known DDVV inequality due to De Smet, Dillen, Verstraelen and Vrancken. The submanifold attaining equality in the DDVV inequality at every point is called Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are studied in this paper using the framework of M\\\"{o}bius geometry. We classify Wintgen ideal submanfiolds of dimension $m>2$ and arbitrary codimension when a canonically defined 2-dimensional distribution $\\mathbb{D}$ is integrable. Such examples come from cones, cylinders, or rotational submanifolds over s","authors_text":"Changping Wang, Tongzhu Li, Xiang Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-21T03:21:52Z","title":"Wintgen ideal submanifolds with a low-dimensional integrable distribution (I)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4742","kind":"arxiv","version":2},"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":"sha256:8bb402791426d09d0e6e26ceb4cd7ef7abed6f7f2580bee038c1cbb21da09655","target":"record","created_at":"2026-05-18T03:35:53Z","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":"c1167864654a5269fef37b85f0d0f64b9386bf2474fd24bf445c77f982eccb6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-21T03:21:52Z","title_canon_sha256":"636d03303d899a0f36dc8fe8653cd271c25ba1e1d5b3f813deb1dd97056546ed"},"schema_version":"1.0","source":{"id":"1301.4742","kind":"arxiv","version":2}},"canonical_sha256":"14cd6f86d6de4e713f69c7b5ac0f4b405474df0efaee2942c7a6babd1c047099","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14cd6f86d6de4e713f69c7b5ac0f4b405474df0efaee2942c7a6babd1c047099","first_computed_at":"2026-05-18T03:35:53.445775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:53.445775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DRD57Zga+o+eju6+T3t7PlYq0RU/rqDusgVcfNUhEw5i/tXLlwe5PV7IZCiVqnaBAuPYlj+mQXZwFpNhr4IhCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:53.446564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bb402791426d09d0e6e26ceb4cd7ef7abed6f7f2580bee038c1cbb21da09655","sha256:1bef2ad6f5973cf7597d54848ea89ca4732124f14493d32e9552de442e7ce8af"],"state_sha256":"fa49999eed534634c836bf2b8f80511a94a48f0b8a5a7ef8ad6a084aa77f3cb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1UXE/2QefKcN+TBJ8ArF/EMrdsNqQ1LUsI3O+qlJVCB1tYa++IZ/z9OCWxRjTRmI3WaXg7R9NSEI7fHLgbW/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:39:06.766115Z","bundle_sha256":"e50f5597f78f5cee29472d0e4b47b07c15b681d8a405cf5a4dde73724ac722fd"}}