{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:2C5SMMMNO4NGNIV2NXDT26MCGC","short_pith_number":"pith:2C5SMMMN","canonical_record":{"source":{"id":"1908.06624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T07:34:56Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"94cdcf3962d371adb7996072c780de7a3e4a16cb2b1e82b8728f6d8941ebefb4","abstract_canon_sha256":"14f51edf90807d3c00d3b9a627210d420c69b2f61defad5ce99a675a3e58afa4"},"schema_version":"1.0"},"canonical_sha256":"d0bb26318d771a66a2ba6dc73d798230b6c2ef8b666b11aa5878ffc08b8aedd7","source":{"kind":"arxiv","id":"1908.06624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06624","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06624v1","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06624","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"2C5SMMMNO4NG","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"2C5SMMMNO4NGNIV2","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"2C5SMMMN","created_at":"2026-07-05T00:39:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:2C5SMMMNO4NGNIV2NXDT26MCGC","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T07:34:56Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"94cdcf3962d371adb7996072c780de7a3e4a16cb2b1e82b8728f6d8941ebefb4","abstract_canon_sha256":"14f51edf90807d3c00d3b9a627210d420c69b2f61defad5ce99a675a3e58afa4"},"schema_version":"1.0"},"canonical_sha256":"d0bb26318d771a66a2ba6dc73d798230b6c2ef8b666b11aa5878ffc08b8aedd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:39:13.439132Z","signature_b64":"YDHM+f+Nq3dzfvOCjvKWFmuRpYP6pxk3/JBDtIw6zBSArvY6DUGbHcOpFBv3OPPnmsT98vsrHiVZIPUAh7WJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0bb26318d771a66a2ba6dc73d798230b6c2ef8b666b11aa5878ffc08b8aedd7","last_reissued_at":"2026-07-05T00:39:13.438641Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:39:13.438641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06624","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":"2026-07-05T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBvSXg5Fg19Rxej016H51P0m6CggyAYzFQFCAjX53bM75YKmZ53RfZ2zPBMhkb0G6yKYRz/WIg5GM52b2g4yDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:27:35.674705Z"},"content_sha256":"3ee96d44c0b58ec360b21ab1ed2076c6bd7811432c9dd5aa89498e8fca9bfde1","schema_version":"1.0","event_id":"sha256:3ee96d44c0b58ec360b21ab1ed2076c6bd7811432c9dd5aa89498e8fca9bfde1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:2C5SMMMNO4NGNIV2NXDT26MCGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some conjectures by Lu and Wenzel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DG","authors_text":"Fagui Li, Jianquan Ge, Yi Zhou, Zhiqin Lu","submitted_at":"2019-08-19T07:34:56Z","abstract_excerpt":"In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward several new conjectures which will be shown equivalent to Conjecture 2. In particular, we prove Conjecture 2 and hence all conjectures in some special cases. For Conjecture 3, we obtain a bigger upper bound $2+\\sqrt{10}/2$, and we also give a weaker answer for the more general Question 1. In addition, we obtain some new simple proofs of the complex BW inequality"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06624","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06624/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqLP381faWN4dESkoqNxFZF5IgXdLVA/uTPP10C6Hvz0Gzlj8q/s/8I50u/jZ3n7XmdhdnULQPCjnk0yZZqABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:27:35.675639Z"},"content_sha256":"9f7f853b453034658e78d8ec59959121b36256bd2ec39f428c7f5d3b21615b48","schema_version":"1.0","event_id":"sha256:9f7f853b453034658e78d8ec59959121b36256bd2ec39f428c7f5d3b21615b48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2C5SMMMNO4NGNIV2NXDT26MCGC/bundle.json","state_url":"https://pith.science/pith/2C5SMMMNO4NGNIV2NXDT26MCGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2C5SMMMNO4NGNIV2NXDT26MCGC/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":"2026-08-16T21:27:35Z","links":{"resolver":"https://pith.science/pith/2C5SMMMNO4NGNIV2NXDT26MCGC","bundle":"https://pith.science/pith/2C5SMMMNO4NGNIV2NXDT26MCGC/bundle.json","state":"https://pith.science/pith/2C5SMMMNO4NGNIV2NXDT26MCGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2C5SMMMNO4NGNIV2NXDT26MCGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2C5SMMMNO4NGNIV2NXDT26MCGC","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":"14f51edf90807d3c00d3b9a627210d420c69b2f61defad5ce99a675a3e58afa4","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T07:34:56Z","title_canon_sha256":"94cdcf3962d371adb7996072c780de7a3e4a16cb2b1e82b8728f6d8941ebefb4"},"schema_version":"1.0","source":{"id":"1908.06624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06624","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06624v1","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06624","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"2C5SMMMNO4NG","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"2C5SMMMNO4NGNIV2","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"2C5SMMMN","created_at":"2026-07-05T00:39:13Z"}],"graph_snapshots":[{"event_id":"sha256:9f7f853b453034658e78d8ec59959121b36256bd2ec39f428c7f5d3b21615b48","target":"graph","created_at":"2026-07-05T00:39:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.06624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward several new conjectures which will be shown equivalent to Conjecture 2. In particular, we prove Conjecture 2 and hence all conjectures in some special cases. For Conjecture 3, we obtain a bigger upper bound $2+\\sqrt{10}/2$, and we also give a weaker answer for the more general Question 1. In addition, we obtain some new simple proofs of the complex BW inequality","authors_text":"Fagui Li, Jianquan Ge, Yi Zhou, Zhiqin Lu","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T07:34:56Z","title":"On some conjectures by Lu and Wenzel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06624","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":"sha256:3ee96d44c0b58ec360b21ab1ed2076c6bd7811432c9dd5aa89498e8fca9bfde1","target":"record","created_at":"2026-07-05T00:39:13Z","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":"14f51edf90807d3c00d3b9a627210d420c69b2f61defad5ce99a675a3e58afa4","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T07:34:56Z","title_canon_sha256":"94cdcf3962d371adb7996072c780de7a3e4a16cb2b1e82b8728f6d8941ebefb4"},"schema_version":"1.0","source":{"id":"1908.06624","kind":"arxiv","version":1}},"canonical_sha256":"d0bb26318d771a66a2ba6dc73d798230b6c2ef8b666b11aa5878ffc08b8aedd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0bb26318d771a66a2ba6dc73d798230b6c2ef8b666b11aa5878ffc08b8aedd7","first_computed_at":"2026-07-05T00:39:13.438641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:13.438641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YDHM+f+Nq3dzfvOCjvKWFmuRpYP6pxk3/JBDtIw6zBSArvY6DUGbHcOpFBv3OPPnmsT98vsrHiVZIPUAh7WJCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:13.439132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ee96d44c0b58ec360b21ab1ed2076c6bd7811432c9dd5aa89498e8fca9bfde1","sha256:9f7f853b453034658e78d8ec59959121b36256bd2ec39f428c7f5d3b21615b48"],"state_sha256":"3539e78095cf6db687ed06c411054030d248ab7955ae175d18ae29d01e07d8b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwPVO1KEDMSH0/Dv6VMexs2e4VC03PLWJB5R37te9pemRGDYtTVLctCIxBidhYpUNhVsBXidmI/IztYZNgJ4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:27:35.699087Z","bundle_sha256":"92f0a1a9c7b3fdaebaa01da3978061b3c8490fde67be0d3c0137f5a913f276de"}}