{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FW4CWMWQNBJI5X6KQHPDPPLGH5","short_pith_number":"pith:FW4CWMWQ","canonical_record":{"source":{"id":"1601.04320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-01-17T18:37:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"177c6fbe4d6a882cb13b36187c03f8dc4c439f20d26dc773d71bbda216c20b9f","abstract_canon_sha256":"ba4232a6266d55bc449faa66183fd526faa4997fa85bca017fd04625e4458330"},"schema_version":"1.0"},"canonical_sha256":"2db82b32d068528edfca81de37bd663f785459ef662c4f016ceb96ebfea97fbd","source":{"kind":"arxiv","id":"1601.04320","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04320","created_at":"2026-05-18T01:21:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04320v2","created_at":"2026-05-18T01:21:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04320","created_at":"2026-05-18T01:21:15Z"},{"alias_kind":"pith_short_12","alias_value":"FW4CWMWQNBJI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FW4CWMWQNBJI5X6K","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FW4CWMWQ","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FW4CWMWQNBJI5X6KQHPDPPLGH5","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-01-17T18:37:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"177c6fbe4d6a882cb13b36187c03f8dc4c439f20d26dc773d71bbda216c20b9f","abstract_canon_sha256":"ba4232a6266d55bc449faa66183fd526faa4997fa85bca017fd04625e4458330"},"schema_version":"1.0"},"canonical_sha256":"2db82b32d068528edfca81de37bd663f785459ef662c4f016ceb96ebfea97fbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:15.422555Z","signature_b64":"YfoTN2ngRZHeIiiqVn3VTNB2q8SsZhSMjUc07W6NsM/rAIHo8oY8VirJ+IPabsfqUiGUNTwHw3i1geVexemqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2db82b32d068528edfca81de37bd663f785459ef662c4f016ceb96ebfea97fbd","last_reissued_at":"2026-05-18T01:21:15.422027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:15.422027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04320","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":"2026-05-18T01:21:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9atxxWiEzRrpD0W3UC6LWh2aeh7E3MBSoAHhTzAw4cpEf352ljZz46muTXnnNUdEOsioI4eY2z8bDJciH2mgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:56:10.169690Z"},"content_sha256":"65712536c1ffaf34606afb7f648f4d775876dbf4b6bb3021237ccb52181dc7f5","schema_version":"1.0","event_id":"sha256:65712536c1ffaf34606afb7f648f4d775876dbf4b6bb3021237ccb52181dc7f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FW4CWMWQNBJI5X6KQHPDPPLGH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of $E_6$ and $E_7$, $E_8$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Hongmei Hu, Naihong Hu","submitted_at":"2016-01-17T18:37:07Z","abstract_excerpt":"Double-bosonization construction in Majid \\cite{majid1} is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \\cite{HH1, HH2} have been depicted how to grow up. This paper continues to elucidate the type-crossing and inductive constructions of exceptional quantum groups of types $E_6$ and $E_7$, $E_8$, respectively, based on the generalized double-bosonization Theorem established in \\cite{HH2}. Thus the Majid's expectation for the inductive constructions of $U_q(\\mathfrak g)$'s for all finite-dimensional complex simple Lie algebras is completely achieved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04320","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":"2026-05-18T01:21:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UT5CsMXdwURyQHp+LRx0vdpwbkmNQJT+cOyeR73R+cZg6gcnTW5fBbyfYNusLZfZZ+TeXe0Irc7t1UoFN74QBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:56:10.170264Z"},"content_sha256":"136aa45e10cf3f0f075d628f9398167d8c686fec464d5b2d8e0a4b4ef21ff2ff","schema_version":"1.0","event_id":"sha256:136aa45e10cf3f0f075d628f9398167d8c686fec464d5b2d8e0a4b4ef21ff2ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5/bundle.json","state_url":"https://pith.science/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5/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":"2026-06-05T01:56:10Z","links":{"resolver":"https://pith.science/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5","bundle":"https://pith.science/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5/bundle.json","state":"https://pith.science/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FW4CWMWQNBJI5X6KQHPDPPLGH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FW4CWMWQNBJI5X6KQHPDPPLGH5","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":"ba4232a6266d55bc449faa66183fd526faa4997fa85bca017fd04625e4458330","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-01-17T18:37:07Z","title_canon_sha256":"177c6fbe4d6a882cb13b36187c03f8dc4c439f20d26dc773d71bbda216c20b9f"},"schema_version":"1.0","source":{"id":"1601.04320","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04320","created_at":"2026-05-18T01:21:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04320v2","created_at":"2026-05-18T01:21:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04320","created_at":"2026-05-18T01:21:15Z"},{"alias_kind":"pith_short_12","alias_value":"FW4CWMWQNBJI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FW4CWMWQNBJI5X6K","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FW4CWMWQ","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:136aa45e10cf3f0f075d628f9398167d8c686fec464d5b2d8e0a4b4ef21ff2ff","target":"graph","created_at":"2026-05-18T01:21:15Z","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":"Double-bosonization construction in Majid \\cite{majid1} is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \\cite{HH1, HH2} have been depicted how to grow up. This paper continues to elucidate the type-crossing and inductive constructions of exceptional quantum groups of types $E_6$ and $E_7$, $E_8$, respectively, based on the generalized double-bosonization Theorem established in \\cite{HH2}. Thus the Majid's expectation for the inductive constructions of $U_q(\\mathfrak g)$'s for all finite-dimensional complex simple Lie algebras is completely achieved","authors_text":"Hongmei Hu, Naihong Hu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-01-17T18:37:07Z","title":"Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of $E_6$ and $E_7$, $E_8$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04320","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":"sha256:65712536c1ffaf34606afb7f648f4d775876dbf4b6bb3021237ccb52181dc7f5","target":"record","created_at":"2026-05-18T01:21:15Z","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":"ba4232a6266d55bc449faa66183fd526faa4997fa85bca017fd04625e4458330","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-01-17T18:37:07Z","title_canon_sha256":"177c6fbe4d6a882cb13b36187c03f8dc4c439f20d26dc773d71bbda216c20b9f"},"schema_version":"1.0","source":{"id":"1601.04320","kind":"arxiv","version":2}},"canonical_sha256":"2db82b32d068528edfca81de37bd663f785459ef662c4f016ceb96ebfea97fbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2db82b32d068528edfca81de37bd663f785459ef662c4f016ceb96ebfea97fbd","first_computed_at":"2026-05-18T01:21:15.422027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:15.422027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YfoTN2ngRZHeIiiqVn3VTNB2q8SsZhSMjUc07W6NsM/rAIHo8oY8VirJ+IPabsfqUiGUNTwHw3i1geVexemqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:15.422555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04320","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65712536c1ffaf34606afb7f648f4d775876dbf4b6bb3021237ccb52181dc7f5","sha256:136aa45e10cf3f0f075d628f9398167d8c686fec464d5b2d8e0a4b4ef21ff2ff"],"state_sha256":"efdeecc50b13a4600dea8741bcee782bb555ac1f442cb4a9620d45db5c29329f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+zDUH834zq+ArQxvg/UhjnJl3OPd2zBpnSjElztPcRYpMbxhufU6hsdLewIlyA07I8Dec7eweXt5bF4C7EeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:56:10.175163Z","bundle_sha256":"176e28658e42d7400282e3d81588e1aa9aeefb8f846ebecf80eb0d68781a8be4"}}