{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LQ2F2G3BAVXXYILFCMQU564HRF","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":"723114585d45407427513e1a5d50def1fc4df279758acaef5efe10290f8e49f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-10T09:57:30Z","title_canon_sha256":"ff0d80a49bc2981289793fc32fc44c2efb0cbd9a0fdd273862cbda4a5b858277"},"schema_version":"1.0","source":{"id":"1809.03223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03223","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03223v1","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03223","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"LQ2F2G3BAVXX","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LQ2F2G3BAVXXYILF","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LQ2F2G3B","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:eeade339d7e868ed33172fc651475193e357077b6327bd8aa24f47d4f8075600","target":"graph","created_at":"2026-05-18T00:06:09Z","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":"Let $\\pi:sl(n|n)\\to A(n-1,n-1)$ be the natural epimorphism of Lie superalgebra. Then $\\dim\\ker\\pi=1$. Let $\\pi^{(t)}:sl^{(t)}(n|n)\\to A^{(t)}(n-1,n-1)$ be the natural epimorphism, where $t=1,2,4$. Let $\\{e_k|k\\in{\\mathbb{Z}}\\}$ be the basis of $\\ker\\pi^{(t)}$ with $e_k\\in sl^{(t)}(n|n)_{(a_tk+b_t)\\delta}$, where $(a_1,b_1)=(1,0)$, $(a_2,b_2)=(2,-1)$ and $(a_4,b_4)=(4,-2)$. The main result of this paper is to explicitly describe an element of $U_q(sl^{(t)}(n|n))$ (and its multi-parameter version) corresponding to $e_1$ (i.e., $k=1$). As for $U_q(sl^{(1)}(n|n))$ (i.e., $t=1$), the author had alr","authors_text":"Hiroyuki Yamane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-10T09:57:30Z","title":"Lowest positive almost central elements of $U_q(sl^{(1)}(n|n))$ $(n\\geq 2)$, $U_q(sl^{(2)}(2n|2n))$ $(n\\geq 2)$ and $U_q(sl^{(4)}(2n+1|2n+1))$ $(n\\geq 1)$ and their multi-parameter quantum affine superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03223","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":"sha256:429f2e3b5e3c1e4ab404cdfb254ff7e9aa98d28d51810dd652ffe0aafbc58fd8","target":"record","created_at":"2026-05-18T00:06:09Z","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":"723114585d45407427513e1a5d50def1fc4df279758acaef5efe10290f8e49f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-10T09:57:30Z","title_canon_sha256":"ff0d80a49bc2981289793fc32fc44c2efb0cbd9a0fdd273862cbda4a5b858277"},"schema_version":"1.0","source":{"id":"1809.03223","kind":"arxiv","version":1}},"canonical_sha256":"5c345d1b61056f7c216513214efb87896a7e15f3db670bf1f4ca4a48b4dbd918","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c345d1b61056f7c216513214efb87896a7e15f3db670bf1f4ca4a48b4dbd918","first_computed_at":"2026-05-18T00:06:09.593473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:09.593473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tmnha30wQjUgFBR5F36drB5REKKIiog4mJrEe4AI3ktw9JraND7kVJZ/6k+6etiV2BY5c3n0ZDXiwckYfcN8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:09.594110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:429f2e3b5e3c1e4ab404cdfb254ff7e9aa98d28d51810dd652ffe0aafbc58fd8","sha256:eeade339d7e868ed33172fc651475193e357077b6327bd8aa24f47d4f8075600"],"state_sha256":"cbe18c31b0e8b1b938b80d26daed75d4a132bd4c49169905aee0aa510caa7281"}