{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:UEW6RFYIJQKYAC33C2Z6AC5NZ3","short_pith_number":"pith:UEW6RFYI","canonical_record":{"source":{"id":"math/0209243","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-09-18T23:58:18Z","cross_cats_sorted":["math-ph","math.GR","math.MP"],"title_canon_sha256":"27ec9647f9dba715de974eaefc1efdb9a0bca33091874e1e20da6e7339d855e7","abstract_canon_sha256":"0b593c9d95e8a436f52358ac132846f22da9d9c31745cf0cbd49e6b21236d656"},"schema_version":"1.0"},"canonical_sha256":"a12de897084c15800b7b16b3e00badcef41d868440fe37b2baf7bb1c777f6787","source":{"kind":"arxiv","id":"math/0209243","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0209243","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0209243v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0209243","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"UEW6RFYIJQKY","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"UEW6RFYIJQKYAC33","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"UEW6RFYI","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:UEW6RFYIJQKYAC33C2Z6AC5NZ3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0209243","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-09-18T23:58:18Z","cross_cats_sorted":["math-ph","math.GR","math.MP"],"title_canon_sha256":"27ec9647f9dba715de974eaefc1efdb9a0bca33091874e1e20da6e7339d855e7","abstract_canon_sha256":"0b593c9d95e8a436f52358ac132846f22da9d9c31745cf0cbd49e6b21236d656"},"schema_version":"1.0"},"canonical_sha256":"a12de897084c15800b7b16b3e00badcef41d868440fe37b2baf7bb1c777f6787","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.422302Z","signature_b64":"9zG09QgIkSWxZLr0US5yYLTI19MWa687taozM/QyTHNICbpQlY42YCj0c4X5Pe/EK3YJnwPrCU2J+QOUwlfzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a12de897084c15800b7b16b3e00badcef41d868440fe37b2baf7bb1c777f6787","last_reissued_at":"2026-05-18T01:38:29.421685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.421685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0209243","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eoF/FN+IFAj/6GkV37MVmO3u88ZAfrm0eBMI4c2ddCT8LuJaHrpWEhV6sElk2Rger9H15Ai+cB32U1AGEU6zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:49:01.718846Z"},"content_sha256":"b700b99ab0917207be1fb3985712b515b68b1b496d290a4124f2b67bf27a69b3","schema_version":"1.0","event_id":"sha256:b700b99ab0917207be1fb3985712b515b68b1b496d290a4124f2b67bf27a69b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:UEW6RFYIJQKYAC33C2Z6AC5NZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"q-Analogue of $A_{m-1}\\oplus A_{n-1}\\subset A_{mn-1}$","license":"","headline":"","cross_cats":["math-ph","math.GR","math.MP"],"primary_cat":"math.QA","authors_text":"A. I. Georgieva, P. P. Raychev, R. P. Roussev, V. G. Gueorguiev","submitted_at":"2002-09-18T23:58:18Z","abstract_excerpt":"A natural embedding $A_{m-1}\\oplus A_{n-1}\\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\\mathcal{A}_q^{-}$ (mn)$\\sim {\\otimes} ^n \\mathcal{A}_q^{-}$(m)$\\sim {\\otimes}^m\\mathcal{A}_q^{-}$(n) algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0209243","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sDKi7h2zvKmcyMiyDzrtqbXQnPTCJqF+LL61+V08xtEWnsgzIeBIn/7GGuoxVaObRxODCH5Sd6p4g/dOR40mBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:49:01.719187Z"},"content_sha256":"61bd33f0b62ac58ee1bb069e0f874237e6d02ca8330a3390af88f373833aa7d7","schema_version":"1.0","event_id":"sha256:61bd33f0b62ac58ee1bb069e0f874237e6d02ca8330a3390af88f373833aa7d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3/bundle.json","state_url":"https://pith.science/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3/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":"2026-05-30T17:49:01Z","links":{"resolver":"https://pith.science/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3","bundle":"https://pith.science/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3/bundle.json","state":"https://pith.science/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEW6RFYIJQKYAC33C2Z6AC5NZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:UEW6RFYIJQKYAC33C2Z6AC5NZ3","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":"0b593c9d95e8a436f52358ac132846f22da9d9c31745cf0cbd49e6b21236d656","cross_cats_sorted":["math-ph","math.GR","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2002-09-18T23:58:18Z","title_canon_sha256":"27ec9647f9dba715de974eaefc1efdb9a0bca33091874e1e20da6e7339d855e7"},"schema_version":"1.0","source":{"id":"math/0209243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0209243","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0209243v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0209243","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"UEW6RFYIJQKY","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"UEW6RFYIJQKYAC33","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"UEW6RFYI","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:61bd33f0b62ac58ee1bb069e0f874237e6d02ca8330a3390af88f373833aa7d7","target":"graph","created_at":"2026-05-18T01:38:29Z","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 natural embedding $A_{m-1}\\oplus A_{n-1}\\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\\mathcal{A}_q^{-}$ (mn)$\\sim {\\otimes} ^n \\mathcal{A}_q^{-}$(m)$\\sim {\\otimes}^m\\mathcal{A}_q^{-}$(n) algebras.","authors_text":"A. I. Georgieva, P. P. Raychev, R. P. Roussev, V. G. Gueorguiev","cross_cats":["math-ph","math.GR","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2002-09-18T23:58:18Z","title":"q-Analogue of $A_{m-1}\\oplus A_{n-1}\\subset A_{mn-1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0209243","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:b700b99ab0917207be1fb3985712b515b68b1b496d290a4124f2b67bf27a69b3","target":"record","created_at":"2026-05-18T01:38:29Z","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":"0b593c9d95e8a436f52358ac132846f22da9d9c31745cf0cbd49e6b21236d656","cross_cats_sorted":["math-ph","math.GR","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2002-09-18T23:58:18Z","title_canon_sha256":"27ec9647f9dba715de974eaefc1efdb9a0bca33091874e1e20da6e7339d855e7"},"schema_version":"1.0","source":{"id":"math/0209243","kind":"arxiv","version":1}},"canonical_sha256":"a12de897084c15800b7b16b3e00badcef41d868440fe37b2baf7bb1c777f6787","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a12de897084c15800b7b16b3e00badcef41d868440fe37b2baf7bb1c777f6787","first_computed_at":"2026-05-18T01:38:29.421685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.421685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9zG09QgIkSWxZLr0US5yYLTI19MWa687taozM/QyTHNICbpQlY42YCj0c4X5Pe/EK3YJnwPrCU2J+QOUwlfzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.422302Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0209243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b700b99ab0917207be1fb3985712b515b68b1b496d290a4124f2b67bf27a69b3","sha256:61bd33f0b62ac58ee1bb069e0f874237e6d02ca8330a3390af88f373833aa7d7"],"state_sha256":"758b3b2e361d826aeefd5aac1931a6add804abf702ea7b482283321d76060ce2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+YMyIxA9L95Bh2Ot27oMPu2caqbeTIcSZ3Z7OkQePy/etXl5bXkF5INtfnK7t7GRZiZrUrvRpZJE/N+y2uTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:49:01.721058Z","bundle_sha256":"ecd0e6924bf7a6b99bdcddccf2187db8d7a2190c6ed5fd49c9333d831d98078b"}}