{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2TUCEZ2B5EE4NTPOY27YK3INL2","short_pith_number":"pith:2TUCEZ2B","canonical_record":{"source":{"id":"1006.3928","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-20T11:29:15Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"b5a9018a2992f23024274837f664b1ca5807866fbf9d6fd660fb04c3580f129f","abstract_canon_sha256":"798ef8f149df09de92c89b9aee884f5e0b196e84d918931780eb46b5610b3af7"},"schema_version":"1.0"},"canonical_sha256":"d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d","source":{"kind":"arxiv","id":"1006.3928","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3928","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3928v4","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3928","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"2TUCEZ2B5EE4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2TUCEZ2B5EE4NTPO","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2TUCEZ2B","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2TUCEZ2B5EE4NTPOY27YK3INL2","target":"record","payload":{"canonical_record":{"source":{"id":"1006.3928","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-20T11:29:15Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"b5a9018a2992f23024274837f664b1ca5807866fbf9d6fd660fb04c3580f129f","abstract_canon_sha256":"798ef8f149df09de92c89b9aee884f5e0b196e84d918931780eb46b5610b3af7"},"schema_version":"1.0"},"canonical_sha256":"d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.206468Z","signature_b64":"bS9kO8DAeUQPLhH2faj+9fbjW1XWERzU5mthEd+mwj5jNT+g/NPscgMbsFXpImwFGOTOgUHZ+kq88HrYi8H9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d","last_reissued_at":"2026-05-18T04:36:51.205898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.205898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.3928","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i4K5+dKMz4/Z5U5uqiVNFkQrTZTj9QDpdIF4bonF3ins52egYkY2Xvgepkdxgcc06YLjj5aFL/PyiDZKTraBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:49:58.178109Z"},"content_sha256":"e763b01a0cbd3374c29fa78239890d391ac4797598c7df51434c8f3f3e6c6403","schema_version":"1.0","event_id":"sha256:e763b01a0cbd3374c29fa78239890d391ac4797598c7df51434c8f3f3e6c6403"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2TUCEZ2B5EE4NTPOY27YK3INL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The multiplication theorem and bases in finite and affine quantum cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Fan Xu, Ming Ding","submitted_at":"2010-06-20T11:29:15Z","abstract_excerpt":"We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \\cite{fanqin}. We apply the formula to construct some $\\mathbb{ZP}$-bases in quantum cluster algebras of finite and affine types. Under the specialization $q$ and coefficients to $1$, these bases are the integral bases of cluster algebra of finite and affine types (see \\cite{CK1} and \\cite{DXX})."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3928","kind":"arxiv","version":4},"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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5fFw/z9tRN6kIXLq60l83MGioRtgDzH1mPreOLH3ogcFXfAs5iWYSTKUjSbYYcLAdGjt1VpYsieoEtPTviaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:49:58.178517Z"},"content_sha256":"0ba875c18b55a9d65377dd42742d63c332ca559961fe5c7e2a103c2b41f1aa7e","schema_version":"1.0","event_id":"sha256:0ba875c18b55a9d65377dd42742d63c332ca559961fe5c7e2a103c2b41f1aa7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TUCEZ2B5EE4NTPOY27YK3INL2/bundle.json","state_url":"https://pith.science/pith/2TUCEZ2B5EE4NTPOY27YK3INL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TUCEZ2B5EE4NTPOY27YK3INL2/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":"2026-05-26T11:49:58Z","links":{"resolver":"https://pith.science/pith/2TUCEZ2B5EE4NTPOY27YK3INL2","bundle":"https://pith.science/pith/2TUCEZ2B5EE4NTPOY27YK3INL2/bundle.json","state":"https://pith.science/pith/2TUCEZ2B5EE4NTPOY27YK3INL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TUCEZ2B5EE4NTPOY27YK3INL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2TUCEZ2B5EE4NTPOY27YK3INL2","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":"798ef8f149df09de92c89b9aee884f5e0b196e84d918931780eb46b5610b3af7","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-20T11:29:15Z","title_canon_sha256":"b5a9018a2992f23024274837f664b1ca5807866fbf9d6fd660fb04c3580f129f"},"schema_version":"1.0","source":{"id":"1006.3928","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3928","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3928v4","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3928","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"2TUCEZ2B5EE4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2TUCEZ2B5EE4NTPO","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2TUCEZ2B","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:0ba875c18b55a9d65377dd42742d63c332ca559961fe5c7e2a103c2b41f1aa7e","target":"graph","created_at":"2026-05-18T04:36:51Z","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":"We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \\cite{fanqin}. We apply the formula to construct some $\\mathbb{ZP}$-bases in quantum cluster algebras of finite and affine types. Under the specialization $q$ and coefficients to $1$, these bases are the integral bases of cluster algebra of finite and affine types (see \\cite{CK1} and \\cite{DXX}).","authors_text":"Fan Xu, Ming Ding","cross_cats":["math.QA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-20T11:29:15Z","title":"The multiplication theorem and bases in finite and affine quantum cluster algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3928","kind":"arxiv","version":4},"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:e763b01a0cbd3374c29fa78239890d391ac4797598c7df51434c8f3f3e6c6403","target":"record","created_at":"2026-05-18T04:36:51Z","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":"798ef8f149df09de92c89b9aee884f5e0b196e84d918931780eb46b5610b3af7","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-20T11:29:15Z","title_canon_sha256":"b5a9018a2992f23024274837f664b1ca5807866fbf9d6fd660fb04c3580f129f"},"schema_version":"1.0","source":{"id":"1006.3928","kind":"arxiv","version":4}},"canonical_sha256":"d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d","first_computed_at":"2026-05-18T04:36:51.205898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:51.205898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bS9kO8DAeUQPLhH2faj+9fbjW1XWERzU5mthEd+mwj5jNT+g/NPscgMbsFXpImwFGOTOgUHZ+kq88HrYi8H9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:51.206468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3928","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e763b01a0cbd3374c29fa78239890d391ac4797598c7df51434c8f3f3e6c6403","sha256:0ba875c18b55a9d65377dd42742d63c332ca559961fe5c7e2a103c2b41f1aa7e"],"state_sha256":"e75842c19b9daef6da49225aa4739cae21a469578b06db08291a831fa8a0f26d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Si2G0ObSWDx8yPbXofWkO+SWZZY/a8ecIInhIvFcVqPk+MkMhWFm5Rari4pHSvefafuIe2Q13qbQUQ+ulo4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:49:58.181266Z","bundle_sha256":"9e3ec06efe2818c2e734a16fd9f085ce00ddacb3fee41558fd43d4c08c243d14"}}