{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:H65AOLVINXJI34PF4H27JOJWTO","short_pith_number":"pith:H65AOLVI","canonical_record":{"source":{"id":"1107.2760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-14T09:11:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a179b7085bd3b0e56796be58a3a74ec922fa44931578ca6d20d3321ed084933","abstract_canon_sha256":"bc31377a6132ddccf9a3931f7b58e93363906a7116b27ad069ba6fe53f42e6a1"},"schema_version":"1.0"},"canonical_sha256":"3fba072ea86dd28df1e5e1f5f4b9369baf35a0891008bafc5bcd4e23af0a4bfb","source":{"kind":"arxiv","id":"1107.2760","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2760","created_at":"2026-05-18T03:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2760v2","created_at":"2026-05-18T03:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2760","created_at":"2026-05-18T03:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"H65AOLVINXJI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H65AOLVINXJI34PF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H65AOLVI","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:H65AOLVINXJI34PF4H27JOJWTO","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-14T09:11:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a179b7085bd3b0e56796be58a3a74ec922fa44931578ca6d20d3321ed084933","abstract_canon_sha256":"bc31377a6132ddccf9a3931f7b58e93363906a7116b27ad069ba6fe53f42e6a1"},"schema_version":"1.0"},"canonical_sha256":"3fba072ea86dd28df1e5e1f5f4b9369baf35a0891008bafc5bcd4e23af0a4bfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:56.582026Z","signature_b64":"tTJnvtYrbToaUPVmDnm338ve+q3PPf/UzCO21D7qTr0WpUkaYDyKuv2YYk4lW1aWnSejVDHeebYXax0rjyRSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fba072ea86dd28df1e5e1f5f4b9369baf35a0891008bafc5bcd4e23af0a4bfb","last_reissued_at":"2026-05-18T03:41:56.581243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:56.581243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2760","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":"2026-05-18T03:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehwjXh5D7bSjTSqAz/9rsj2azT/l1QecXephSMPPNBf3HsseO0dn3Wr/Nk/nhXUNNCf+YO5wV2KVlU4SDE9WBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T11:44:39.899796Z"},"content_sha256":"0694073b393e3d61457246cc0abe3a52cbfdbf1e159d4f0fd61fae57cd3a8fcc","schema_version":"1.0","event_id":"sha256:0694073b393e3d61457246cc0abe3a52cbfdbf1e159d4f0fd61fae57cd3a8fcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:H65AOLVINXJI34PF4H27JOJWTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Sebastian Zwicknagl","submitted_at":"2011-07-14T09:11:30Z","abstract_excerpt":"We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster algebra. As an application, we describe the topology on the spectra of quantized coordinate rings such as quantum matrices and the quantized function algebra of the general linear group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2760","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":"2026-05-18T03:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzIfC8BRWfBNsxh/R+0sS5TYq2AFVhFO87F2zmwE9VM2uOP8CO2WncStkHa9ccjX3nAJlHcGoG0xV6TaNuNaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T11:44:39.900149Z"},"content_sha256":"059030f0e077f4f14e6b55d66c0d34706a393dc1c57aead67c4eea106c5865b4","schema_version":"1.0","event_id":"sha256:059030f0e077f4f14e6b55d66c0d34706a393dc1c57aead67c4eea106c5865b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H65AOLVINXJI34PF4H27JOJWTO/bundle.json","state_url":"https://pith.science/pith/H65AOLVINXJI34PF4H27JOJWTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H65AOLVINXJI34PF4H27JOJWTO/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":"2026-07-06T11:44:39Z","links":{"resolver":"https://pith.science/pith/H65AOLVINXJI34PF4H27JOJWTO","bundle":"https://pith.science/pith/H65AOLVINXJI34PF4H27JOJWTO/bundle.json","state":"https://pith.science/pith/H65AOLVINXJI34PF4H27JOJWTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H65AOLVINXJI34PF4H27JOJWTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:H65AOLVINXJI34PF4H27JOJWTO","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":"bc31377a6132ddccf9a3931f7b58e93363906a7116b27ad069ba6fe53f42e6a1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-14T09:11:30Z","title_canon_sha256":"2a179b7085bd3b0e56796be58a3a74ec922fa44931578ca6d20d3321ed084933"},"schema_version":"1.0","source":{"id":"1107.2760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2760","created_at":"2026-05-18T03:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2760v2","created_at":"2026-05-18T03:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2760","created_at":"2026-05-18T03:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"H65AOLVINXJI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H65AOLVINXJI34PF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H65AOLVI","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:059030f0e077f4f14e6b55d66c0d34706a393dc1c57aead67c4eea106c5865b4","target":"graph","created_at":"2026-05-18T03:41:56Z","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 describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster algebra. As an application, we describe the topology on the spectra of quantized coordinate rings such as quantum matrices and the quantized function algebra of the general linear group.","authors_text":"Sebastian Zwicknagl","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-14T09:11:30Z","title":"Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2760","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":"sha256:0694073b393e3d61457246cc0abe3a52cbfdbf1e159d4f0fd61fae57cd3a8fcc","target":"record","created_at":"2026-05-18T03:41:56Z","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":"bc31377a6132ddccf9a3931f7b58e93363906a7116b27ad069ba6fe53f42e6a1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-07-14T09:11:30Z","title_canon_sha256":"2a179b7085bd3b0e56796be58a3a74ec922fa44931578ca6d20d3321ed084933"},"schema_version":"1.0","source":{"id":"1107.2760","kind":"arxiv","version":2}},"canonical_sha256":"3fba072ea86dd28df1e5e1f5f4b9369baf35a0891008bafc5bcd4e23af0a4bfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fba072ea86dd28df1e5e1f5f4b9369baf35a0891008bafc5bcd4e23af0a4bfb","first_computed_at":"2026-05-18T03:41:56.581243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:56.581243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tTJnvtYrbToaUPVmDnm338ve+q3PPf/UzCO21D7qTr0WpUkaYDyKuv2YYk4lW1aWnSejVDHeebYXax0rjyRSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:56.582026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0694073b393e3d61457246cc0abe3a52cbfdbf1e159d4f0fd61fae57cd3a8fcc","sha256:059030f0e077f4f14e6b55d66c0d34706a393dc1c57aead67c4eea106c5865b4"],"state_sha256":"020bb3e33b1796e3f7f70ed1ac93b33af1c4869168bb4cd47757d05cdda3e06f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4NPnMlfHMn1ifrCEbxe+pfb66BqBVDSVi56XyNlLNhvOgMVu0bpCCmr5Yk1LVcaWHbBRDmn7Km0AEHzDqXTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T11:44:39.902194Z","bundle_sha256":"0278d710fdd4010e64952f99b32e48f3e7662201a33b185ce20dc953d70f2482"}}