{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:3M7L63U5TYBHZ5TQJMSM57C2NI","short_pith_number":"pith:3M7L63U5","canonical_record":{"source":{"id":"2401.04616","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-01-09T15:38:34Z","cross_cats_sorted":["hep-th","math.RA","math.RT"],"title_canon_sha256":"2aa5d824ebab98f7f51fc59df705062d2297afe3eb0cdc01b2bc6a102b34ed37","abstract_canon_sha256":"afbf1f96ae88663542910af56650e7e0f342f3bc07d2984f2ce25acb2073bd1d"},"schema_version":"1.0"},"canonical_sha256":"db3ebf6e9d9e027cf6704b24cefc5a6a03c9963456653fc691a3d9b3fa8f420e","source":{"kind":"arxiv","id":"2401.04616","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.04616","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"2401.04616v3","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04616","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"3M7L63U5TYBH","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"3M7L63U5TYBHZ5TQ","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"3M7L63U5","created_at":"2026-07-05T09:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:3M7L63U5TYBHZ5TQJMSM57C2NI","target":"record","payload":{"canonical_record":{"source":{"id":"2401.04616","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-01-09T15:38:34Z","cross_cats_sorted":["hep-th","math.RA","math.RT"],"title_canon_sha256":"2aa5d824ebab98f7f51fc59df705062d2297afe3eb0cdc01b2bc6a102b34ed37","abstract_canon_sha256":"afbf1f96ae88663542910af56650e7e0f342f3bc07d2984f2ce25acb2073bd1d"},"schema_version":"1.0"},"canonical_sha256":"db3ebf6e9d9e027cf6704b24cefc5a6a03c9963456653fc691a3d9b3fa8f420e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:27:52.232796Z","signature_b64":"V3bSqTdogRRp+Enz6oZbkB+tLrWte3iNEQi30hBhyGAeTQSC0oU2zMSPm6rPaZtLFL8P+c+dfWqkZY/94UP9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db3ebf6e9d9e027cf6704b24cefc5a6a03c9963456653fc691a3d9b3fa8f420e","last_reissued_at":"2026-07-05T09:27:52.232312Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:27:52.232312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.04616","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6R720LKl8412g+Nk+ZZzUpdrb3ItTUpNx7GIFNRYSTXXA+dt24bFlfGt5NAtEarKB16anwhIbzQ2EQEoNxrFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T10:41:25.901912Z"},"content_sha256":"a2087f9f024f4e3a0f9457775079df6d05e5e521a7c4c129aeb974921785b4da","schema_version":"1.0","event_id":"sha256:a2087f9f024f4e3a0f9457775079df6d05e5e521a7c4c129aeb974921785b4da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:3M7L63U5TYBHZ5TQJMSM57C2NI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations of shifted quantum affine algebras and cluster algebras I. The simply-laced case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Bernard Leclerc, Christof Geiss, David Hernandez","submitted_at":"2024-01-09T15:38:34Z","abstract_excerpt":"We introduce a family of cluster algebras of infinite rank associated with root systems of type $A$, $D$, $E$. We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categories $\\mathcal{O}_\\mathbb{Z}$ of the corresponding shifted quantum affine algebras. The cluster variables of a class of distinguished initial seeds are certain formal power series defined by E. Frenkel and the second author, which satisfy a system of functional relations called $QQ$-system. We conjecture that all cluster monomials are classes of simple objects of $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04616","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.04616/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+/4YlZpNkMtfReQzy0YgMv8jDoY4VlXoLyA3O0JEbPo8Y6l706YldaTjCwX/mwBLreREaqrQH5+dtS8YY/XCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T10:41:25.902835Z"},"content_sha256":"406537014332e92f6d86e981dcf39d8add5d25884c945fef298dc9eaa932b36a","schema_version":"1.0","event_id":"sha256:406537014332e92f6d86e981dcf39d8add5d25884c945fef298dc9eaa932b36a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3M7L63U5TYBHZ5TQJMSM57C2NI/bundle.json","state_url":"https://pith.science/pith/3M7L63U5TYBHZ5TQJMSM57C2NI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3M7L63U5TYBHZ5TQJMSM57C2NI/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":"2026-08-10T10:41:25Z","links":{"resolver":"https://pith.science/pith/3M7L63U5TYBHZ5TQJMSM57C2NI","bundle":"https://pith.science/pith/3M7L63U5TYBHZ5TQJMSM57C2NI/bundle.json","state":"https://pith.science/pith/3M7L63U5TYBHZ5TQJMSM57C2NI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3M7L63U5TYBHZ5TQJMSM57C2NI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3M7L63U5TYBHZ5TQJMSM57C2NI","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":"afbf1f96ae88663542910af56650e7e0f342f3bc07d2984f2ce25acb2073bd1d","cross_cats_sorted":["hep-th","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-01-09T15:38:34Z","title_canon_sha256":"2aa5d824ebab98f7f51fc59df705062d2297afe3eb0cdc01b2bc6a102b34ed37"},"schema_version":"1.0","source":{"id":"2401.04616","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.04616","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"2401.04616v3","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04616","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"3M7L63U5TYBH","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"3M7L63U5TYBHZ5TQ","created_at":"2026-07-05T09:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"3M7L63U5","created_at":"2026-07-05T09:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:406537014332e92f6d86e981dcf39d8add5d25884c945fef298dc9eaa932b36a","target":"graph","created_at":"2026-07-05T09:27:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.04616/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a family of cluster algebras of infinite rank associated with root systems of type $A$, $D$, $E$. We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categories $\\mathcal{O}_\\mathbb{Z}$ of the corresponding shifted quantum affine algebras. The cluster variables of a class of distinguished initial seeds are certain formal power series defined by E. Frenkel and the second author, which satisfy a system of functional relations called $QQ$-system. We conjecture that all cluster monomials are classes of simple objects of $\\mathcal","authors_text":"Bernard Leclerc, Christof Geiss, David Hernandez","cross_cats":["hep-th","math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-01-09T15:38:34Z","title":"Representations of shifted quantum affine algebras and cluster algebras I. The simply-laced case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04616","kind":"arxiv","version":3},"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:a2087f9f024f4e3a0f9457775079df6d05e5e521a7c4c129aeb974921785b4da","target":"record","created_at":"2026-07-05T09:27:52Z","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":"afbf1f96ae88663542910af56650e7e0f342f3bc07d2984f2ce25acb2073bd1d","cross_cats_sorted":["hep-th","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-01-09T15:38:34Z","title_canon_sha256":"2aa5d824ebab98f7f51fc59df705062d2297afe3eb0cdc01b2bc6a102b34ed37"},"schema_version":"1.0","source":{"id":"2401.04616","kind":"arxiv","version":3}},"canonical_sha256":"db3ebf6e9d9e027cf6704b24cefc5a6a03c9963456653fc691a3d9b3fa8f420e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db3ebf6e9d9e027cf6704b24cefc5a6a03c9963456653fc691a3d9b3fa8f420e","first_computed_at":"2026-07-05T09:27:52.232312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:27:52.232312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V3bSqTdogRRp+Enz6oZbkB+tLrWte3iNEQi30hBhyGAeTQSC0oU2zMSPm6rPaZtLFL8P+c+dfWqkZY/94UP9Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:27:52.232796Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.04616","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2087f9f024f4e3a0f9457775079df6d05e5e521a7c4c129aeb974921785b4da","sha256:406537014332e92f6d86e981dcf39d8add5d25884c945fef298dc9eaa932b36a"],"state_sha256":"32c33bc8b7f39c2340dd7a76809c250ac91131af915fc6ffb07594380f2679d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3rolRwX+Clr3fX4ZonNIFVEhk8pudV6CqY2FQVvksZoYNkGnZmM9sjh7XuYzLqR9Zc9MtGHKPbXKBJCDj+6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T10:41:25.909696Z","bundle_sha256":"0c470f1d86b267624e8fd84215986375d965edb45ceb067878f0e58bb2f49069"}}