{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BLAVYH7HDPBF7ENR5PSKNBIA5B","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":"66e6383ed6ce6367e228d1611c29f7f15dcbcde4ca2f6da78af10b9332e20864","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-01-28T11:19:32Z","title_canon_sha256":"fddf461f3ff379a3aff1dbc0b06c852e64c94996afffd722b34e52aa9e3e4aa3"},"schema_version":"1.0","source":{"id":"2501.16859","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16859","created_at":"2026-07-05T10:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16859v2","created_at":"2026-07-05T10:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16859","created_at":"2026-07-05T10:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"BLAVYH7HDPBF","created_at":"2026-07-05T10:06:48Z"},{"alias_kind":"pith_short_16","alias_value":"BLAVYH7HDPBF7ENR","created_at":"2026-07-05T10:06:48Z"},{"alias_kind":"pith_short_8","alias_value":"BLAVYH7H","created_at":"2026-07-05T10:06:48Z"}],"graph_snapshots":[{"event_id":"sha256:38fca59049c817e461e3b9dfa54f35485db52730a63a63ddd627735e3cfb2584","target":"graph","created_at":"2026-07-05T10:06:48Z","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/2501.16859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that finite length representations of shifted quantum affine algebras in category $\\mathcal{O}^{\\mathrm{sh}}$ are stable by fusion product. This implies that in the topological Grothendieck ring $K_0(\\mathcal{O}^{\\mathrm{sh}})$ the Grothendieck group of finite length representations forms a non-topological subring. We also conjecture this subring is isomorphic to the cluster algebra discovered in arXiv:2401.04616. In the course of our proofs, we establish that any simple representation in category $\\mathcal{O}^{\\mathrm{sh}}$ descends to a truncation, for certain truncation parameters ","authors_text":"David Hernandez, Huafeng Zhang","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-01-28T11:19:32Z","title":"Jordan-H\\\"older property for shifted quantum affine algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16859","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:a64a6dbf8beb71fa5c670b7626854388bac0de17be1b65c543c837e455abbbf0","target":"record","created_at":"2026-07-05T10:06:48Z","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":"66e6383ed6ce6367e228d1611c29f7f15dcbcde4ca2f6da78af10b9332e20864","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-01-28T11:19:32Z","title_canon_sha256":"fddf461f3ff379a3aff1dbc0b06c852e64c94996afffd722b34e52aa9e3e4aa3"},"schema_version":"1.0","source":{"id":"2501.16859","kind":"arxiv","version":2}},"canonical_sha256":"0ac15c1fe71bc25f91b1ebe4a68500e876b0171c05eb2bebc5b08d3ad7fa7a57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac15c1fe71bc25f91b1ebe4a68500e876b0171c05eb2bebc5b08d3ad7fa7a57","first_computed_at":"2026-07-05T10:06:48.128393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:48.128393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61adRz9MiStwYmNBDBFqPEbcKl9Ybiz9aOKSQgqfY6Gw68IEF/5dXgc1iLbQguqjlW3DLYZ6wjf/ZStu3CVwAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:48.128854Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.16859","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a64a6dbf8beb71fa5c670b7626854388bac0de17be1b65c543c837e455abbbf0","sha256:38fca59049c817e461e3b9dfa54f35485db52730a63a63ddd627735e3cfb2584"],"state_sha256":"ac98d45b40eabadcdf4bde6648305d9b51d75409bbf23ee046761ba2bb4539b6"}