{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5DCL2WEMX4UNCE6OJGSDIJR3JT","short_pith_number":"pith:5DCL2WEM","canonical_record":{"source":{"id":"2408.09855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T09:57:51Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1fa1974cbfd2f94a74cdac2bd6b223fc87d9aaa1b5f3798d582ab68057f01efa","abstract_canon_sha256":"ff5a606503d6c861bbe73716832b34c94132e7c51f36b75b0cbeeeb364645b72"},"schema_version":"1.0"},"canonical_sha256":"e8c4bd588cbf28d113ce49a434263b4cf2cd6d56883a995b0703ee481aa890fb","source":{"kind":"arxiv","id":"2408.09855","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09855","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09855v2","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09855","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"5DCL2WEMX4UN","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"pith_short_16","alias_value":"5DCL2WEMX4UNCE6O","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"pith_short_8","alias_value":"5DCL2WEM","created_at":"2026-07-05T10:44:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5DCL2WEMX4UNCE6OJGSDIJR3JT","target":"record","payload":{"canonical_record":{"source":{"id":"2408.09855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T09:57:51Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1fa1974cbfd2f94a74cdac2bd6b223fc87d9aaa1b5f3798d582ab68057f01efa","abstract_canon_sha256":"ff5a606503d6c861bbe73716832b34c94132e7c51f36b75b0cbeeeb364645b72"},"schema_version":"1.0"},"canonical_sha256":"e8c4bd588cbf28d113ce49a434263b4cf2cd6d56883a995b0703ee481aa890fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:44:38.337611Z","signature_b64":"vUhNoVWgL/Y3T4icnCCKGV6fJx/95qspdokQvS0KiXKOuLitbhKaDxJW8lkCz7L8nZQZeCaa0qeVyh842RnsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c4bd588cbf28d113ce49a434263b4cf2cd6d56883a995b0703ee481aa890fb","last_reissued_at":"2026-07-05T10:44:38.337087Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:44:38.337087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.09855","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":"2026-07-05T10:44:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyiQPdprS/rYfJLm7K89J1nt8FVTPutsJ1kRrlSF7m6x+dmeGSehwuIoFpYjnlJ9SuTseOj5aK56omUfxgbiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:01:22.019606Z"},"content_sha256":"841eb1382d588961927633c2e04755c45ab9f78b0fe746a94713d0fff9927f30","schema_version":"1.0","event_id":"sha256:841eb1382d588961927633c2e04755c45ab9f78b0fe746a94713d0fff9927f30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5DCL2WEMX4UNCE6OJGSDIJR3JT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $q$-immanants and higher quantum Capelli identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Alexander Molev, Ming Liu, Naihuan Jing","submitted_at":"2024-08-19T09:57:51Z","abstract_excerpt":"We construct polynomials ${\\mathbb{S}}_{\\mu}(z)$ parameterized by Young diagrams $\\mu$, whose coefficients are central elements of the quantized enveloping algebra ${\\rm U}_q({\\mathfrak{gl}}_n)$. Their constant terms coincide with the central elements provided by the general construction of Drinfeld and Reshetikhin. For another special value of $z$, we get $q$-analogues of Okounkov's quantum immanants for ${\\mathfrak{gl}}_n$. We show that the Harish-Chandra image of ${\\mathbb{S}}_{\\mu}(z)$ is a factorial Schur polynomial. We also prove quantum analogues of the higher Capelli identities and der"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09855","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.09855/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":"2026-07-05T10:44:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MS/BexL8gTSjTtWEtN40pkawHmkp/Ki4L2iDRLbX3XSsEALwJ2XBAkq8UmTcHV9slWg+J2+uGifv4aPcntj2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:01:22.020163Z"},"content_sha256":"551c4aac01c2edda8459fca58ec2bad40da84f1a9088bdb7cde4217ab3381e92","schema_version":"1.0","event_id":"sha256:551c4aac01c2edda8459fca58ec2bad40da84f1a9088bdb7cde4217ab3381e92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT/bundle.json","state_url":"https://pith.science/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT/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":"2026-08-14T08:01:22Z","links":{"resolver":"https://pith.science/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT","bundle":"https://pith.science/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT/bundle.json","state":"https://pith.science/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DCL2WEMX4UNCE6OJGSDIJR3JT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5DCL2WEMX4UNCE6OJGSDIJR3JT","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":"ff5a606503d6c861bbe73716832b34c94132e7c51f36b75b0cbeeeb364645b72","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T09:57:51Z","title_canon_sha256":"1fa1974cbfd2f94a74cdac2bd6b223fc87d9aaa1b5f3798d582ab68057f01efa"},"schema_version":"1.0","source":{"id":"2408.09855","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09855","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09855v2","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09855","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"5DCL2WEMX4UN","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"pith_short_16","alias_value":"5DCL2WEMX4UNCE6O","created_at":"2026-07-05T10:44:38Z"},{"alias_kind":"pith_short_8","alias_value":"5DCL2WEM","created_at":"2026-07-05T10:44:38Z"}],"graph_snapshots":[{"event_id":"sha256:551c4aac01c2edda8459fca58ec2bad40da84f1a9088bdb7cde4217ab3381e92","target":"graph","created_at":"2026-07-05T10:44:38Z","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/2408.09855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct polynomials ${\\mathbb{S}}_{\\mu}(z)$ parameterized by Young diagrams $\\mu$, whose coefficients are central elements of the quantized enveloping algebra ${\\rm U}_q({\\mathfrak{gl}}_n)$. Their constant terms coincide with the central elements provided by the general construction of Drinfeld and Reshetikhin. For another special value of $z$, we get $q$-analogues of Okounkov's quantum immanants for ${\\mathfrak{gl}}_n$. We show that the Harish-Chandra image of ${\\mathbb{S}}_{\\mu}(z)$ is a factorial Schur polynomial. We also prove quantum analogues of the higher Capelli identities and der","authors_text":"Alexander Molev, Ming Liu, Naihuan Jing","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T09:57:51Z","title":"The $q$-immanants and higher quantum Capelli identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09855","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":"sha256:841eb1382d588961927633c2e04755c45ab9f78b0fe746a94713d0fff9927f30","target":"record","created_at":"2026-07-05T10:44:38Z","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":"ff5a606503d6c861bbe73716832b34c94132e7c51f36b75b0cbeeeb364645b72","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T09:57:51Z","title_canon_sha256":"1fa1974cbfd2f94a74cdac2bd6b223fc87d9aaa1b5f3798d582ab68057f01efa"},"schema_version":"1.0","source":{"id":"2408.09855","kind":"arxiv","version":2}},"canonical_sha256":"e8c4bd588cbf28d113ce49a434263b4cf2cd6d56883a995b0703ee481aa890fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c4bd588cbf28d113ce49a434263b4cf2cd6d56883a995b0703ee481aa890fb","first_computed_at":"2026-07-05T10:44:38.337087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:44:38.337087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vUhNoVWgL/Y3T4icnCCKGV6fJx/95qspdokQvS0KiXKOuLitbhKaDxJW8lkCz7L8nZQZeCaa0qeVyh842RnsDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:44:38.337611Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.09855","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:841eb1382d588961927633c2e04755c45ab9f78b0fe746a94713d0fff9927f30","sha256:551c4aac01c2edda8459fca58ec2bad40da84f1a9088bdb7cde4217ab3381e92"],"state_sha256":"5e654dbb14297fca9cf3e84a64666bef9ce26c3c023017621cbcfa14d453d1c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7S+nuaLVGpaI61yEz3Duuk2faWWk9yeLMbk1lZv1rg2BUwJo02UouiX6LLPmE/jV/+PHaCkwslchhsGnfj8KDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:01:22.025763Z","bundle_sha256":"036de69ea24ac717853fabee0133d6391665e1dabfe16184a694dc4620b9b4ed"}}