{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MIPMBLFCHPALKIVEGYP3YJTICN","short_pith_number":"pith:MIPMBLFC","canonical_record":{"source":{"id":"2109.11310","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-23T11:50:29Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"02794ee7723bde8d4fc00bdf105b3bddac07554832bbc36c71f3b2a9bef313b9","abstract_canon_sha256":"ebd5477a67d106c2d955e09fadd0f88842d9abd36143ce77591e8f65db31a5c5"},"schema_version":"1.0"},"canonical_sha256":"621ec0aca23bc0b522a4361fbc266813749dd9526ac0464a5a1ac643536c5650","source":{"kind":"arxiv","id":"2109.11310","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11310","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11310v3","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11310","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"MIPMBLFCHPAL","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"pith_short_16","alias_value":"MIPMBLFCHPALKIVE","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"pith_short_8","alias_value":"MIPMBLFC","created_at":"2026-07-05T04:44:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MIPMBLFCHPALKIVEGYP3YJTICN","target":"record","payload":{"canonical_record":{"source":{"id":"2109.11310","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-23T11:50:29Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"02794ee7723bde8d4fc00bdf105b3bddac07554832bbc36c71f3b2a9bef313b9","abstract_canon_sha256":"ebd5477a67d106c2d955e09fadd0f88842d9abd36143ce77591e8f65db31a5c5"},"schema_version":"1.0"},"canonical_sha256":"621ec0aca23bc0b522a4361fbc266813749dd9526ac0464a5a1ac643536c5650","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:28.409794Z","signature_b64":"BbDQZ92KkKWVVYNwcxhoNIEM1xJH0PnMVjRBCsgPLoPCnjcO84fXsEbe2qOq+jEvBRL8NrEtfVbmt2Qff7MRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621ec0aca23bc0b522a4361fbc266813749dd9526ac0464a5a1ac643536c5650","last_reissued_at":"2026-07-05T04:44:28.409418Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:28.409418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.11310","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":"2026-07-05T04:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvK1sMZZCctqLB45NmgLE1iyc8FpLuomP46daSRBZTyy/dQxor1YRMxN2V+cRxcXBTilrnrocAtyOqLCorw+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:49:07.318104Z"},"content_sha256":"a52d0f64748eb36d6354a4b47bcddc7af1f7ab3ca3624321b67c376d3da86e88","schema_version":"1.0","event_id":"sha256:a52d0f64748eb36d6354a4b47bcddc7af1f7ab3ca3624321b67c376d3da86e88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MIPMBLFCHPALKIVEGYP3YJTICN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factorization of classical characters twisted by roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Arvind Ayyer, Nishu Kumari","submitted_at":"2021-09-23T11:50:29Z","abstract_excerpt":"For a fixed integer $t \\geq 2$, we consider the irreducible characters of representations of the classical groups of types A, B, C and D, namely $\\text{GL}_{tn}, \\text{SO}_{2tn+1}, \\text{Sp}_{2tn}$ and $\\text{O}_{2tn}$, evaluated at elements $\\omega^k x_i$ for $0 \\leq k \\leq t-1$ and $1 \\leq i \\leq n$, where $\\omega$ is a primitive $t$'th root of unity. The case of $\\text{GL}_{tn}$ was considered by D. J. Littlewood (AMS press, 1950) and independently by D. Prasad (Israel J. Math., 2016). In this article, we give a uniform approach for all cases. In this article, we give a uniform approach for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11310","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/2109.11310/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":"2026-07-05T04:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XosQfHyI7hxHIMLdZ3cYTOFTkzLFExJ1iGY6X8v8R/3juk63K5NKKer0RcFa7dGS7ktwmKHyR7pGtHnhfp8sDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:49:07.318850Z"},"content_sha256":"617392646d66d4146d410bfad49b29fb6f779f6b1605c581184cb6715c17f9cb","schema_version":"1.0","event_id":"sha256:617392646d66d4146d410bfad49b29fb6f779f6b1605c581184cb6715c17f9cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIPMBLFCHPALKIVEGYP3YJTICN/bundle.json","state_url":"https://pith.science/pith/MIPMBLFCHPALKIVEGYP3YJTICN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIPMBLFCHPALKIVEGYP3YJTICN/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":"2026-08-16T08:49:07Z","links":{"resolver":"https://pith.science/pith/MIPMBLFCHPALKIVEGYP3YJTICN","bundle":"https://pith.science/pith/MIPMBLFCHPALKIVEGYP3YJTICN/bundle.json","state":"https://pith.science/pith/MIPMBLFCHPALKIVEGYP3YJTICN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIPMBLFCHPALKIVEGYP3YJTICN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MIPMBLFCHPALKIVEGYP3YJTICN","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":"ebd5477a67d106c2d955e09fadd0f88842d9abd36143ce77591e8f65db31a5c5","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-23T11:50:29Z","title_canon_sha256":"02794ee7723bde8d4fc00bdf105b3bddac07554832bbc36c71f3b2a9bef313b9"},"schema_version":"1.0","source":{"id":"2109.11310","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11310","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11310v3","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11310","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"MIPMBLFCHPAL","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"pith_short_16","alias_value":"MIPMBLFCHPALKIVE","created_at":"2026-07-05T04:44:28Z"},{"alias_kind":"pith_short_8","alias_value":"MIPMBLFC","created_at":"2026-07-05T04:44:28Z"}],"graph_snapshots":[{"event_id":"sha256:617392646d66d4146d410bfad49b29fb6f779f6b1605c581184cb6715c17f9cb","target":"graph","created_at":"2026-07-05T04:44:28Z","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/2109.11310/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a fixed integer $t \\geq 2$, we consider the irreducible characters of representations of the classical groups of types A, B, C and D, namely $\\text{GL}_{tn}, \\text{SO}_{2tn+1}, \\text{Sp}_{2tn}$ and $\\text{O}_{2tn}$, evaluated at elements $\\omega^k x_i$ for $0 \\leq k \\leq t-1$ and $1 \\leq i \\leq n$, where $\\omega$ is a primitive $t$'th root of unity. The case of $\\text{GL}_{tn}$ was considered by D. J. Littlewood (AMS press, 1950) and independently by D. Prasad (Israel J. Math., 2016). In this article, we give a uniform approach for all cases. In this article, we give a uniform approach for","authors_text":"Arvind Ayyer, Nishu Kumari","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-23T11:50:29Z","title":"Factorization of classical characters twisted by roots of unity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11310","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:a52d0f64748eb36d6354a4b47bcddc7af1f7ab3ca3624321b67c376d3da86e88","target":"record","created_at":"2026-07-05T04:44:28Z","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":"ebd5477a67d106c2d955e09fadd0f88842d9abd36143ce77591e8f65db31a5c5","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-09-23T11:50:29Z","title_canon_sha256":"02794ee7723bde8d4fc00bdf105b3bddac07554832bbc36c71f3b2a9bef313b9"},"schema_version":"1.0","source":{"id":"2109.11310","kind":"arxiv","version":3}},"canonical_sha256":"621ec0aca23bc0b522a4361fbc266813749dd9526ac0464a5a1ac643536c5650","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"621ec0aca23bc0b522a4361fbc266813749dd9526ac0464a5a1ac643536c5650","first_computed_at":"2026-07-05T04:44:28.409418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:28.409418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbDQZ92KkKWVVYNwcxhoNIEM1xJH0PnMVjRBCsgPLoPCnjcO84fXsEbe2qOq+jEvBRL8NrEtfVbmt2Qff7MRAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:28.409794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11310","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a52d0f64748eb36d6354a4b47bcddc7af1f7ab3ca3624321b67c376d3da86e88","sha256:617392646d66d4146d410bfad49b29fb6f779f6b1605c581184cb6715c17f9cb"],"state_sha256":"b258fc9043facf82979801b32e35d5ae36938626bbfd14620a28efedc56ec6cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K6Ums9gFdcc4MoLXcYnCZpMIhiovnR7iKPF3pm2mWRzb7uskqe2ltUwgsauEtjN6ldhS2pn9osvSUGKHEC+fBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:49:07.323745Z","bundle_sha256":"cd9c77dd918ba3ba17e04af51e1b1aac0b58c98f2b000eaf4d9e9e720719ec73"}}