{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:DT43LXZ4EPOR5TCIT5MBYGPXD7","short_pith_number":"pith:DT43LXZ4","schema_version":"1.0","canonical_sha256":"1cf9b5df3c23dd1ecc489f581c19f71fd140ade8079de190a228c932ef7a9c2b","source":{"kind":"arxiv","id":"2105.12369","version":1},"attestation_state":"computed","paper":{"title":"Harmonic Analysis on GL(n) over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Roger Howe, Shamgar Gurevich","submitted_at":"2021-05-26T07:23:18Z","abstract_excerpt":"There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio\n  trace(\\pi(g)) / dim(\\pi),\nfor an irreducible representation \\pi of G and an element g of G. It turns out [Gurevich-Howe15, Gurevich-Howe17] that for classical groups G over finite fields there are several (compatible) invariants of representations that provide strong information on the character ratios. We call these invariants collectively rank. Rank suggests a new way to organ"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2105.12369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-05-26T07:23:18Z","cross_cats_sorted":[],"title_canon_sha256":"02232d2f1dea082cefbf4721a3edc9dc0335bab723ef2da0e8c291b689cf9870","abstract_canon_sha256":"136470ea75c16cbd4b5f3c53376e0bfc5b32709456a83b50b2c5372fd66a79f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:43:38.092764Z","signature_b64":"R2RJTbLdVYYBeNQCR3LKEt6XLJxDa2TM/npaA0E+Y/4kF1nDYoPoAjnxuWOKY4vYpE0e3WWnNjoMj2TMb0DbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cf9b5df3c23dd1ecc489f581c19f71fd140ade8079de190a228c932ef7a9c2b","last_reissued_at":"2026-07-05T02:43:38.092327Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:43:38.092327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic Analysis on GL(n) over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Roger Howe, Shamgar Gurevich","submitted_at":"2021-05-26T07:23:18Z","abstract_excerpt":"There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio\n  trace(\\pi(g)) / dim(\\pi),\nfor an irreducible representation \\pi of G and an element g of G. It turns out [Gurevich-Howe15, Gurevich-Howe17] that for classical groups G over finite fields there are several (compatible) invariants of representations that provide strong information on the character ratios. We call these invariants collectively rank. Rank suggests a new way to organ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.12369","kind":"arxiv","version":1},"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/2105.12369/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2105.12369","created_at":"2026-07-05T02:43:38.092391+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.12369v1","created_at":"2026-07-05T02:43:38.092391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.12369","created_at":"2026-07-05T02:43:38.092391+00:00"},{"alias_kind":"pith_short_12","alias_value":"DT43LXZ4EPOR","created_at":"2026-07-05T02:43:38.092391+00:00"},{"alias_kind":"pith_short_16","alias_value":"DT43LXZ4EPOR5TCI","created_at":"2026-07-05T02:43:38.092391+00:00"},{"alias_kind":"pith_short_8","alias_value":"DT43LXZ4","created_at":"2026-07-05T02:43:38.092391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.12216","citing_title":"Classical interpolation categories","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7","json":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7.json","graph_json":"https://pith.science/api/pith-number/DT43LXZ4EPOR5TCIT5MBYGPXD7/graph.json","events_json":"https://pith.science/api/pith-number/DT43LXZ4EPOR5TCIT5MBYGPXD7/events.json","paper":"https://pith.science/paper/DT43LXZ4"},"agent_actions":{"view_html":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7","download_json":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7.json","view_paper":"https://pith.science/paper/DT43LXZ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.12369&json=true","fetch_graph":"https://pith.science/api/pith-number/DT43LXZ4EPOR5TCIT5MBYGPXD7/graph.json","fetch_events":"https://pith.science/api/pith-number/DT43LXZ4EPOR5TCIT5MBYGPXD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7/action/storage_attestation","attest_author":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7/action/author_attestation","sign_citation":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7/action/citation_signature","submit_replication":"https://pith.science/pith/DT43LXZ4EPOR5TCIT5MBYGPXD7/action/replication_record"}},"created_at":"2026-07-05T02:43:38.092391+00:00","updated_at":"2026-07-05T02:43:38.092391+00:00"}