{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CYXK5YWE5Y3GRGLJ6IC6HIHQWD","short_pith_number":"pith:CYXK5YWE","schema_version":"1.0","canonical_sha256":"162eaee2c4ee36689969f205e3a0f0b0cbb9b7d6905a08b19bfb604a0121e3ce","source":{"kind":"arxiv","id":"1908.03392","version":1},"attestation_state":"computed","paper":{"title":"Typical representations for level zero Bernstein components of ${\\rm GL}_n(F)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Santosh Nadimpalli","submitted_at":"2019-08-09T10:05:56Z","abstract_excerpt":"Let $F$ be a non-discrete non-Archimedean locally compact field. In this article for a level zero Bernstein component $s$, we classify those irreducible smooth representations of ${\\rm GL}_n{\\integers{F}}$ (called typical representations) whose appearance in a smooth irreducible representation $\\pi$ of ${\\rm GL}_n{F}$ implies that the cuspidal support of $\\pi$ is $s$. These results extend, for level zero representations, the results of Henniart and Pa\\v{s}k\\={u}nas on cuspidal representations. The results are independent of the characteristic of the base field."},"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":"1908.03392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-08-09T10:05:56Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0012a7d96b50c1791a1e4ff8f7415b2783943f8ccd49dcebb87042463a3263a9","abstract_canon_sha256":"7aa0f6874f48d39c08a734cb34ab571e2e8c4ce5f0a30c3eb7f5236b2f1710e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:39.576484Z","signature_b64":"RCuxkoKkb1B2nUplw36omwL97OyF29BFEyf/pR3I+JHG5d2PywIoovqaV6Sz6Q6N9OIehFDwmWOL+xNu9U7CCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"162eaee2c4ee36689969f205e3a0f0b0cbb9b7d6905a08b19bfb604a0121e3ce","last_reissued_at":"2026-07-04T23:52:39.576084Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:39.576084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Typical representations for level zero Bernstein components of ${\\rm GL}_n(F)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Santosh Nadimpalli","submitted_at":"2019-08-09T10:05:56Z","abstract_excerpt":"Let $F$ be a non-discrete non-Archimedean locally compact field. In this article for a level zero Bernstein component $s$, we classify those irreducible smooth representations of ${\\rm GL}_n{\\integers{F}}$ (called typical representations) whose appearance in a smooth irreducible representation $\\pi$ of ${\\rm GL}_n{F}$ implies that the cuspidal support of $\\pi$ is $s$. These results extend, for level zero representations, the results of Henniart and Pa\\v{s}k\\={u}nas on cuspidal representations. The results are independent of the characteristic of the base field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03392","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/1908.03392/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":"1908.03392","created_at":"2026-07-04T23:52:39.576141+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03392v1","created_at":"2026-07-04T23:52:39.576141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03392","created_at":"2026-07-04T23:52:39.576141+00:00"},{"alias_kind":"pith_short_12","alias_value":"CYXK5YWE5Y3G","created_at":"2026-07-04T23:52:39.576141+00:00"},{"alias_kind":"pith_short_16","alias_value":"CYXK5YWE5Y3GRGLJ","created_at":"2026-07-04T23:52:39.576141+00:00"},{"alias_kind":"pith_short_8","alias_value":"CYXK5YWE","created_at":"2026-07-04T23:52:39.576141+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD","json":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD.json","graph_json":"https://pith.science/api/pith-number/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/graph.json","events_json":"https://pith.science/api/pith-number/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/events.json","paper":"https://pith.science/paper/CYXK5YWE"},"agent_actions":{"view_html":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD","download_json":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD.json","view_paper":"https://pith.science/paper/CYXK5YWE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03392&json=true","fetch_graph":"https://pith.science/api/pith-number/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/graph.json","fetch_events":"https://pith.science/api/pith-number/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/action/storage_attestation","attest_author":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/action/author_attestation","sign_citation":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/action/citation_signature","submit_replication":"https://pith.science/pith/CYXK5YWE5Y3GRGLJ6IC6HIHQWD/action/replication_record"}},"created_at":"2026-07-04T23:52:39.576141+00:00","updated_at":"2026-07-04T23:52:39.576141+00:00"}