{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HZC3XK5DPNIPTJFPHH5SC33DT6","short_pith_number":"pith:HZC3XK5D","schema_version":"1.0","canonical_sha256":"3e45bbaba37b50f9a4af39fb216f639f996c5745bb7c9d68d0fae3a709d4eb39","source":{"kind":"arxiv","id":"1902.02686","version":3},"attestation_state":"computed","paper":{"title":"Local coefficients and gamma factors for principal series of covering groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dani Szpruch, Fan Gao, Freydoon Shahidi","submitted_at":"2019-02-07T15:29:48Z","abstract_excerpt":"We consider an $n$-fold Brylinski-Deligne cover of a reductive group over a $p$-adic field. Since the space of Whittaker functionals of an irreducible genuine representation of such a cover is not one-dimensional, one can consider a local coefficients matrix arising from an intertwining operator, which is the natural analogue of the local coefficients in the linear case. In this paper, we concentrate on genuine principal series and establish some fundamental properties of such a local coefficients matrix, including the investigation of its arithmetic invariants. As a consequence, we prove a fo"},"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":"1902.02686","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-07T15:29:48Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"12f7bfacc9b465ad23199abd7054c049f79c16e50e6c34f3405b44f70cf47df1","abstract_canon_sha256":"ce6e45175ddc807ea91a917beb8f04f3c6738499496b18e5649d72976a2db864"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:21:32.713512Z","signature_b64":"7B0uffv9FCSh2h1+zwDZE2lkavZ48+dDZLaGBQoqTxjLjAFIkkqBH09e4tu6I9fy7r6F0Vb+A0kgGTi1NcfjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e45bbaba37b50f9a4af39fb216f639f996c5745bb7c9d68d0fae3a709d4eb39","last_reissued_at":"2026-07-05T00:21:32.713021Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:21:32.713021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local coefficients and gamma factors for principal series of covering groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dani Szpruch, Fan Gao, Freydoon Shahidi","submitted_at":"2019-02-07T15:29:48Z","abstract_excerpt":"We consider an $n$-fold Brylinski-Deligne cover of a reductive group over a $p$-adic field. Since the space of Whittaker functionals of an irreducible genuine representation of such a cover is not one-dimensional, one can consider a local coefficients matrix arising from an intertwining operator, which is the natural analogue of the local coefficients in the linear case. In this paper, we concentrate on genuine principal series and establish some fundamental properties of such a local coefficients matrix, including the investigation of its arithmetic invariants. As a consequence, we prove a fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02686","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/1902.02686/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":"1902.02686","created_at":"2026-07-05T00:21:32.713078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02686v3","created_at":"2026-07-05T00:21:32.713078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02686","created_at":"2026-07-05T00:21:32.713078+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZC3XK5DPNIP","created_at":"2026-07-05T00:21:32.713078+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZC3XK5DPNIPTJFP","created_at":"2026-07-05T00:21:32.713078+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZC3XK5D","created_at":"2026-07-05T00:21:32.713078+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13143","citing_title":"Eisenstein Series on Metaplectic Covers and Multiple Dirichlet Series","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6","json":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6.json","graph_json":"https://pith.science/api/pith-number/HZC3XK5DPNIPTJFPHH5SC33DT6/graph.json","events_json":"https://pith.science/api/pith-number/HZC3XK5DPNIPTJFPHH5SC33DT6/events.json","paper":"https://pith.science/paper/HZC3XK5D"},"agent_actions":{"view_html":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6","download_json":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6.json","view_paper":"https://pith.science/paper/HZC3XK5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02686&json=true","fetch_graph":"https://pith.science/api/pith-number/HZC3XK5DPNIPTJFPHH5SC33DT6/graph.json","fetch_events":"https://pith.science/api/pith-number/HZC3XK5DPNIPTJFPHH5SC33DT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6/action/storage_attestation","attest_author":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6/action/author_attestation","sign_citation":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6/action/citation_signature","submit_replication":"https://pith.science/pith/HZC3XK5DPNIPTJFPHH5SC33DT6/action/replication_record"}},"created_at":"2026-07-05T00:21:32.713078+00:00","updated_at":"2026-07-05T00:21:32.713078+00:00"}