{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GCNGERCM73GY64UYRODN2ME5GR","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":"545e830a576dc9363d31b338c0943c453cee2a3413396e08bfe61b684755ddc5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-22T10:25:18Z","title_canon_sha256":"4484cddb61ad7c4f31d77b27e5e44cfdc36e0beca3d1839e21a5cf0eaf867b9d"},"schema_version":"1.0","source":{"id":"1408.5252","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5252","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5252v4","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5252","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"GCNGERCM73GY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCNGERCM73GY64UY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCNGERCM","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:7708d88316274a59f229aff96c7c0c923dd980ace02c4e62fb2d06e49a430503","target":"graph","created_at":"2026-05-18T01:37:49Z","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"},"paper":{"abstract_excerpt":"After extending the theory of Rankin-Selberg local factors to pairs of $\\ell$-modular representations of Whittaker type, of general linear groups over a non-archimedean local field, we study the reduction modulo $\\ell$ of $\\ell$-adic local factors and their relation to these $\\ell$-modular local factors. While the $\\ell$-modular local $\\gamma$-factor we associate to such a pair turns out to always coincide with the reduction modulo $\\ell$ of the $\\ell$-adic $\\gamma$-factor of any Whittaker lifts of this pair, the local $L$-factor exhibits a more interesting behaviour; always dividing the reduc","authors_text":"Nadir Matringe, Robert Kurinczuk","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-22T10:25:18Z","title":"Rankin-Selberg local factors modulo $\\ell$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5252","kind":"arxiv","version":4},"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":"sha256:3550b667f9d31e0cb3693fb2160d863ea6daa44fde30cd7db3ef9d1db0129b11","target":"record","created_at":"2026-05-18T01:37:49Z","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":"545e830a576dc9363d31b338c0943c453cee2a3413396e08bfe61b684755ddc5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-08-22T10:25:18Z","title_canon_sha256":"4484cddb61ad7c4f31d77b27e5e44cfdc36e0beca3d1839e21a5cf0eaf867b9d"},"schema_version":"1.0","source":{"id":"1408.5252","kind":"arxiv","version":4}},"canonical_sha256":"309a62444cfecd8f72988b86dd309d347341efc4614ff056883c5e5c49747a61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"309a62444cfecd8f72988b86dd309d347341efc4614ff056883c5e5c49747a61","first_computed_at":"2026-05-18T01:37:49.381234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:49.381234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eBl5eAlXFRPm07Y5YOcoF3KsoYx+de3uYSFsbu13mXbmvM0yl+2YVjUENUGUaBd7EswaBtjb4rBNHn6dOjodDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:49.381838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5252","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3550b667f9d31e0cb3693fb2160d863ea6daa44fde30cd7db3ef9d1db0129b11","sha256:7708d88316274a59f229aff96c7c0c923dd980ace02c4e62fb2d06e49a430503"],"state_sha256":"d5fa8cc3138cb1aaf91153899a015f3349d9a48d78b378c4f7523b468e9a1f4a"}