{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RTT4PRSVHRYB2BLOFBIUC6A2MY","short_pith_number":"pith:RTT4PRSV","schema_version":"1.0","canonical_sha256":"8ce7c7c6553c701d056e285141781a6622159d95e69396ce7dc8823a9cb603fa","source":{"kind":"arxiv","id":"2408.07805","version":1},"attestation_state":"computed","paper":{"title":"Reduction to depth zero for tame p-adic groups via Hecke algebra isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Jeffrey D. Adler, Jessica Fintzen, Kazuma Ohara, Manish Mishra","submitted_at":"2024-08-14T20:30:27Z","abstract_excerpt":"Let $F$ be a nonarchimedean local field of residual characteristic $p$. Let $G$ denote a connected reductive group over $F$ that splits over a tamely ramified extension of $F$. Let $(K ,\\rho)$ be a type as constructed by Kim and Yu. We show that there exists a twisted Levi subgroup $G^0 \\subset G$ and a type $(K^0, \\rho^0)$ for $G^0$ such that the corresponding Hecke algebras $\\mathcal{H}(G(F), (K, \\rho))$ and $\\mathcal{H}(G^0(F), (K^0, \\rho^0))$ are isomorphic. If $p$ does not divide the order of the absolute Weyl group of $G$, then every Bernstein block is equivalent to modules over such a H"},"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":"2408.07805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-08-14T20:30:27Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ed00b116040f5d4a95d77ea33b5215c2b6aea24f8b79139a2d7b25a8f6d581f4","abstract_canon_sha256":"69ca84e5be491175f3b5bb8f9c7474e3e14fe2df758317a3289d4dd4cfac4cde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:55:40.147452Z","signature_b64":"hXUGfEj5MTYGU03EMCwsU0gSW+1z79j9uf22c65yT7ScspMZRl4gw3GkZuBeQ4h0R9ClN96Svb5JT0GtkiWQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ce7c7c6553c701d056e285141781a6622159d95e69396ce7dc8823a9cb603fa","last_reissued_at":"2026-07-05T08:55:40.146993Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:55:40.146993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reduction to depth zero for tame p-adic groups via Hecke algebra isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Jeffrey D. Adler, Jessica Fintzen, Kazuma Ohara, Manish Mishra","submitted_at":"2024-08-14T20:30:27Z","abstract_excerpt":"Let $F$ be a nonarchimedean local field of residual characteristic $p$. Let $G$ denote a connected reductive group over $F$ that splits over a tamely ramified extension of $F$. Let $(K ,\\rho)$ be a type as constructed by Kim and Yu. We show that there exists a twisted Levi subgroup $G^0 \\subset G$ and a type $(K^0, \\rho^0)$ for $G^0$ such that the corresponding Hecke algebras $\\mathcal{H}(G(F), (K, \\rho))$ and $\\mathcal{H}(G^0(F), (K^0, \\rho^0))$ are isomorphic. If $p$ does not divide the order of the absolute Weyl group of $G$, then every Bernstein block is equivalent to modules over such a H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07805","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/2408.07805/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":"2408.07805","created_at":"2026-07-05T08:55:40.147050+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.07805v1","created_at":"2026-07-05T08:55:40.147050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07805","created_at":"2026-07-05T08:55:40.147050+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTT4PRSVHRYB","created_at":"2026-07-05T08:55:40.147050+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTT4PRSVHRYB2BLO","created_at":"2026-07-05T08:55:40.147050+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTT4PRSV","created_at":"2026-07-05T08:55:40.147050+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21313","citing_title":"On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\\mathrm{GL}_n$","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03036","citing_title":"Pinned Jordan Decomposition of Characters and Depth-Zero Hecke Algebras","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03036","citing_title":"Pinned Jordan Decomposition of Characters and Depth-Zero Hecke Algebras","ref_index":32,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY","json":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY.json","graph_json":"https://pith.science/api/pith-number/RTT4PRSVHRYB2BLOFBIUC6A2MY/graph.json","events_json":"https://pith.science/api/pith-number/RTT4PRSVHRYB2BLOFBIUC6A2MY/events.json","paper":"https://pith.science/paper/RTT4PRSV"},"agent_actions":{"view_html":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY","download_json":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY.json","view_paper":"https://pith.science/paper/RTT4PRSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.07805&json=true","fetch_graph":"https://pith.science/api/pith-number/RTT4PRSVHRYB2BLOFBIUC6A2MY/graph.json","fetch_events":"https://pith.science/api/pith-number/RTT4PRSVHRYB2BLOFBIUC6A2MY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY/action/storage_attestation","attest_author":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY/action/author_attestation","sign_citation":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY/action/citation_signature","submit_replication":"https://pith.science/pith/RTT4PRSVHRYB2BLOFBIUC6A2MY/action/replication_record"}},"created_at":"2026-07-05T08:55:40.147050+00:00","updated_at":"2026-07-05T08:55:40.147050+00:00"}