{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NOFS4GCKHCJ3FAYLO6PUA75POD","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":"b3121e4e5ca22d001650701c1921f89f088d84c5f518cbb13c6fc9d6953a2625","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-08-14T20:23:09Z","title_canon_sha256":"86e5cbdcbcc70b682374bc3f6b4500dc7f593704c5b9b8345559a30aaa589e10"},"schema_version":"1.0","source":{"id":"2408.07801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.07801","created_at":"2026-07-05T08:55:40Z"},{"alias_kind":"arxiv_version","alias_value":"2408.07801v1","created_at":"2026-07-05T08:55:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07801","created_at":"2026-07-05T08:55:40Z"},{"alias_kind":"pith_short_12","alias_value":"NOFS4GCKHCJ3","created_at":"2026-07-05T08:55:40Z"},{"alias_kind":"pith_short_16","alias_value":"NOFS4GCKHCJ3FAYL","created_at":"2026-07-05T08:55:40Z"},{"alias_kind":"pith_short_8","alias_value":"NOFS4GCK","created_at":"2026-07-05T08:55:40Z"}],"graph_snapshots":[{"event_id":"sha256:70a042ba4e915b22e8afa4ed2c3782184fc40f4a21590eabc6ead5d1cd91be19","target":"graph","created_at":"2026-07-05T08:55:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.07801/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ denote a connected reductive group over a nonarchimedean local field $F$ of residue characteristic $p$, and let $\\mathcal{C}$ denote an algebraically closed field of characteristic $\\ell \\neq p$. If $\\rho$ is an irreducible, smooth $\\mathcal{C}$-representation of a compact, open subgroup $K$ of $G(F)$, then the pair $(K,\\rho)$ gives rise to a Hecke algebra $\\mathcal{H}(G(F),(K, \\rho))$. For a large class of pairs $(K,\\rho)$, we show that $\\mathcal{H}(G(F),(K, \\rho))$ is a semi-direct product of an affine Hecke algebra with explicit parameters with a twisted group algebra, and that it i","authors_text":"Jeffrey D. Adler, Jessica Fintzen, Kazuma Ohara, Manish Mishra","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-08-14T20:23:09Z","title":"Structure of Hecke algebras arising from types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07801","kind":"arxiv","version":1},"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":"sha256:2abd7bd7a248d6ac697c47af8b8c35af0fd3f87f775d0a008a38d8b54febe141","target":"record","created_at":"2026-07-05T08:55:40Z","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":"b3121e4e5ca22d001650701c1921f89f088d84c5f518cbb13c6fc9d6953a2625","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-08-14T20:23:09Z","title_canon_sha256":"86e5cbdcbcc70b682374bc3f6b4500dc7f593704c5b9b8345559a30aaa589e10"},"schema_version":"1.0","source":{"id":"2408.07801","kind":"arxiv","version":1}},"canonical_sha256":"6b8b2e184a3893b2830b779f407faf70e49fadd48913d05a38af67dc042f1baf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b8b2e184a3893b2830b779f407faf70e49fadd48913d05a38af67dc042f1baf","first_computed_at":"2026-07-05T08:55:40.039493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:55:40.039493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j23rnnByY5exx43e60NtGTsgr1m4g//m/+SgRoXzPDG2p0pyatevDFb2PizjJkkhLosdzp7HIWMsk1tBEF4BDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:55:40.039918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.07801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2abd7bd7a248d6ac697c47af8b8c35af0fd3f87f775d0a008a38d8b54febe141","sha256:70a042ba4e915b22e8afa4ed2c3782184fc40f4a21590eabc6ead5d1cd91be19"],"state_sha256":"2d685b86bee4ed566b91afe1943a7772f24e6e24b3019346511e4ed8efebb461"}