{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:U4U3GEECUZTJ5BHOZBO3OMHKCS","short_pith_number":"pith:U4U3GEEC","schema_version":"1.0","canonical_sha256":"a729b31082a6669e84eec85db730ea14a9b8ed6c2a7b573fcaa572c47c402c98","source":{"kind":"arxiv","id":"1610.02645","version":1},"attestation_state":"computed","paper":{"title":"On $L$-packets and depth for $SL_2(K)$ and its inner form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anne-Marie Aubert, Maarten Solleveld, Roger Plymen, Sergio Mendes","submitted_at":"2016-10-09T08:47:57Z","abstract_excerpt":"We consider the group $SL_2(K)$, where $K$ is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of $SL_2 (K)$ is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame.\n  We also work out a classification of all $L$-packets for $SL_2 (K)$ and for its non-split inner form, and we provide explicit formulae for the depths of their $L$-parameters."},"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":"1610.02645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-09T08:47:57Z","cross_cats_sorted":[],"title_canon_sha256":"e02bd576a8b218015b018cbdf96a05e4d9e57c448f221eed0df4b7ea3827c703","abstract_canon_sha256":"440f96302e75e6055bce78a03dba98f1e8c3884355d56a590d4f33f724257139"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:34.861882Z","signature_b64":"8HhPdZH3fEuAKIbcMMrAptWxFbpb2bz+Y1ODAKgBjC57BMpNjGFkn7i/goQYnW3nJHPa2pJrBWM4SuxiwNZlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a729b31082a6669e84eec85db730ea14a9b8ed6c2a7b573fcaa572c47c402c98","last_reissued_at":"2026-05-17T23:55:34.861475Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:34.861475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $L$-packets and depth for $SL_2(K)$ and its inner form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anne-Marie Aubert, Maarten Solleveld, Roger Plymen, Sergio Mendes","submitted_at":"2016-10-09T08:47:57Z","abstract_excerpt":"We consider the group $SL_2(K)$, where $K$ is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of $SL_2 (K)$ is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame.\n  We also work out a classification of all $L$-packets for $SL_2 (K)$ and for its non-split inner form, and we provide explicit formulae for the depths of their $L$-parameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02645","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":""},"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":"1610.02645","created_at":"2026-05-17T23:55:34.861531+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.02645v1","created_at":"2026-05-17T23:55:34.861531+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02645","created_at":"2026-05-17T23:55:34.861531+00:00"},{"alias_kind":"pith_short_12","alias_value":"U4U3GEECUZTJ","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"U4U3GEECUZTJ5BHO","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"U4U3GEEC","created_at":"2026-05-18T12:30:46.583412+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/U4U3GEECUZTJ5BHOZBO3OMHKCS","json":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS.json","graph_json":"https://pith.science/api/pith-number/U4U3GEECUZTJ5BHOZBO3OMHKCS/graph.json","events_json":"https://pith.science/api/pith-number/U4U3GEECUZTJ5BHOZBO3OMHKCS/events.json","paper":"https://pith.science/paper/U4U3GEEC"},"agent_actions":{"view_html":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS","download_json":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS.json","view_paper":"https://pith.science/paper/U4U3GEEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.02645&json=true","fetch_graph":"https://pith.science/api/pith-number/U4U3GEECUZTJ5BHOZBO3OMHKCS/graph.json","fetch_events":"https://pith.science/api/pith-number/U4U3GEECUZTJ5BHOZBO3OMHKCS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS/action/storage_attestation","attest_author":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS/action/author_attestation","sign_citation":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS/action/citation_signature","submit_replication":"https://pith.science/pith/U4U3GEECUZTJ5BHOZBO3OMHKCS/action/replication_record"}},"created_at":"2026-05-17T23:55:34.861531+00:00","updated_at":"2026-05-17T23:55:34.861531+00:00"}