{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U4U3GEECUZTJ5BHOZBO3OMHKCS","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":"440f96302e75e6055bce78a03dba98f1e8c3884355d56a590d4f33f724257139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-09T08:47:57Z","title_canon_sha256":"e02bd576a8b218015b018cbdf96a05e4d9e57c448f221eed0df4b7ea3827c703"},"schema_version":"1.0","source":{"id":"1610.02645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02645","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02645v1","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02645","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"U4U3GEECUZTJ","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U4U3GEECUZTJ5BHO","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U4U3GEEC","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:91f414414d9fb7699bcab2bc6f7df6b1f07ccd3c0c47db32907ea5d29bccecf2","target":"graph","created_at":"2026-05-17T23:55:34Z","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":"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.","authors_text":"Anne-Marie Aubert, Maarten Solleveld, Roger Plymen, Sergio Mendes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-09T08:47:57Z","title":"On $L$-packets and depth for $SL_2(K)$ and its inner form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02645","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:dc29b02ef29d37553d7ac3503cd1499aba58d611f377b376b340dd90f57c20f9","target":"record","created_at":"2026-05-17T23:55:34Z","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":"440f96302e75e6055bce78a03dba98f1e8c3884355d56a590d4f33f724257139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-09T08:47:57Z","title_canon_sha256":"e02bd576a8b218015b018cbdf96a05e4d9e57c448f221eed0df4b7ea3827c703"},"schema_version":"1.0","source":{"id":"1610.02645","kind":"arxiv","version":1}},"canonical_sha256":"a729b31082a6669e84eec85db730ea14a9b8ed6c2a7b573fcaa572c47c402c98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a729b31082a6669e84eec85db730ea14a9b8ed6c2a7b573fcaa572c47c402c98","first_computed_at":"2026-05-17T23:55:34.861475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:34.861475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HhPdZH3fEuAKIbcMMrAptWxFbpb2bz+Y1ODAKgBjC57BMpNjGFkn7i/goQYnW3nJHPa2pJrBWM4SuxiwNZlAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:34.861882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc29b02ef29d37553d7ac3503cd1499aba58d611f377b376b340dd90f57c20f9","sha256:91f414414d9fb7699bcab2bc6f7df6b1f07ccd3c0c47db32907ea5d29bccecf2"],"state_sha256":"81d0b4fa60a73eb7759370866b321b805150b591d3fd8fc35bdf24cf674e9476"}