{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4JQHRCOUYTED5XK74WQXA7KZYG","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":"be721c191e091e487ac385f81a0bc87a2191eb11b4204416cf5b152491b531d5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-28T18:10:13Z","title_canon_sha256":"552db294d6912ec2538d37249cb34dad80630df0796efa9e6c489a2172481f45"},"schema_version":"1.0","source":{"id":"1308.6239","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6239","created_at":"2026-05-18T02:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6239v3","created_at":"2026-05-18T02:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6239","created_at":"2026-05-18T02:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"4JQHRCOUYTED","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4JQHRCOUYTED5XK7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4JQHRCOU","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:0095bf57164ce65e433c997c03aa0ecceea9d2d8f377aa3cef30429f71eb5ca4","target":"graph","created_at":"2026-05-18T02:12:11Z","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":"Let p be a prime number, and F a nonarchimedean local field of residual characteristic p. We explore the interaction between the pro-p-Iwahori-Hecke algebras of the group GL_n(F) and its derived subgroup SL_n(F). Using the interplay between these two algebras, we deduce two main results. The first is an equivalence of categories between Hecke modules in characteristic p over the pro-p-Iwahori-Hecke algebra of SL_2(Q_p) and smooth mod-p representations of SL_2(Q_p) generated by their pro-p-Iwahori-invariants. The second is a \"numerical correspondence\" between packets of supersingular Hecke modu","authors_text":"Karol Koziol","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-28T18:10:13Z","title":"Pro-p-Iwahori invariants for SL_2 and L-packets of Hecke modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6239","kind":"arxiv","version":3},"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":"sha256:95086fc5affea0234e76e327cf26d3f45a1a98676ac6549ead29188a3f1c3631","target":"record","created_at":"2026-05-18T02:12:11Z","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":"be721c191e091e487ac385f81a0bc87a2191eb11b4204416cf5b152491b531d5","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-28T18:10:13Z","title_canon_sha256":"552db294d6912ec2538d37249cb34dad80630df0796efa9e6c489a2172481f45"},"schema_version":"1.0","source":{"id":"1308.6239","kind":"arxiv","version":3}},"canonical_sha256":"e2607889d4c4c83edd5fe5a1707d59c1b8df5768013d9235bbfd90ebc68b1a75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2607889d4c4c83edd5fe5a1707d59c1b8df5768013d9235bbfd90ebc68b1a75","first_computed_at":"2026-05-18T02:12:11.750229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:11.750229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sSb1UYx7KuOUEiNP0E+YhIsQXKbTMzf8hZUovbu/FXQvpTTYzph3xG6cWBfc9tV7v1rXuntn4K1AywCM9SLdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:11.750979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6239","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95086fc5affea0234e76e327cf26d3f45a1a98676ac6549ead29188a3f1c3631","sha256:0095bf57164ce65e433c997c03aa0ecceea9d2d8f377aa3cef30429f71eb5ca4"],"state_sha256":"96bc93f7d33e2a00b8423eef171b76d754670012beb505bbf3b997c6db4576a3"}