{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LKUCRPVBZUVSPZOJ6XTAR5U7GD","short_pith_number":"pith:LKUCRPVB","canonical_record":{"source":{"id":"1210.0646","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-02T04:26:38Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f43b075799323ee2c5200ae65ca3d4c019f193023ec7ae6b253b9fdb2b8357fe","abstract_canon_sha256":"34975cf633e0e9b011e297bef619b1e5d9b896d2daf80c388e9b5fdd17d563ae"},"schema_version":"1.0"},"canonical_sha256":"5aa828bea1cd2b27e5c9f5e608f69f30e2622397366f2e07e8b579bf1b03c88e","source":{"kind":"arxiv","id":"1210.0646","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0646","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0646v4","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0646","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"LKUCRPVBZUVS","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LKUCRPVBZUVSPZOJ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LKUCRPVB","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LKUCRPVBZUVSPZOJ6XTAR5U7GD","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0646","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-02T04:26:38Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"f43b075799323ee2c5200ae65ca3d4c019f193023ec7ae6b253b9fdb2b8357fe","abstract_canon_sha256":"34975cf633e0e9b011e297bef619b1e5d9b896d2daf80c388e9b5fdd17d563ae"},"schema_version":"1.0"},"canonical_sha256":"5aa828bea1cd2b27e5c9f5e608f69f30e2622397366f2e07e8b579bf1b03c88e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:38.836923Z","signature_b64":"kZGmkhgkcio7zYVoDARcw6qVHm7MUtF2My+oX5W/X52RWw4UkAUe9DvjlLBLusG0wzUk8rdnzaglwrfTOLKlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5aa828bea1cd2b27e5c9f5e608f69f30e2622397366f2e07e8b579bf1b03c88e","last_reissued_at":"2026-05-18T01:24:38.836380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:38.836380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0646","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0J4hU5rofhKPc0MYx//aLxxvdeUF7POIkuAJf8grDytVfX/CQj2AjNSONO4mE87dtIt8cC9UTJ3i88nDidsFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:50:20.081818Z"},"content_sha256":"259c85170f5c092e8b3a6e2c02de8330710364360a9a7a6074d1539990ee0391","schema_version":"1.0","event_id":"sha256:259c85170f5c092e8b3a6e2c02de8330710364360a9a7a6074d1539990ee0391"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LKUCRPVBZUVSPZOJ6XTAR5U7GD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A classification of the irreducible mod-p representations of U(1,1)(Q_p^2/Q_p)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Karol Koziol","submitted_at":"2012-10-02T04:26:38Z","abstract_excerpt":"Let p be a prime number. We classify all smooth irreducible mod-p representations of the unramified unitary group U(1,1)(Q_p^2/Q_p) in two variables. We then investigate Langlands parameters in characteristic p associated to U(1,1)(Q_p^2/Q_p), and propose a correspondence between certain equivalence classes of Langlands parameters and certain isomorphism classes of semisimple L-packets on U(1,1)(Q_p^2/Q_p)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0646","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZueVQ0wWT7VAl2Eh7y6pdij3NHqqJf7JbnFM5Q3HdUVBtMR5CDe+hOAglfkdssIkrMKGbzHBzi0fY93ZO+dsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:50:20.082174Z"},"content_sha256":"39e11cba5feb0d5244e7875a89ebe8fd337fbcb1f17fcf7b6df0348d62c98fa8","schema_version":"1.0","event_id":"sha256:39e11cba5feb0d5244e7875a89ebe8fd337fbcb1f17fcf7b6df0348d62c98fa8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD/bundle.json","state_url":"https://pith.science/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T20:50:20Z","links":{"resolver":"https://pith.science/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD","bundle":"https://pith.science/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD/bundle.json","state":"https://pith.science/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKUCRPVBZUVSPZOJ6XTAR5U7GD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LKUCRPVBZUVSPZOJ6XTAR5U7GD","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":"34975cf633e0e9b011e297bef619b1e5d9b896d2daf80c388e9b5fdd17d563ae","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-02T04:26:38Z","title_canon_sha256":"f43b075799323ee2c5200ae65ca3d4c019f193023ec7ae6b253b9fdb2b8357fe"},"schema_version":"1.0","source":{"id":"1210.0646","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0646","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0646v4","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0646","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"LKUCRPVBZUVS","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LKUCRPVBZUVSPZOJ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LKUCRPVB","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:39e11cba5feb0d5244e7875a89ebe8fd337fbcb1f17fcf7b6df0348d62c98fa8","target":"graph","created_at":"2026-05-18T01:24:38Z","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. We classify all smooth irreducible mod-p representations of the unramified unitary group U(1,1)(Q_p^2/Q_p) in two variables. We then investigate Langlands parameters in characteristic p associated to U(1,1)(Q_p^2/Q_p), and propose a correspondence between certain equivalence classes of Langlands parameters and certain isomorphism classes of semisimple L-packets on U(1,1)(Q_p^2/Q_p).","authors_text":"Karol Koziol","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-02T04:26:38Z","title":"A classification of the irreducible mod-p representations of U(1,1)(Q_p^2/Q_p)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0646","kind":"arxiv","version":4},"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":"sha256:259c85170f5c092e8b3a6e2c02de8330710364360a9a7a6074d1539990ee0391","target":"record","created_at":"2026-05-18T01:24:38Z","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":"34975cf633e0e9b011e297bef619b1e5d9b896d2daf80c388e9b5fdd17d563ae","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-02T04:26:38Z","title_canon_sha256":"f43b075799323ee2c5200ae65ca3d4c019f193023ec7ae6b253b9fdb2b8357fe"},"schema_version":"1.0","source":{"id":"1210.0646","kind":"arxiv","version":4}},"canonical_sha256":"5aa828bea1cd2b27e5c9f5e608f69f30e2622397366f2e07e8b579bf1b03c88e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5aa828bea1cd2b27e5c9f5e608f69f30e2622397366f2e07e8b579bf1b03c88e","first_computed_at":"2026-05-18T01:24:38.836380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:38.836380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZGmkhgkcio7zYVoDARcw6qVHm7MUtF2My+oX5W/X52RWw4UkAUe9DvjlLBLusG0wzUk8rdnzaglwrfTOLKlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:38.836923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0646","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:259c85170f5c092e8b3a6e2c02de8330710364360a9a7a6074d1539990ee0391","sha256:39e11cba5feb0d5244e7875a89ebe8fd337fbcb1f17fcf7b6df0348d62c98fa8"],"state_sha256":"b3a5847f4866d705fa1ce2c142390bb4a0185867b3a17dda199771c83ff38143"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0bPsBC9JF1UACS9TIfq6R1F9iAa09sHhBIn59x8zDWdg0EOuvoxOxhR7GcVB590oKQ+RGTsATW0AD4wN2fcFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:50:20.084543Z","bundle_sha256":"2cdabdfda3d9dec61d17b79e7afd7bdc07fb16dc83e060cb0a5582d72edd5d79"}}