{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2WD3DN7WI57ELINT5VEHEECSE5","short_pith_number":"pith:2WD3DN7W","schema_version":"1.0","canonical_sha256":"d587b1b7f6477e45a1b3ed487210522778d2a2bf36b39bdc7dfe8959bdedee4c","source":{"kind":"arxiv","id":"1812.03162","version":1},"attestation_state":"computed","paper":{"title":"A reciprocal branching problem for automorphic representations and global Vogan packets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Baiying Liu, Bin Xu, Dihua Jiang","submitted_at":"2018-12-07T18:52:24Z","abstract_excerpt":"Let $G$ be a group and $H$ be a subgroup of $G$. The classical branching rule (or symmetry breaking) asks: For an irreducible representation $\\pi$ of $G$, determine the occurrence of an irreducible representation $\\sigma$ of $H$ in the restriction of $\\pi$ to $H$. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation $\\sigma$ of $H$, find an irreducible representation $\\pi$ of $G$ such that $\\sigma$ occurs in the restriction of $\\pi$ to $H$. For automorphic representations of classical groups, the branching problem has been addressed "},"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":"1812.03162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-07T18:52:24Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"24b651f59b781b189f1eb4cef33ec2a5411b6f689b608decf052dc7e4bd34aea","abstract_canon_sha256":"aa07755fdf2ae2941c3a0edf97a74e0f7b5d39a2b38600ace2f13eb40b93ffe1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:50.766402Z","signature_b64":"dXQ61S5zGD7Ru7ZGh8DW6dopKqAxv4vSol3Tgcs/RVpUfkSQ1b30mnwR12+Y5AiWOMu5hb5KAh9aaVol7Q0jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d587b1b7f6477e45a1b3ed487210522778d2a2bf36b39bdc7dfe8959bdedee4c","last_reissued_at":"2026-05-17T23:58:50.765922Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:50.765922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A reciprocal branching problem for automorphic representations and global Vogan packets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Baiying Liu, Bin Xu, Dihua Jiang","submitted_at":"2018-12-07T18:52:24Z","abstract_excerpt":"Let $G$ be a group and $H$ be a subgroup of $G$. The classical branching rule (or symmetry breaking) asks: For an irreducible representation $\\pi$ of $G$, determine the occurrence of an irreducible representation $\\sigma$ of $H$ in the restriction of $\\pi$ to $H$. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation $\\sigma$ of $H$, find an irreducible representation $\\pi$ of $G$ such that $\\sigma$ occurs in the restriction of $\\pi$ to $H$. For automorphic representations of classical groups, the branching problem has been addressed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03162","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":"1812.03162","created_at":"2026-05-17T23:58:50.765994+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.03162v1","created_at":"2026-05-17T23:58:50.765994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03162","created_at":"2026-05-17T23:58:50.765994+00:00"},{"alias_kind":"pith_short_12","alias_value":"2WD3DN7WI57E","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2WD3DN7WI57ELINT","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2WD3DN7W","created_at":"2026-05-18T12:32:02.567920+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/2WD3DN7WI57ELINT5VEHEECSE5","json":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5.json","graph_json":"https://pith.science/api/pith-number/2WD3DN7WI57ELINT5VEHEECSE5/graph.json","events_json":"https://pith.science/api/pith-number/2WD3DN7WI57ELINT5VEHEECSE5/events.json","paper":"https://pith.science/paper/2WD3DN7W"},"agent_actions":{"view_html":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5","download_json":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5.json","view_paper":"https://pith.science/paper/2WD3DN7W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.03162&json=true","fetch_graph":"https://pith.science/api/pith-number/2WD3DN7WI57ELINT5VEHEECSE5/graph.json","fetch_events":"https://pith.science/api/pith-number/2WD3DN7WI57ELINT5VEHEECSE5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5/action/storage_attestation","attest_author":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5/action/author_attestation","sign_citation":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5/action/citation_signature","submit_replication":"https://pith.science/pith/2WD3DN7WI57ELINT5VEHEECSE5/action/replication_record"}},"created_at":"2026-05-17T23:58:50.765994+00:00","updated_at":"2026-05-17T23:58:50.765994+00:00"}