{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:I4PWFF3YZ4X5GJE4SLE37OTUZX","short_pith_number":"pith:I4PWFF3Y","schema_version":"1.0","canonical_sha256":"471f629778cf2fd3249c92c9bfba74cdfc6e7198727bdf38745a7095817a5f02","source":{"kind":"arxiv","id":"1303.3541","version":2},"attestation_state":"computed","paper":{"title":"F-method for symmetry breaking operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.DG","math.MP"],"primary_cat":"math.RT","authors_text":"Toshiyuki Kobayashi","submitted_at":"2013-03-14T18:34:53Z","abstract_excerpt":"We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators.\n  First, we give geometric criteria for finiteness property of linearly independent continuous (respectively, differential) operators that intertwine two induced representations of reductive Lie groups and their reductive subgroups.\n  Second, we extend the F-method known for local operators to non-local operators. We then illustrate the idea by concrete examples in conformal geometry, and explain how the F-method works for detailed analysis of symmet"},"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":"1303.3541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-14T18:34:53Z","cross_cats_sorted":["math-ph","math.CA","math.DG","math.MP"],"title_canon_sha256":"a4f50e0455d70d17d46d68aace620f8cb3fd4d28a0a32a8543065c4f98ef421f","abstract_canon_sha256":"cd28ebe7a732aae3283d6f2c467de02c6ab7874c74580b89f3e52db8a162f681"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:38.023374Z","signature_b64":"alcMgSiIHqnvEQ81J5SS9Uuj13VHfc4F9tmswWh+stErLFstpRSk6/9hy4lnyX6Vz0HO2u6T/Cb4qWScKdm7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"471f629778cf2fd3249c92c9bfba74cdfc6e7198727bdf38745a7095817a5f02","last_reissued_at":"2026-05-18T03:04:38.022559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:38.022559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"F-method for symmetry breaking operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.DG","math.MP"],"primary_cat":"math.RT","authors_text":"Toshiyuki Kobayashi","submitted_at":"2013-03-14T18:34:53Z","abstract_excerpt":"We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators.\n  First, we give geometric criteria for finiteness property of linearly independent continuous (respectively, differential) operators that intertwine two induced representations of reductive Lie groups and their reductive subgroups.\n  Second, we extend the F-method known for local operators to non-local operators. We then illustrate the idea by concrete examples in conformal geometry, and explain how the F-method works for detailed analysis of symmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3541","kind":"arxiv","version":2},"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":"1303.3541","created_at":"2026-05-18T03:04:38.022704+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3541v2","created_at":"2026-05-18T03:04:38.022704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3541","created_at":"2026-05-18T03:04:38.022704+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4PWFF3YZ4X5","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4PWFF3YZ4X5GJE4","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4PWFF3Y","created_at":"2026-05-18T12:27:46.883200+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/I4PWFF3YZ4X5GJE4SLE37OTUZX","json":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX.json","graph_json":"https://pith.science/api/pith-number/I4PWFF3YZ4X5GJE4SLE37OTUZX/graph.json","events_json":"https://pith.science/api/pith-number/I4PWFF3YZ4X5GJE4SLE37OTUZX/events.json","paper":"https://pith.science/paper/I4PWFF3Y"},"agent_actions":{"view_html":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX","download_json":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX.json","view_paper":"https://pith.science/paper/I4PWFF3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3541&json=true","fetch_graph":"https://pith.science/api/pith-number/I4PWFF3YZ4X5GJE4SLE37OTUZX/graph.json","fetch_events":"https://pith.science/api/pith-number/I4PWFF3YZ4X5GJE4SLE37OTUZX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX/action/storage_attestation","attest_author":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX/action/author_attestation","sign_citation":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX/action/citation_signature","submit_replication":"https://pith.science/pith/I4PWFF3YZ4X5GJE4SLE37OTUZX/action/replication_record"}},"created_at":"2026-05-18T03:04:38.022704+00:00","updated_at":"2026-05-18T03:04:38.022704+00:00"}