{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SUZ4RD5QEWMWJMZPHXLQALYLQA","short_pith_number":"pith:SUZ4RD5Q","canonical_record":{"source":{"id":"1212.6862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-31T11:21:54Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3fd76a7ec378c09d509eb2d533b9aa6bede34d708ce8f0ab301614efed2e7f43","abstract_canon_sha256":"b9a5e870966ddf2fe1030cd9dfc307d828302d09dff719e18edf53c86b2c3f28"},"schema_version":"1.0"},"canonical_sha256":"9533c88fb0259964b32f3dd7002f0b801238d5e6f9a3aba2312ab751952b05b4","source":{"kind":"arxiv","id":"1212.6862","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6862","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6862v2","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6862","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUZ4RD5QEWMW","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SUZ4RD5QEWMWJMZP","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SUZ4RD5Q","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SUZ4RD5QEWMWJMZPHXLQALYLQA","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-31T11:21:54Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3fd76a7ec378c09d509eb2d533b9aa6bede34d708ce8f0ab301614efed2e7f43","abstract_canon_sha256":"b9a5e870966ddf2fe1030cd9dfc307d828302d09dff719e18edf53c86b2c3f28"},"schema_version":"1.0"},"canonical_sha256":"9533c88fb0259964b32f3dd7002f0b801238d5e6f9a3aba2312ab751952b05b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:38.221763Z","signature_b64":"craonbYWEIBeF9uBFs6aG2UZqRHE+R8YcycmPab9v64Q2DkvzGYkgRwau5nB80A0ZEjyMJkMEkHz23qGduuYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9533c88fb0259964b32f3dd7002f0b801238d5e6f9a3aba2312ab751952b05b4","last_reissued_at":"2026-05-18T03:04:38.221034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:38.221034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6862","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tx1mcEjUhXlcbOeW3SOZEQFBXYD2EXiXwG7E80LgoQ0tWicBI1PV7tgO6gEZEoVupUW/7ZyB2PQsyTaPIQs3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:41:38.563407Z"},"content_sha256":"49b6c253cdb7d619e725403459772fc3d97196dba2722d543c8ea2c6bd64c250","schema_version":"1.0","event_id":"sha256:49b6c253cdb7d619e725403459772fc3d97196dba2722d543c8ea2c6bd64c250"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SUZ4RD5QEWMWJMZPHXLQALYLQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"F-method for constructing equivariant differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RT","authors_text":"Toshiyuki Kobayashi","submitted_at":"2012-12-31T11:21:54Z","abstract_excerpt":"Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that arise in parabolic geometry and in automorphic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6862","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TtfPDAikxW+OykFW0458yv3z2ppgssfiGa5UGahbW5h/ExJnBtpsS0k/FlmK0xG84OeJbI9kRxd27f0a/lK8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:41:38.564103Z"},"content_sha256":"f760369e47a73b267fdd7f70fb31394a4b172539c0b7bd88b03e90e799b96e70","schema_version":"1.0","event_id":"sha256:f760369e47a73b267fdd7f70fb31394a4b172539c0b7bd88b03e90e799b96e70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA/bundle.json","state_url":"https://pith.science/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA/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":"2026-06-09T01:41:38Z","links":{"resolver":"https://pith.science/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA","bundle":"https://pith.science/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA/bundle.json","state":"https://pith.science/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUZ4RD5QEWMWJMZPHXLQALYLQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SUZ4RD5QEWMWJMZPHXLQALYLQA","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":"b9a5e870966ddf2fe1030cd9dfc307d828302d09dff719e18edf53c86b2c3f28","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-31T11:21:54Z","title_canon_sha256":"3fd76a7ec378c09d509eb2d533b9aa6bede34d708ce8f0ab301614efed2e7f43"},"schema_version":"1.0","source":{"id":"1212.6862","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6862","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6862v2","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6862","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUZ4RD5QEWMW","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SUZ4RD5QEWMWJMZP","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SUZ4RD5Q","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:f760369e47a73b267fdd7f70fb31394a4b172539c0b7bd88b03e90e799b96e70","target":"graph","created_at":"2026-05-18T03:04:38Z","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":"Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that arise in parabolic geometry and in automorphic forms.","authors_text":"Toshiyuki Kobayashi","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-31T11:21:54Z","title":"F-method for constructing equivariant differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6862","kind":"arxiv","version":2},"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":"sha256:49b6c253cdb7d619e725403459772fc3d97196dba2722d543c8ea2c6bd64c250","target":"record","created_at":"2026-05-18T03:04:38Z","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":"b9a5e870966ddf2fe1030cd9dfc307d828302d09dff719e18edf53c86b2c3f28","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-31T11:21:54Z","title_canon_sha256":"3fd76a7ec378c09d509eb2d533b9aa6bede34d708ce8f0ab301614efed2e7f43"},"schema_version":"1.0","source":{"id":"1212.6862","kind":"arxiv","version":2}},"canonical_sha256":"9533c88fb0259964b32f3dd7002f0b801238d5e6f9a3aba2312ab751952b05b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9533c88fb0259964b32f3dd7002f0b801238d5e6f9a3aba2312ab751952b05b4","first_computed_at":"2026-05-18T03:04:38.221034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:38.221034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"craonbYWEIBeF9uBFs6aG2UZqRHE+R8YcycmPab9v64Q2DkvzGYkgRwau5nB80A0ZEjyMJkMEkHz23qGduuYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:38.221763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6862","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49b6c253cdb7d619e725403459772fc3d97196dba2722d543c8ea2c6bd64c250","sha256:f760369e47a73b267fdd7f70fb31394a4b172539c0b7bd88b03e90e799b96e70"],"state_sha256":"6f3dc1f01bb396451cce61a190caa0f044f9d32c664344fbdd9198ddfba60e38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eIc0dr4LCWW6AddStTwb/bZ2dZBqF1A1lB1+Kj0e5dSyWS5itceB2prkVxSpCHMNmKHYvstWW/2Tz5DK1UOvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:41:38.567780Z","bundle_sha256":"e3ed48dfe2f93bbac729525a269c47d6ed4fc1111d4e9f7c1e13f2adc954be76"}}