{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:G7CZ2NHADKZITRYAIBVOMYC3SL","short_pith_number":"pith:G7CZ2NHA","canonical_record":{"source":{"id":"1608.08356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T08:17:15Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"7390a109cfd9022796f2281ee48af7b3766b0892e48768588bba1f1f626316b3","abstract_canon_sha256":"cdc8fc200bbd3f17d447338088b7bb8565528ddfbd4da3b8ddb0bad5dea2259a"},"schema_version":"1.0"},"canonical_sha256":"37c59d34e01ab289c700406ae6605b92f16609835fc2413576c0e5d652b783b9","source":{"kind":"arxiv","id":"1608.08356","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08356","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08356v2","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08356","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"G7CZ2NHADKZI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7CZ2NHADKZITRYA","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7CZ2NHA","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:G7CZ2NHADKZITRYAIBVOMYC3SL","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T08:17:15Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"7390a109cfd9022796f2281ee48af7b3766b0892e48768588bba1f1f626316b3","abstract_canon_sha256":"cdc8fc200bbd3f17d447338088b7bb8565528ddfbd4da3b8ddb0bad5dea2259a"},"schema_version":"1.0"},"canonical_sha256":"37c59d34e01ab289c700406ae6605b92f16609835fc2413576c0e5d652b783b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:12.275554Z","signature_b64":"SyOM50FalmOB4msAVz8sWy5dSJL5Mqch6C+B/er+CU3fpcj6nrTwl9Atbx1B1xXRr8cQDOJQUrnT/4zQGWXrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37c59d34e01ab289c700406ae6605b92f16609835fc2413576c0e5d652b783b9","last_reissued_at":"2026-05-17T23:49:12.274979Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:12.274979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08356","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":"2026-05-17T23:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4UWBJKg5QeXyrIQ+/i1iHPTc0DmUeXgJYEn4llPMosEZ9ZrZcw+xCvPAFix33eQo7TrLBqNvOQZJTWPHenSDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:00:35.814903Z"},"content_sha256":"635954f6eda3335fceca39e7a481a6249e0370975838fb886b39553ab246cbf3","schema_version":"1.0","event_id":"sha256:635954f6eda3335fceca39e7a481a6249e0370975838fb886b39553ab246cbf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:G7CZ2NHADKZITRYAIBVOMYC3SL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global analysis by hidden symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.RT","authors_text":"Toshiyuki Kobayashi","submitted_at":"2016-08-30T08:17:15Z","abstract_excerpt":"Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects:\n  (A) global analysis on X by using representations of G (hidden symmetry);\n  (B) global analysis on X by using representations of G';\n  (C) branching laws of representations of G when restricted to the subgroup G'.\n  We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08356","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":"2026-05-17T23:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AS1tEZb9Ldc7sh6KAI/52rlNinNFni7/qr/OlgBoWCvlE5ScCCl/f81rv9VVBXXnAZi+DTgNSW3Xusiie7Y7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:00:35.815338Z"},"content_sha256":"7ccdf195a50194ae5ba0bd6c065883d14e66db3e68bfc69f89f8b1d69c54f69e","schema_version":"1.0","event_id":"sha256:7ccdf195a50194ae5ba0bd6c065883d14e66db3e68bfc69f89f8b1d69c54f69e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7CZ2NHADKZITRYAIBVOMYC3SL/bundle.json","state_url":"https://pith.science/pith/G7CZ2NHADKZITRYAIBVOMYC3SL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7CZ2NHADKZITRYAIBVOMYC3SL/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":"2026-05-26T17:00:35Z","links":{"resolver":"https://pith.science/pith/G7CZ2NHADKZITRYAIBVOMYC3SL","bundle":"https://pith.science/pith/G7CZ2NHADKZITRYAIBVOMYC3SL/bundle.json","state":"https://pith.science/pith/G7CZ2NHADKZITRYAIBVOMYC3SL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7CZ2NHADKZITRYAIBVOMYC3SL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G7CZ2NHADKZITRYAIBVOMYC3SL","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":"cdc8fc200bbd3f17d447338088b7bb8565528ddfbd4da3b8ddb0bad5dea2259a","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T08:17:15Z","title_canon_sha256":"7390a109cfd9022796f2281ee48af7b3766b0892e48768588bba1f1f626316b3"},"schema_version":"1.0","source":{"id":"1608.08356","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08356","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08356v2","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08356","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"G7CZ2NHADKZI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7CZ2NHADKZITRYA","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7CZ2NHA","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:7ccdf195a50194ae5ba0bd6c065883d14e66db3e68bfc69f89f8b1d69c54f69e","target":"graph","created_at":"2026-05-17T23:49:12Z","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":"Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects:\n  (A) global analysis on X by using representations of G (hidden symmetry);\n  (B) global analysis on X by using representations of G';\n  (C) branching laws of representations of G when restricted to the subgroup G'.\n  We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting ","authors_text":"Toshiyuki Kobayashi","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T08:17:15Z","title":"Global analysis by hidden symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08356","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":"sha256:635954f6eda3335fceca39e7a481a6249e0370975838fb886b39553ab246cbf3","target":"record","created_at":"2026-05-17T23:49:12Z","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":"cdc8fc200bbd3f17d447338088b7bb8565528ddfbd4da3b8ddb0bad5dea2259a","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-30T08:17:15Z","title_canon_sha256":"7390a109cfd9022796f2281ee48af7b3766b0892e48768588bba1f1f626316b3"},"schema_version":"1.0","source":{"id":"1608.08356","kind":"arxiv","version":2}},"canonical_sha256":"37c59d34e01ab289c700406ae6605b92f16609835fc2413576c0e5d652b783b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37c59d34e01ab289c700406ae6605b92f16609835fc2413576c0e5d652b783b9","first_computed_at":"2026-05-17T23:49:12.274979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:12.274979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SyOM50FalmOB4msAVz8sWy5dSJL5Mqch6C+B/er+CU3fpcj6nrTwl9Atbx1B1xXRr8cQDOJQUrnT/4zQGWXrBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:12.275554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08356","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:635954f6eda3335fceca39e7a481a6249e0370975838fb886b39553ab246cbf3","sha256:7ccdf195a50194ae5ba0bd6c065883d14e66db3e68bfc69f89f8b1d69c54f69e"],"state_sha256":"a9268440bcc2c13b3a6eee7371c04f25c004c799106ce662c53a97db4bfcf38d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XhI1WrvWEg0he5GHJlsqSpmGQGdcw5NslD2+2PXOGjN8jVoc6lRd5V1hvQHMmFwAVrA805pcC+a+JwXBnJ0CDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:00:35.818026Z","bundle_sha256":"8f6ca9c5b14b89e3a53625e96b348d36faedccb0d350b868392483326a084133"}}