{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MCFEBPLBV4YTQVZO4LB5W3YJSB","short_pith_number":"pith:MCFEBPLB","canonical_record":{"source":{"id":"1509.05633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-18T13:50:49Z","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.RT"],"title_canon_sha256":"e94390d2b5b9e3dbc36b18881b08755c50a389f900252330513ee0e9bda7f2f2","abstract_canon_sha256":"c277780a3daef3064dea3f8c13bf28d4eca74309cd8cca15ef70ba2d491a3c60"},"schema_version":"1.0"},"canonical_sha256":"608a40bd61af3138572ee2c3db6f09904ae652b104f24edb3f6133f1516e6b9a","source":{"kind":"arxiv","id":"1509.05633","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05633","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05633v1","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05633","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"pith_short_12","alias_value":"MCFEBPLBV4YT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MCFEBPLBV4YTQVZO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MCFEBPLB","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MCFEBPLBV4YTQVZO4LB5W3YJSB","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-18T13:50:49Z","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.RT"],"title_canon_sha256":"e94390d2b5b9e3dbc36b18881b08755c50a389f900252330513ee0e9bda7f2f2","abstract_canon_sha256":"c277780a3daef3064dea3f8c13bf28d4eca74309cd8cca15ef70ba2d491a3c60"},"schema_version":"1.0"},"canonical_sha256":"608a40bd61af3138572ee2c3db6f09904ae652b104f24edb3f6133f1516e6b9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:42.727878Z","signature_b64":"OXifYOq/Vd24y4pffDQyQK6MH/KfEXrvYPUyfjguE8RwglBzdnAMZ4A8Aj+fF4YtDQ0nsU3/w6s6WuAbqjOjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"608a40bd61af3138572ee2c3db6f09904ae652b104f24edb3f6133f1516e6b9a","last_reissued_at":"2026-05-18T01:32:42.727462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:42.727462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05633","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5D86DdtTkBqWHpVfxpZHyzxkLcQHQwaZk/ZzupVRrDZhN4OYLV0CTvDUBnpfbz23sVrSO1ewtX28U4UrxiYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:13:04.820681Z"},"content_sha256":"35e44c439bfc42dc0c296185ef2714cee88584cb13a9325ddc2cbae613dd9d71","schema_version":"1.0","event_id":"sha256:35e44c439bfc42dc0c296185ef2714cee88584cb13a9325ddc2cbae613dd9d71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MCFEBPLBV4YTQVZO4LB5W3YJSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Giuseppe Sellaroli","submitted_at":"2015-09-18T13:50:49Z","abstract_excerpt":"The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. This paper generalises it to arbitrary Lie groups, possibly non-compact. The result relies on knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05633","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWZGuChlAOfsp3vVCRy2hOBoUCxqGqy1X2yRJUHiUSJBuAThWIYtP1L3We1jqYZD4UjSUjvN1x3GsRTzAQA7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:13:04.821215Z"},"content_sha256":"04f34871c796261ae84b27294159198e941dfb27d5050eb4ff60cb409e3ad530","schema_version":"1.0","event_id":"sha256:04f34871c796261ae84b27294159198e941dfb27d5050eb4ff60cb409e3ad530"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB/bundle.json","state_url":"https://pith.science/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB/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":"2026-06-12T07:13:04Z","links":{"resolver":"https://pith.science/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB","bundle":"https://pith.science/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB/bundle.json","state":"https://pith.science/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MCFEBPLBV4YTQVZO4LB5W3YJSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MCFEBPLBV4YTQVZO4LB5W3YJSB","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":"c277780a3daef3064dea3f8c13bf28d4eca74309cd8cca15ef70ba2d491a3c60","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-18T13:50:49Z","title_canon_sha256":"e94390d2b5b9e3dbc36b18881b08755c50a389f900252330513ee0e9bda7f2f2"},"schema_version":"1.0","source":{"id":"1509.05633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05633","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05633v1","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05633","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"pith_short_12","alias_value":"MCFEBPLBV4YT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MCFEBPLBV4YTQVZO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MCFEBPLB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:04f34871c796261ae84b27294159198e941dfb27d5050eb4ff60cb409e3ad530","target":"graph","created_at":"2026-05-18T01:32:42Z","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":"The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. This paper generalises it to arbitrary Lie groups, possibly non-compact. The result relies on knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representati","authors_text":"Giuseppe Sellaroli","cross_cats":["gr-qc","hep-th","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-18T13:50:49Z","title":"Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05633","kind":"arxiv","version":1},"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":"sha256:35e44c439bfc42dc0c296185ef2714cee88584cb13a9325ddc2cbae613dd9d71","target":"record","created_at":"2026-05-18T01:32:42Z","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":"c277780a3daef3064dea3f8c13bf28d4eca74309cd8cca15ef70ba2d491a3c60","cross_cats_sorted":["gr-qc","hep-th","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-18T13:50:49Z","title_canon_sha256":"e94390d2b5b9e3dbc36b18881b08755c50a389f900252330513ee0e9bda7f2f2"},"schema_version":"1.0","source":{"id":"1509.05633","kind":"arxiv","version":1}},"canonical_sha256":"608a40bd61af3138572ee2c3db6f09904ae652b104f24edb3f6133f1516e6b9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"608a40bd61af3138572ee2c3db6f09904ae652b104f24edb3f6133f1516e6b9a","first_computed_at":"2026-05-18T01:32:42.727462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:42.727462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXifYOq/Vd24y4pffDQyQK6MH/KfEXrvYPUyfjguE8RwglBzdnAMZ4A8Aj+fF4YtDQ0nsU3/w6s6WuAbqjOjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:42.727878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35e44c439bfc42dc0c296185ef2714cee88584cb13a9325ddc2cbae613dd9d71","sha256:04f34871c796261ae84b27294159198e941dfb27d5050eb4ff60cb409e3ad530"],"state_sha256":"e0d8d160113691ba2333780214eed2f4e0c3ab0e61b3e22c7c759dc684bf041e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GdxIHj3HnyCr0kDZPmFYaBeRDoW3VHQzyE+QQ460ZT3aom/xA9/TVjA0YgkQOS86iqMHUWPT2afTe7wFbiV9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:13:04.823916Z","bundle_sha256":"9306ff0d8859ea0cfb27147838b596bdbfeb34aa20b621ec9c2b529c63822e5a"}}