{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PSKIVUFMXAQBN73XMSPPZGWZDP","short_pith_number":"pith:PSKIVUFM","schema_version":"1.0","canonical_sha256":"7c948ad0acb82016ff77649efc9ad91bfb1c33cb171a40c6a8292a0e048eedd3","source":{"kind":"arxiv","id":"1407.2706","version":1},"attestation_state":"computed","paper":{"title":"SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.RT","authors_text":"C. Carmeli, R. Fioresi, S. D. Kwok","submitted_at":"2014-07-10T06:30:24Z","abstract_excerpt":"The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\\mathbf C}^{1|1})^\\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we g"},"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":"1407.2706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-10T06:30:24Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"15506f900440ceeb70fdc84fec0e4e76cb6cf896e45734d3ef2af7383387fdaf","abstract_canon_sha256":"0804bff705ed1f958b0b4e0fc2ff6f0f7d5b9cb91925b428abdd04420d97e966"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:03.418662Z","signature_b64":"g0ZfsnIETsejWBFJfaYP5lSz3Ghu0EvJY6KCHw022H6T4y8xSWwJnH45lgEPSlC4M0b8+Aq32Yrsag8Q0qP9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c948ad0acb82016ff77649efc9ad91bfb1c33cb171a40c6a8292a0e048eedd3","last_reissued_at":"2026-05-18T01:25:03.417906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:03.417906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.RT","authors_text":"C. Carmeli, R. Fioresi, S. D. Kwok","submitted_at":"2014-07-10T06:30:24Z","abstract_excerpt":"The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\\mathbf C}^{1|1})^\\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2706","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":"1407.2706","created_at":"2026-05-18T01:25:03.418018+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.2706v1","created_at":"2026-05-18T01:25:03.418018+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2706","created_at":"2026-05-18T01:25:03.418018+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSKIVUFMXAQB","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSKIVUFMXAQBN73X","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSKIVUFM","created_at":"2026-05-18T12:28:43.426989+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/PSKIVUFMXAQBN73XMSPPZGWZDP","json":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP.json","graph_json":"https://pith.science/api/pith-number/PSKIVUFMXAQBN73XMSPPZGWZDP/graph.json","events_json":"https://pith.science/api/pith-number/PSKIVUFMXAQBN73XMSPPZGWZDP/events.json","paper":"https://pith.science/paper/PSKIVUFM"},"agent_actions":{"view_html":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP","download_json":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP.json","view_paper":"https://pith.science/paper/PSKIVUFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.2706&json=true","fetch_graph":"https://pith.science/api/pith-number/PSKIVUFMXAQBN73XMSPPZGWZDP/graph.json","fetch_events":"https://pith.science/api/pith-number/PSKIVUFMXAQBN73XMSPPZGWZDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP/action/storage_attestation","attest_author":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP/action/author_attestation","sign_citation":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP/action/citation_signature","submit_replication":"https://pith.science/pith/PSKIVUFMXAQBN73XMSPPZGWZDP/action/replication_record"}},"created_at":"2026-05-18T01:25:03.418018+00:00","updated_at":"2026-05-18T01:25:03.418018+00:00"}