{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZNH3YZTEOLJG4N2VHIFQR4ZPXG","short_pith_number":"pith:ZNH3YZTE","schema_version":"1.0","canonical_sha256":"cb4fbc666472d26e37553a0b08f32fb9af5311ab55e1c4c4c3a97547fc977353","source":{"kind":"arxiv","id":"1403.4463","version":1},"attestation_state":"computed","paper":{"title":"Generalized spin representations. Part 2: Cartan-Bott periodicity for the split real En series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Max Horn, Ralf K\\\"ohl","submitted_at":"2014-03-18T14:12:22Z","abstract_excerpt":"In this article we analyze the quotients of the maximal compact subalgebras of the split real Kac-Moody algebras of the En series resulting from the generalized spin representations introduced in part 1. It turns out that these quotients satisfy a Cartan-Bott periodicity.\n  Our findings are also meaningful in the finite-dimensional cases of A2 + A1, A4, D5, E6, E7, E8, where it turns out that the generalized spin representation is injective. Consequently the observed Cartan-Bott periodicity provides a structural explanation for the seemingly sporadic isomorphism types of the maximal compact Li"},"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":"1403.4463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-18T14:12:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"dfddb84c5a16236b1e74f46f72f48f354363825d57cd967b5c86009e4351b556","abstract_canon_sha256":"c307f227321f8fea007fe610df61b9d3cfea2e70a9057d67dd6007b79c044613"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:05.721074Z","signature_b64":"b+JLasXNGaYDzduKzy7JiJTJOu4p54wfEV01y69DcOC3GtNZDH64h67HAKE/0XSUYfFg/X2lMfnNqIRsrCKJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb4fbc666472d26e37553a0b08f32fb9af5311ab55e1c4c4c3a97547fc977353","last_reissued_at":"2026-05-18T02:56:05.720649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:05.720649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized spin representations. Part 2: Cartan-Bott periodicity for the split real En series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Max Horn, Ralf K\\\"ohl","submitted_at":"2014-03-18T14:12:22Z","abstract_excerpt":"In this article we analyze the quotients of the maximal compact subalgebras of the split real Kac-Moody algebras of the En series resulting from the generalized spin representations introduced in part 1. It turns out that these quotients satisfy a Cartan-Bott periodicity.\n  Our findings are also meaningful in the finite-dimensional cases of A2 + A1, A4, D5, E6, E7, E8, where it turns out that the generalized spin representation is injective. Consequently the observed Cartan-Bott periodicity provides a structural explanation for the seemingly sporadic isomorphism types of the maximal compact Li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4463","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":"1403.4463","created_at":"2026-05-18T02:56:05.720706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.4463v1","created_at":"2026-05-18T02:56:05.720706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4463","created_at":"2026-05-18T02:56:05.720706+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZNH3YZTEOLJG","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZNH3YZTEOLJG4N2V","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZNH3YZTE","created_at":"2026-05-18T12:28:59.999130+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/ZNH3YZTEOLJG4N2VHIFQR4ZPXG","json":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG.json","graph_json":"https://pith.science/api/pith-number/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/graph.json","events_json":"https://pith.science/api/pith-number/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/events.json","paper":"https://pith.science/paper/ZNH3YZTE"},"agent_actions":{"view_html":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG","download_json":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG.json","view_paper":"https://pith.science/paper/ZNH3YZTE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.4463&json=true","fetch_graph":"https://pith.science/api/pith-number/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/graph.json","fetch_events":"https://pith.science/api/pith-number/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/action/storage_attestation","attest_author":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/action/author_attestation","sign_citation":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/action/citation_signature","submit_replication":"https://pith.science/pith/ZNH3YZTEOLJG4N2VHIFQR4ZPXG/action/replication_record"}},"created_at":"2026-05-18T02:56:05.720706+00:00","updated_at":"2026-05-18T02:56:05.720706+00:00"}