{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:J4MWWVLC2N2K5HXRSHQXGG7XU4","short_pith_number":"pith:J4MWWVLC","schema_version":"1.0","canonical_sha256":"4f196b5562d374ae9ef191e1731bf7a7351813a389798a4c0485d59989f2d1e7","source":{"kind":"arxiv","id":"1503.08461","version":1},"attestation_state":"computed","paper":{"title":"Non-compact groups of inner type and factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Arlo Caine, Doug Pickrell","submitted_at":"2015-03-29T17:21:27Z","abstract_excerpt":"We investigate Birkhoff (or triangular) factorization and (what we propose to call) root subgroup factorization for elements of a noncompact simple Lie group $G_0$ of inner type. For compact groups root subgroup factorization is related to Bott-Samelson desingularization, and many striking applications have been discovered by Lu (\\cite{Lu}). In this paper, in the inner noncompact case, we obtain parallel characterizations of the Birkhoff components of $G_0$ and an analogous construction of root subgroup coordinates for the Birkhoff components. As in the compact case, we show that the restricti"},"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":"1503.08461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-03-29T17:21:27Z","cross_cats_sorted":[],"title_canon_sha256":"3a07de97ec7cff5872107934a12587d0d65801cd9f877a551426ac3882033d66","abstract_canon_sha256":"52119f2a3298eefe7e14ff422b5f64090054b7d1b6baee5be0cffaa3c0271e56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:02.433708Z","signature_b64":"TWBxwGC9I1Y+pgVP+c4Pss8xyybwTNUYJmfYx7BCBGwj9/C/RZWumCs/S8TUSixtfY+WK/BNC3FXsJO89tv9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f196b5562d374ae9ef191e1731bf7a7351813a389798a4c0485d59989f2d1e7","last_reissued_at":"2026-05-18T00:41:02.433027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:02.433027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-compact groups of inner type and factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Arlo Caine, Doug Pickrell","submitted_at":"2015-03-29T17:21:27Z","abstract_excerpt":"We investigate Birkhoff (or triangular) factorization and (what we propose to call) root subgroup factorization for elements of a noncompact simple Lie group $G_0$ of inner type. For compact groups root subgroup factorization is related to Bott-Samelson desingularization, and many striking applications have been discovered by Lu (\\cite{Lu}). In this paper, in the inner noncompact case, we obtain parallel characterizations of the Birkhoff components of $G_0$ and an analogous construction of root subgroup coordinates for the Birkhoff components. As in the compact case, we show that the restricti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08461","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":"1503.08461","created_at":"2026-05-18T00:41:02.433135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08461v1","created_at":"2026-05-18T00:41:02.433135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08461","created_at":"2026-05-18T00:41:02.433135+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4MWWVLC2N2K","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4MWWVLC2N2K5HXR","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4MWWVLC","created_at":"2026-05-18T12:29:27.538025+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/J4MWWVLC2N2K5HXRSHQXGG7XU4","json":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4.json","graph_json":"https://pith.science/api/pith-number/J4MWWVLC2N2K5HXRSHQXGG7XU4/graph.json","events_json":"https://pith.science/api/pith-number/J4MWWVLC2N2K5HXRSHQXGG7XU4/events.json","paper":"https://pith.science/paper/J4MWWVLC"},"agent_actions":{"view_html":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4","download_json":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4.json","view_paper":"https://pith.science/paper/J4MWWVLC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08461&json=true","fetch_graph":"https://pith.science/api/pith-number/J4MWWVLC2N2K5HXRSHQXGG7XU4/graph.json","fetch_events":"https://pith.science/api/pith-number/J4MWWVLC2N2K5HXRSHQXGG7XU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4/action/storage_attestation","attest_author":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4/action/author_attestation","sign_citation":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4/action/citation_signature","submit_replication":"https://pith.science/pith/J4MWWVLC2N2K5HXRSHQXGG7XU4/action/replication_record"}},"created_at":"2026-05-18T00:41:02.433135+00:00","updated_at":"2026-05-18T00:41:02.433135+00:00"}