{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XXXXVWJ5EGA2GJPHSIOA376B2Z","short_pith_number":"pith:XXXXVWJ5","schema_version":"1.0","canonical_sha256":"bdef7ad93d2181a325e7921c0dffc1d645f4199c581010b02f93706b2a81a637","source":{"kind":"arxiv","id":"1407.4500","version":1},"attestation_state":"computed","paper":{"title":"Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Wei{\\ss}e, Bertrand Eynard, Ga\\\"etan Borot","submitted_at":"2014-07-16T21:01:47Z","abstract_excerpt":"We study a class of scalar, linear, non-local Riemann-Hilbert problems (RHP) involving finite subgroups of PSL(2,C). We associate to such problems a (maybe infinite) root system and describe the relevance of the orbits of the Weyl group in the construction of its solutions. As an application, we study in detail the large N expansion of SU(N) or SO(N) or Sp(2N) Chern-Simons partition function Z_N(M) of 3-manifolds M that are either rational homology spheres or more generally Seifert fibered spaces. It has a matrix model-like representation, whose spectral curve can be characterized in terms of "},"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":"1407.4500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-16T21:01:47Z","cross_cats_sorted":["math.GT","math.MP"],"title_canon_sha256":"990d6c7d9de9b54a8b7e9565410d3305a5215fcc5b635471a37b78a0d8ad39a2","abstract_canon_sha256":"aba8384315bd55b90703409ad379fa991b6d94364f5d6fa68cd262465e9ca915"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:34.068370Z","signature_b64":"xRCDI/sS50nXWlAj6+QAYB7rCW1ZC3b9jyrzHWPHCHfNhOVP+llEOf8ZpVmfVpTLI6qftNBVAgoh/z7POrjWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdef7ad93d2181a325e7921c0dffc1d645f4199c581010b02f93706b2a81a637","last_reissued_at":"2026-05-18T00:47:34.067772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:34.067772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Wei{\\ss}e, Bertrand Eynard, Ga\\\"etan Borot","submitted_at":"2014-07-16T21:01:47Z","abstract_excerpt":"We study a class of scalar, linear, non-local Riemann-Hilbert problems (RHP) involving finite subgroups of PSL(2,C). We associate to such problems a (maybe infinite) root system and describe the relevance of the orbits of the Weyl group in the construction of its solutions. As an application, we study in detail the large N expansion of SU(N) or SO(N) or Sp(2N) Chern-Simons partition function Z_N(M) of 3-manifolds M that are either rational homology spheres or more generally Seifert fibered spaces. It has a matrix model-like representation, whose spectral curve can be characterized in terms of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4500","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":"1407.4500","created_at":"2026-05-18T00:47:34.067854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4500v1","created_at":"2026-05-18T00:47:34.067854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4500","created_at":"2026-05-18T00:47:34.067854+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXXXVWJ5EGA2","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXXXVWJ5EGA2GJPH","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXXXVWJ5","created_at":"2026-05-18T12:28:57.508820+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/XXXXVWJ5EGA2GJPHSIOA376B2Z","json":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z.json","graph_json":"https://pith.science/api/pith-number/XXXXVWJ5EGA2GJPHSIOA376B2Z/graph.json","events_json":"https://pith.science/api/pith-number/XXXXVWJ5EGA2GJPHSIOA376B2Z/events.json","paper":"https://pith.science/paper/XXXXVWJ5"},"agent_actions":{"view_html":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z","download_json":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z.json","view_paper":"https://pith.science/paper/XXXXVWJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4500&json=true","fetch_graph":"https://pith.science/api/pith-number/XXXXVWJ5EGA2GJPHSIOA376B2Z/graph.json","fetch_events":"https://pith.science/api/pith-number/XXXXVWJ5EGA2GJPHSIOA376B2Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z/action/storage_attestation","attest_author":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z/action/author_attestation","sign_citation":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z/action/citation_signature","submit_replication":"https://pith.science/pith/XXXXVWJ5EGA2GJPHSIOA376B2Z/action/replication_record"}},"created_at":"2026-05-18T00:47:34.067854+00:00","updated_at":"2026-05-18T00:47:34.067854+00:00"}