{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:PIKIBTZHVQDTWS4AEDZKUPWDAQ","short_pith_number":"pith:PIKIBTZH","schema_version":"1.0","canonical_sha256":"7a1480cf27ac073b4b8020f2aa3ec3041adfef369aa50ff08ff5a708653e2644","source":{"kind":"arxiv","id":"hep-th/9902029","version":3},"attestation_state":"computed","paper":{"title":"Vacuum structure in supersymmetric Yang-Mills theories with any gauge group","license":"","headline":"","cross_cats":["math-ph","math.GR","math.MP"],"primary_cat":"hep-th","authors_text":"A.V. Smilga, V.G. Kac","submitted_at":"1999-02-03T13:49:21Z","abstract_excerpt":"We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical problem of classifying the flat connections on 3-torus. The latter problem is equivalent to the problem of classification of commuting triples of elements in a connected simply connected compact Lie group which is solved in this paper. In particular, we show that for higher orthogonal SO(N), N > 6, and for all exceptional groups the moduli space of flat "},"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":"hep-th/9902029","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-02-03T13:49:21Z","cross_cats_sorted":["math-ph","math.GR","math.MP"],"title_canon_sha256":"88b3544db4e6fd7510b02cad2d8d75db6d89a4b654d5eb2d8502a30e7ad3036b","abstract_canon_sha256":"f2f3394a471caf44bafd848964205edf04a56236c26ade587158fc7420167842"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:19.075951Z","signature_b64":"XaJThNNcmf5qkhtuQNaQ/yR3LCFsTKc8xqlr3g59KwYPhYDKEQUWlMcRdVx2Qt6KlmcxKrWd4uc5PcOTVi+QBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a1480cf27ac073b4b8020f2aa3ec3041adfef369aa50ff08ff5a708653e2644","last_reissued_at":"2026-05-18T00:57:19.075185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:19.075185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vacuum structure in supersymmetric Yang-Mills theories with any gauge group","license":"","headline":"","cross_cats":["math-ph","math.GR","math.MP"],"primary_cat":"hep-th","authors_text":"A.V. Smilga, V.G. Kac","submitted_at":"1999-02-03T13:49:21Z","abstract_excerpt":"We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical problem of classifying the flat connections on 3-torus. The latter problem is equivalent to the problem of classification of commuting triples of elements in a connected simply connected compact Lie group which is solved in this paper. In particular, we show that for higher orthogonal SO(N), N > 6, and for all exceptional groups the moduli space of flat "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9902029","kind":"arxiv","version":3},"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":"hep-th/9902029","created_at":"2026-05-18T00:57:19.075303+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9902029v3","created_at":"2026-05-18T00:57:19.075303+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9902029","created_at":"2026-05-18T00:57:19.075303+00:00"},{"alias_kind":"pith_short_12","alias_value":"PIKIBTZHVQDT","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"PIKIBTZHVQDTWS4A","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"PIKIBTZH","created_at":"2026-05-18T12:25:49.631198+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2602.11696","citing_title":"Symmetry Spans and Enforced Gaplessness","ref_index":124,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ","json":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ.json","graph_json":"https://pith.science/api/pith-number/PIKIBTZHVQDTWS4AEDZKUPWDAQ/graph.json","events_json":"https://pith.science/api/pith-number/PIKIBTZHVQDTWS4AEDZKUPWDAQ/events.json","paper":"https://pith.science/paper/PIKIBTZH"},"agent_actions":{"view_html":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ","download_json":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ.json","view_paper":"https://pith.science/paper/PIKIBTZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9902029&json=true","fetch_graph":"https://pith.science/api/pith-number/PIKIBTZHVQDTWS4AEDZKUPWDAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PIKIBTZHVQDTWS4AEDZKUPWDAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ/action/storage_attestation","attest_author":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ/action/author_attestation","sign_citation":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ/action/citation_signature","submit_replication":"https://pith.science/pith/PIKIBTZHVQDTWS4AEDZKUPWDAQ/action/replication_record"}},"created_at":"2026-05-18T00:57:19.075303+00:00","updated_at":"2026-05-18T00:57:19.075303+00:00"}