{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HSREZPU3ZCUGEBPDQR5II53AFJ","short_pith_number":"pith:HSREZPU3","schema_version":"1.0","canonical_sha256":"3ca24cbe9bc8a86205e3847a8477602a65f2038cc862461bb0971e35d46e6ad9","source":{"kind":"arxiv","id":"1708.00560","version":1},"attestation_state":"computed","paper":{"title":"Theta functions for lattices of SU(3) hyper-roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Robert Coquereaux","submitted_at":"2017-08-02T00:32:02Z","abstract_excerpt":"We recall the definition of the hyper-roots that can be associated to modules-categories over the fusion categories defined by the choice of a simple Lie group G together with a positive integer k. This definition was proposed in 2000, using another language, by Adrian Ocneanu. If G=SU(2), the obtained hyper-roots coincide with the usual roots for ADE Dynkin diagrams. We consider the associated lattices when G=SU(3) and determine their theta functions in a number of cases; these functions can be expressed as modular forms twisted by appropriate Dirichlet characters."},"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":"1708.00560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-08-02T00:32:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0c946e03a697e7d664b170e74e92bf12e9181ab106b9166c807486fa52cbb696","abstract_canon_sha256":"a23385de4abaea02e74b24dfab07d748fc63bd6029f001ac144d2220947b8753"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:11.544343Z","signature_b64":"yZZ5ay2oFOuF6f9kQ57Vb6eoIRBhHZzopbi/DpgKTza8uU1IgVGF/l2LT3MIzL3v3mA17+wa8TLD5kA+bmmDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ca24cbe9bc8a86205e3847a8477602a65f2038cc862461bb0971e35d46e6ad9","last_reissued_at":"2026-05-18T00:11:11.543575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:11.543575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theta functions for lattices of SU(3) hyper-roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Robert Coquereaux","submitted_at":"2017-08-02T00:32:02Z","abstract_excerpt":"We recall the definition of the hyper-roots that can be associated to modules-categories over the fusion categories defined by the choice of a simple Lie group G together with a positive integer k. This definition was proposed in 2000, using another language, by Adrian Ocneanu. If G=SU(2), the obtained hyper-roots coincide with the usual roots for ADE Dynkin diagrams. We consider the associated lattices when G=SU(3) and determine their theta functions in a number of cases; these functions can be expressed as modular forms twisted by appropriate Dirichlet characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00560","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":"1708.00560","created_at":"2026-05-18T00:11:11.543710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.00560v1","created_at":"2026-05-18T00:11:11.543710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00560","created_at":"2026-05-18T00:11:11.543710+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSREZPU3ZCUG","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSREZPU3ZCUGEBPD","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSREZPU3","created_at":"2026-05-18T12:31:18.294218+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/HSREZPU3ZCUGEBPDQR5II53AFJ","json":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ.json","graph_json":"https://pith.science/api/pith-number/HSREZPU3ZCUGEBPDQR5II53AFJ/graph.json","events_json":"https://pith.science/api/pith-number/HSREZPU3ZCUGEBPDQR5II53AFJ/events.json","paper":"https://pith.science/paper/HSREZPU3"},"agent_actions":{"view_html":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ","download_json":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ.json","view_paper":"https://pith.science/paper/HSREZPU3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.00560&json=true","fetch_graph":"https://pith.science/api/pith-number/HSREZPU3ZCUGEBPDQR5II53AFJ/graph.json","fetch_events":"https://pith.science/api/pith-number/HSREZPU3ZCUGEBPDQR5II53AFJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ/action/storage_attestation","attest_author":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ/action/author_attestation","sign_citation":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ/action/citation_signature","submit_replication":"https://pith.science/pith/HSREZPU3ZCUGEBPDQR5II53AFJ/action/replication_record"}},"created_at":"2026-05-18T00:11:11.543710+00:00","updated_at":"2026-05-18T00:11:11.543710+00:00"}