{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V7HGZHDCXXTA63E6SCRSBZWTOF","short_pith_number":"pith:V7HGZHDC","schema_version":"1.0","canonical_sha256":"afce6c9c62bde60f6c9e90a320e6d37165c6a66a9b9420d24b3027c490a40ae9","source":{"kind":"arxiv","id":"1711.05343","version":1},"attestation_state":"computed","paper":{"title":"On Infinite Order Simple Current Extensions of Vertex Operator Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.CT","authors_text":"Jean Auger, Matt Rupert","submitted_at":"2017-11-14T22:54:26Z","abstract_excerpt":"We construct a direct sum completion $\\mathcal{C}_{\\oplus}$ of a given braided monoidal category $\\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of vertex operator algebras as seen in \\cite{CKL}. As an example, we construct the vertex operator algebra $V_L$ associated to an even lattice $L$ as an infinite order simple current extension of the Heisenberg VOA and recover the structure of its module category through categorical considerations."},"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":"1711.05343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-11-14T22:54:26Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"708e9b2c8a0fc39f918a4b64340bf14f5ba9726272dd65b5433f172ee212a951","abstract_canon_sha256":"38756d8c8666c52c28f411f2107ce0847a56046f906f0b31e8b44d15ad9628aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:33.593929Z","signature_b64":"5LimKmwV1Z3Cb/7iji3Pxr18GNLx+KBTXkyUoGvElwkH8a5YwsKE66XbswJXhcCvslDqWOtXzenDQ5fw8rpRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afce6c9c62bde60f6c9e90a320e6d37165c6a66a9b9420d24b3027c490a40ae9","last_reissued_at":"2026-05-18T00:30:33.593222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:33.593222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Infinite Order Simple Current Extensions of Vertex Operator Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.CT","authors_text":"Jean Auger, Matt Rupert","submitted_at":"2017-11-14T22:54:26Z","abstract_excerpt":"We construct a direct sum completion $\\mathcal{C}_{\\oplus}$ of a given braided monoidal category $\\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of vertex operator algebras as seen in \\cite{CKL}. As an example, we construct the vertex operator algebra $V_L$ associated to an even lattice $L$ as an infinite order simple current extension of the Heisenberg VOA and recover the structure of its module category through categorical considerations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05343","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":"1711.05343","created_at":"2026-05-18T00:30:33.593366+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05343v1","created_at":"2026-05-18T00:30:33.593366+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05343","created_at":"2026-05-18T00:30:33.593366+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7HGZHDCXXTA","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7HGZHDCXXTA63E6","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7HGZHDC","created_at":"2026-05-18T12:31:49.984773+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/V7HGZHDCXXTA63E6SCRSBZWTOF","json":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF.json","graph_json":"https://pith.science/api/pith-number/V7HGZHDCXXTA63E6SCRSBZWTOF/graph.json","events_json":"https://pith.science/api/pith-number/V7HGZHDCXXTA63E6SCRSBZWTOF/events.json","paper":"https://pith.science/paper/V7HGZHDC"},"agent_actions":{"view_html":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF","download_json":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF.json","view_paper":"https://pith.science/paper/V7HGZHDC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05343&json=true","fetch_graph":"https://pith.science/api/pith-number/V7HGZHDCXXTA63E6SCRSBZWTOF/graph.json","fetch_events":"https://pith.science/api/pith-number/V7HGZHDCXXTA63E6SCRSBZWTOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF/action/storage_attestation","attest_author":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF/action/author_attestation","sign_citation":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF/action/citation_signature","submit_replication":"https://pith.science/pith/V7HGZHDCXXTA63E6SCRSBZWTOF/action/replication_record"}},"created_at":"2026-05-18T00:30:33.593366+00:00","updated_at":"2026-05-18T00:30:33.593366+00:00"}