{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V7HGZHDCXXTA63E6SCRSBZWTOF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"38756d8c8666c52c28f411f2107ce0847a56046f906f0b31e8b44d15ad9628aa","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-11-14T22:54:26Z","title_canon_sha256":"708e9b2c8a0fc39f918a4b64340bf14f5ba9726272dd65b5433f172ee212a951"},"schema_version":"1.0","source":{"id":"1711.05343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05343","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05343v1","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05343","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"V7HGZHDCXXTA","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V7HGZHDCXXTA63E6","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V7HGZHDC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:bd4708f025807d13497e10f01831515fe05b362645c764c36f43a64913e51ebf","target":"graph","created_at":"2026-05-18T00:30:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Jean Auger, Matt Rupert","cross_cats":["math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-11-14T22:54:26Z","title":"On Infinite Order Simple Current Extensions of Vertex Operator Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05343","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:20060eae97a16e22325e20343cd60885a00c5e8efc8da698dbb482374f50d66c","target":"record","created_at":"2026-05-18T00:30:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"38756d8c8666c52c28f411f2107ce0847a56046f906f0b31e8b44d15ad9628aa","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-11-14T22:54:26Z","title_canon_sha256":"708e9b2c8a0fc39f918a4b64340bf14f5ba9726272dd65b5433f172ee212a951"},"schema_version":"1.0","source":{"id":"1711.05343","kind":"arxiv","version":1}},"canonical_sha256":"afce6c9c62bde60f6c9e90a320e6d37165c6a66a9b9420d24b3027c490a40ae9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afce6c9c62bde60f6c9e90a320e6d37165c6a66a9b9420d24b3027c490a40ae9","first_computed_at":"2026-05-18T00:30:33.593222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:33.593222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5LimKmwV1Z3Cb/7iji3Pxr18GNLx+KBTXkyUoGvElwkH8a5YwsKE66XbswJXhcCvslDqWOtXzenDQ5fw8rpRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:33.593929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20060eae97a16e22325e20343cd60885a00c5e8efc8da698dbb482374f50d66c","sha256:bd4708f025807d13497e10f01831515fe05b362645c764c36f43a64913e51ebf"],"state_sha256":"ae84dcf3a24462db80d08dc679f4ec6598a4f7edcfe955a01eebf4c737c53a03"}