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Suppose $I(\\cdot, z)$ is an intertwining operator of type $({array}{c} M^{3} M^{1} M^{2} {array}) $. We construct an $A_{g_1g_2}(V)$-$A_{g_2}(V)$-bimodule $A_{g_1g_2, g_2}(M^1)$ which determines the action of $M^1$ from the bottom level of $M^2$ to the bottom level of $M^3$ and explored its connections with fusion rules."},"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":"2204.00238","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.QA","submitted_at":"2022-04-01T06:57:31Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"d0b62dbce348f89561d14b082c757f12481f50c3351f3f50b5d5ac0c8608751a","abstract_canon_sha256":"0c90bb018a1c94eed2590e863e380ab2cf2736b17734151e42706522117b22de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:42.887487Z","signature_b64":"JIePE85Ihyr/IZLaoY/wjsAnYjVRalORzwyroVbLszvDGVi3bAaQndpHOwM7cU5+AJTmGyqi/9I6qOoQ8gDPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cfb120c2f6881fc494dfbe10d6e6043d1315cc303dd31322d6b42e696ae75d1","last_reissued_at":"2026-06-23T01:12:42.886984Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:42.886984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bimodues associated to twisted modules of vertex operator algebras and fusion rules","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Yiyi Zhu","submitted_at":"2022-04-01T06:57:31Z","abstract_excerpt":"Let $V$ be a vertex operator algebra, $T\\in \\mathbb{N}$ and $(M^k, Y_{M^k})$ for $k=1, 2, 3$ be a $g_k$-twisted module, where $g_k$ are commuting automorphisms of $V$ such that $g_k^T=1$ for $k=1, 2, 3$ and $g_3=g_1g_2$. Suppose $I(\\cdot, z)$ is an intertwining operator of type $({array}{c} M^{3} M^{1} M^{2} {array}) $. We construct an $A_{g_1g_2}(V)$-$A_{g_2}(V)$-bimodule $A_{g_1g_2, g_2}(M^1)$ which determines the action of $M^1$ from the bottom level of $M^2$ to the bottom level of $M^3$ and explored its connections with fusion rules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00238","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.00238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2204.00238","created_at":"2026-06-23T01:12:42.887048+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.00238v3","created_at":"2026-06-23T01:12:42.887048+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00238","created_at":"2026-06-23T01:12:42.887048+00:00"},{"alias_kind":"pith_short_12","alias_value":"LT5REDBPNCA7","created_at":"2026-06-23T01:12:42.887048+00:00"},{"alias_kind":"pith_short_16","alias_value":"LT5REDBPNCA7YSKN","created_at":"2026-06-23T01:12:42.887048+00:00"},{"alias_kind":"pith_short_8","alias_value":"LT5REDBP","created_at":"2026-06-23T01:12:42.887048+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/LT5REDBPNCA7YSKN7PQQ23TAIP","json":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP.json","graph_json":"https://pith.science/api/pith-number/LT5REDBPNCA7YSKN7PQQ23TAIP/graph.json","events_json":"https://pith.science/api/pith-number/LT5REDBPNCA7YSKN7PQQ23TAIP/events.json","paper":"https://pith.science/paper/LT5REDBP"},"agent_actions":{"view_html":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP","download_json":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP.json","view_paper":"https://pith.science/paper/LT5REDBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.00238&json=true","fetch_graph":"https://pith.science/api/pith-number/LT5REDBPNCA7YSKN7PQQ23TAIP/graph.json","fetch_events":"https://pith.science/api/pith-number/LT5REDBPNCA7YSKN7PQQ23TAIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP/action/storage_attestation","attest_author":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP/action/author_attestation","sign_citation":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP/action/citation_signature","submit_replication":"https://pith.science/pith/LT5REDBPNCA7YSKN7PQQ23TAIP/action/replication_record"}},"created_at":"2026-06-23T01:12:42.887048+00:00","updated_at":"2026-06-23T01:12:42.887048+00:00"}