{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VKN2ZVUD4EKA23Z7JXHB73JWE5","short_pith_number":"pith:VKN2ZVUD","schema_version":"1.0","canonical_sha256":"aa9bacd683e1140d6f3f4dce1fed3627498ec545be3b4dba414066e4322ed619","source":{"kind":"arxiv","id":"1702.05845","version":3},"attestation_state":"computed","paper":{"title":"Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Yi-Zhi Huang","submitted_at":"2017-02-20T03:25:46Z","abstract_excerpt":"We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$ and $g_{3}$ be automorphisms of $V$. We prove that for $g_{1}$-, $g_{2}$- and $g_{3}$-twisted $V$-modules $W_{1}$, $W_{2}$ and $W_{3}$, respectively, such that the vertex operator map for $W_{3}$ is injective, if there exists a twisted intertwining operator of type ${W_{3}\\choose W_{1}W_{2}}$ such that the images of its component operators span $W_{3}$, then $"},"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":"1702.05845","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-02-20T03:25:46Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"8ed67e1729d105eeb07a505ae2a80dcdfcf800e457618cd7073d132a360b78de","abstract_canon_sha256":"db0310d33efdc00df0bddb241a383078febf03ee5bfb49d897c6fe59dfe0ca9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:41.884964Z","signature_b64":"dzaMcD5QAicbtW5ZeQDQdVcFtNfMcKKTYJSorlzL+DdJkoM0QbdCQwEdeoqxyN5BnyJpCuNITOtJuSRgcoS5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa9bacd683e1140d6f3f4dce1fed3627498ec545be3b4dba414066e4322ed619","last_reissued_at":"2026-05-18T00:34:41.884197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:41.884197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Yi-Zhi Huang","submitted_at":"2017-02-20T03:25:46Z","abstract_excerpt":"We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$ and $g_{3}$ be automorphisms of $V$. We prove that for $g_{1}$-, $g_{2}$- and $g_{3}$-twisted $V$-modules $W_{1}$, $W_{2}$ and $W_{3}$, respectively, such that the vertex operator map for $W_{3}$ is injective, if there exists a twisted intertwining operator of type ${W_{3}\\choose W_{1}W_{2}}$ such that the images of its component operators span $W_{3}$, then $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05845","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":"1702.05845","created_at":"2026-05-18T00:34:41.884327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05845v3","created_at":"2026-05-18T00:34:41.884327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05845","created_at":"2026-05-18T00:34:41.884327+00:00"},{"alias_kind":"pith_short_12","alias_value":"VKN2ZVUD4EKA","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VKN2ZVUD4EKA23Z7","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VKN2ZVUD","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/VKN2ZVUD4EKA23Z7JXHB73JWE5","json":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5.json","graph_json":"https://pith.science/api/pith-number/VKN2ZVUD4EKA23Z7JXHB73JWE5/graph.json","events_json":"https://pith.science/api/pith-number/VKN2ZVUD4EKA23Z7JXHB73JWE5/events.json","paper":"https://pith.science/paper/VKN2ZVUD"},"agent_actions":{"view_html":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5","download_json":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5.json","view_paper":"https://pith.science/paper/VKN2ZVUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05845&json=true","fetch_graph":"https://pith.science/api/pith-number/VKN2ZVUD4EKA23Z7JXHB73JWE5/graph.json","fetch_events":"https://pith.science/api/pith-number/VKN2ZVUD4EKA23Z7JXHB73JWE5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5/action/storage_attestation","attest_author":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5/action/author_attestation","sign_citation":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5/action/citation_signature","submit_replication":"https://pith.science/pith/VKN2ZVUD4EKA23Z7JXHB73JWE5/action/replication_record"}},"created_at":"2026-05-18T00:34:41.884327+00:00","updated_at":"2026-05-18T00:34:41.884327+00:00"}