{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IZYUCD4GIPPYOK7A2GDXJWIGMD","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":"c05d25fd060de031d297f7a17a1fe6eed5941d23c635f9909feb533a4574bb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-08-29T02:10:34Z","title_canon_sha256":"e307aadaf15dff1e1cbd668461bf4c81ff7b300df23d68149b1d6ac908bac1cb"},"schema_version":"1.0","source":{"id":"1608.07890","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07890","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07890v3","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07890","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"IZYUCD4GIPPY","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IZYUCD4GIPPYOK7A","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IZYUCD4G","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:ace78796e093f7f3c790cd14743b681c520481420bf38e927fac2b14ef6fc6a4","target":"graph","created_at":"2026-05-18T00:34:57Z","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":"Let $M(1)$ be the vertex operator algebra with the Virasoro element $\\omega$ associated to the Heisenberg algebra of rank $1$ and let $M(1)^{+}$ be the subalgebra of $M(1)$ consisting of the fixed points of an automorphism of $M(1)$ of order $2$. We classify the simple weak $M(1)^{+}$-modules with a non-zero element $w$ such that for some integer $s\\geq 2$, $\\omega_i w\\in{\\mathbb C}w$ ($i=\\lfloor s/2\\rfloor+1,\\lfloor s/2\\rfloor+2,\\ldots,s-1$), $\\omega_{s}w\\in{\\mathbb C}^{\\times}w$, and $\\omega_i w=0$ for all $i>s$. The result says that any such simple weak $M(1)^{+}$-module is isomorphic to so","authors_text":"Kenichiro Tanabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-08-29T02:10:34Z","title":"Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank $1$ by an automorphism of order $2$ and Whittaker vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07890","kind":"arxiv","version":3},"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":"sha256:789053d5716d544ec7034380875b580b96c20ded540138da560082e4f9daea48","target":"record","created_at":"2026-05-18T00:34:57Z","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":"c05d25fd060de031d297f7a17a1fe6eed5941d23c635f9909feb533a4574bb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-08-29T02:10:34Z","title_canon_sha256":"e307aadaf15dff1e1cbd668461bf4c81ff7b300df23d68149b1d6ac908bac1cb"},"schema_version":"1.0","source":{"id":"1608.07890","kind":"arxiv","version":3}},"canonical_sha256":"4671410f8643df872be0d18774d90660e5ce0831c9c7824e28ff99c0dfd8c976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4671410f8643df872be0d18774d90660e5ce0831c9c7824e28ff99c0dfd8c976","first_computed_at":"2026-05-18T00:34:57.817819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:57.817819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GBXrkdyyI/3xsVaXYIOjDAz0Iu6wLCRJRm3ZOpnAtOL+yBDwM4jdBDkUAx/NpbJTZv2R1QgY8Jgco2xsbVjMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:57.818367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07890","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:789053d5716d544ec7034380875b580b96c20ded540138da560082e4f9daea48","sha256:ace78796e093f7f3c790cd14743b681c520481420bf38e927fac2b14ef6fc6a4"],"state_sha256":"6b4c25ad28737e948c23a91a3f7083ca13045d9e82e6358720dba78fc94779f4"}