{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3LEUOEDBVAKSMQTJFEW7IHEL5Q","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":"cfad016d9025b22b100e4475c2ef12814096c8f3e2cec634154e9a4154e7339b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-20T16:25:40Z","title_canon_sha256":"1a1effcaeacc38c42275c1eecf4b3721da25a622570c3cc7e68b7b9c031d860a"},"schema_version":"1.0","source":{"id":"2606.22135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22135","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22135v1","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22135","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"3LEUOEDBVAKS","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"pith_short_16","alias_value":"3LEUOEDBVAKSMQTJ","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"pith_short_8","alias_value":"3LEUOEDB","created_at":"2026-06-23T02:13:29Z"}],"graph_snapshots":[{"event_id":"sha256:88203a0e379fc363bd6e09dd91db269000d51df47390168450af8634780ce1f8","target":"graph","created_at":"2026-06-23T02:13:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.22135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $V$ be a vertex operator algebra, and let $W^1$ and $W^2$ be restricted $V$-modules. We construct a generalized $V$-module $\\mathcal{H}(W^1, W^2)$ characterized by canonical universal properties. We show that, under suitable hypotheses, $ \\mathcal{H}(W^1, W^2)$ realizes the internal Hom object in the tensor category of restricted $V$-modules. Although our construction differs from Li's, we show that it agrees with the natural logarithmic generalization of Li's module $\\Delta(W^1, W^2)$. We further establish a canonical isomorphism between $\\mathcal{H} \\big(W^1,(W^2 )^\\prime \\big)$ and the ","authors_text":"Chao Yang, Yiyi Zhu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-20T16:25:40Z","title":"Finiteness and Construction of Internal Hom for Vertex Operator Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22135","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":"sha256:869281f2630bc60882973c91bc31826e7994f00d7f7c2b18469f3ad7cceb9d54","target":"record","created_at":"2026-06-23T02:13:29Z","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":"cfad016d9025b22b100e4475c2ef12814096c8f3e2cec634154e9a4154e7339b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-20T16:25:40Z","title_canon_sha256":"1a1effcaeacc38c42275c1eecf4b3721da25a622570c3cc7e68b7b9c031d860a"},"schema_version":"1.0","source":{"id":"2606.22135","kind":"arxiv","version":1}},"canonical_sha256":"dac9471061a815264269292df41c8bec27ceaa49aebc28ea6f39431e6450ae8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dac9471061a815264269292df41c8bec27ceaa49aebc28ea6f39431e6450ae8b","first_computed_at":"2026-06-23T02:13:29.163441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:29.163441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiDERam++P5bFllABOYXobRaxEiSn1cDmXOtIRGbk/XieLa70khF8E+3Di730F1/J13tBWgtwslxf+Wvf4+uBA==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:29.163845Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:869281f2630bc60882973c91bc31826e7994f00d7f7c2b18469f3ad7cceb9d54","sha256:88203a0e379fc363bd6e09dd91db269000d51df47390168450af8634780ce1f8"],"state_sha256":"c3d020b1b9db9fc976dd52a989ca31ee4dfbb0dd6d9961116df3c72c13ea3a91"}