{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YAAFRZDBKMDMIF64G5PRZSOF6N","short_pith_number":"pith:YAAFRZDB","canonical_record":{"source":{"id":"2205.05481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-05-11T13:23:03Z","cross_cats_sorted":[],"title_canon_sha256":"ad8c08d78871feeb752c797fccbb94613264c6b2d00a30e1a2210ddddcf43abd","abstract_canon_sha256":"18efecc70d20468d5004751c1b5c61ca208028bd763441849e7695302031bacb"},"schema_version":"1.0"},"canonical_sha256":"c00058e4615306c417dc375f1cc9c5f34ec542a9d3ce7b8c46a8d8768e5b2918","source":{"kind":"arxiv","id":"2205.05481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.05481","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"2205.05481v1","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.05481","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"YAAFRZDBKMDM","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"pith_short_16","alias_value":"YAAFRZDBKMDMIF64","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"pith_short_8","alias_value":"YAAFRZDB","created_at":"2026-07-05T04:22:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YAAFRZDBKMDMIF64G5PRZSOF6N","target":"record","payload":{"canonical_record":{"source":{"id":"2205.05481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-05-11T13:23:03Z","cross_cats_sorted":[],"title_canon_sha256":"ad8c08d78871feeb752c797fccbb94613264c6b2d00a30e1a2210ddddcf43abd","abstract_canon_sha256":"18efecc70d20468d5004751c1b5c61ca208028bd763441849e7695302031bacb"},"schema_version":"1.0"},"canonical_sha256":"c00058e4615306c417dc375f1cc9c5f34ec542a9d3ce7b8c46a8d8768e5b2918","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:22:26.179414Z","signature_b64":"5xYMOVnxymXhvlhfaGA7FZhRxN7ji4OHh1XfzS8xfhpwqvdrgePMZotg/HdwJOs6E1npWsvQS9dJuKUlS2puAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c00058e4615306c417dc375f1cc9c5f34ec542a9d3ce7b8c46a8d8768e5b2918","last_reissued_at":"2026-07-05T04:22:26.179046Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:22:26.179046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.05481","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:22:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Kt+QRV9WtCN0Br2/d2BOlU18oJsMk1gI/erivR/JLQVnO8U7s6QQKsy76aOjd7AGUpVZ4EWZFRJR0/sfCh/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:01:11.998654Z"},"content_sha256":"488ce2817685ef6041b5a31de455b02f3292d610e287994144492f1f87ea577e","schema_version":"1.0","event_id":"sha256:488ce2817685ef6041b5a31de455b02f3292d610e287994144492f1f87ea577e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YAAFRZDBKMDMIF64G5PRZSOF6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular representations and $A_{n}(V)$-$A_{m}(V)$ bimodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Haisheng Li","submitted_at":"2022-05-11T13:23:03Z","abstract_excerpt":"This paper is to establish a natural connection between regular representations for a vertex operator algebra $V$ and $A_{n}(V)$-$A_{m}(V)$ bimodules of Dong and Jiang. Let $W$ be a weak $V$-module and let $(m,n)$ be a pair of nonnegative integers. We study two quotient spaces $A_{n,m}^{\\dagger}(W)$ and $A^{\\diamond}_{n,m}(W)$ of $W$.\n  It is proved that the dual space $A^{\\dagger}_{n,m}(W)^{*}$ viewed as a subspace of $W^*$ coincides with the level-$(m,n)$ vacuum subspace of the regular representation module $\\mathfrak{D}_{(-1)}(W)$. By making use of this connection, we obtain an $A_{n}(V)$-$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.05481","kind":"arxiv","version":1},"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/2205.05481/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:22:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGRsmRwHObIQUBsIpd10yHcUnjRZCWqSQKg/7xX2tgUwmkVikR6x3S3n7myE6rdvQ0thNe30LBhhZnkrRduvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:01:11.999172Z"},"content_sha256":"5ea80e0eea1551603c8fb9a6669d8a8f6b1caf17e7b18baf2dfdef92418f61ff","schema_version":"1.0","event_id":"sha256:5ea80e0eea1551603c8fb9a6669d8a8f6b1caf17e7b18baf2dfdef92418f61ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAAFRZDBKMDMIF64G5PRZSOF6N/bundle.json","state_url":"https://pith.science/pith/YAAFRZDBKMDMIF64G5PRZSOF6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAAFRZDBKMDMIF64G5PRZSOF6N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T15:01:12Z","links":{"resolver":"https://pith.science/pith/YAAFRZDBKMDMIF64G5PRZSOF6N","bundle":"https://pith.science/pith/YAAFRZDBKMDMIF64G5PRZSOF6N/bundle.json","state":"https://pith.science/pith/YAAFRZDBKMDMIF64G5PRZSOF6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAAFRZDBKMDMIF64G5PRZSOF6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YAAFRZDBKMDMIF64G5PRZSOF6N","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":"18efecc70d20468d5004751c1b5c61ca208028bd763441849e7695302031bacb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-05-11T13:23:03Z","title_canon_sha256":"ad8c08d78871feeb752c797fccbb94613264c6b2d00a30e1a2210ddddcf43abd"},"schema_version":"1.0","source":{"id":"2205.05481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.05481","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"2205.05481v1","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.05481","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"YAAFRZDBKMDM","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"pith_short_16","alias_value":"YAAFRZDBKMDMIF64","created_at":"2026-07-05T04:22:26Z"},{"alias_kind":"pith_short_8","alias_value":"YAAFRZDB","created_at":"2026-07-05T04:22:26Z"}],"graph_snapshots":[{"event_id":"sha256:5ea80e0eea1551603c8fb9a6669d8a8f6b1caf17e7b18baf2dfdef92418f61ff","target":"graph","created_at":"2026-07-05T04:22:26Z","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/2205.05481/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is to establish a natural connection between regular representations for a vertex operator algebra $V$ and $A_{n}(V)$-$A_{m}(V)$ bimodules of Dong and Jiang. Let $W$ be a weak $V$-module and let $(m,n)$ be a pair of nonnegative integers. We study two quotient spaces $A_{n,m}^{\\dagger}(W)$ and $A^{\\diamond}_{n,m}(W)$ of $W$.\n  It is proved that the dual space $A^{\\dagger}_{n,m}(W)^{*}$ viewed as a subspace of $W^*$ coincides with the level-$(m,n)$ vacuum subspace of the regular representation module $\\mathfrak{D}_{(-1)}(W)$. By making use of this connection, we obtain an $A_{n}(V)$-$","authors_text":"Haisheng Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-05-11T13:23:03Z","title":"Regular representations and $A_{n}(V)$-$A_{m}(V)$ bimodules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.05481","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":"sha256:488ce2817685ef6041b5a31de455b02f3292d610e287994144492f1f87ea577e","target":"record","created_at":"2026-07-05T04:22:26Z","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":"18efecc70d20468d5004751c1b5c61ca208028bd763441849e7695302031bacb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2022-05-11T13:23:03Z","title_canon_sha256":"ad8c08d78871feeb752c797fccbb94613264c6b2d00a30e1a2210ddddcf43abd"},"schema_version":"1.0","source":{"id":"2205.05481","kind":"arxiv","version":1}},"canonical_sha256":"c00058e4615306c417dc375f1cc9c5f34ec542a9d3ce7b8c46a8d8768e5b2918","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c00058e4615306c417dc375f1cc9c5f34ec542a9d3ce7b8c46a8d8768e5b2918","first_computed_at":"2026-07-05T04:22:26.179046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:22:26.179046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xYMOVnxymXhvlhfaGA7FZhRxN7ji4OHh1XfzS8xfhpwqvdrgePMZotg/HdwJOs6E1npWsvQS9dJuKUlS2puAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:22:26.179414Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.05481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:488ce2817685ef6041b5a31de455b02f3292d610e287994144492f1f87ea577e","sha256:5ea80e0eea1551603c8fb9a6669d8a8f6b1caf17e7b18baf2dfdef92418f61ff"],"state_sha256":"84c24a84f40baf08c55db7e59ba4ff7acf3633faf5c9e438b688343be4a0d91e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vFwhql1wxxk0GgD23Y3tLPFUjRk5FfV8rij0P5bNLKEoRZGkqkjTArachBlHFvoWwV3CnEurz2hLVRsKWpBZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:01:12.004092Z","bundle_sha256":"f7f263f24dcb3593eb1fc700018d9f3a4005f3c46fe3fe7c219d9d15e054449f"}}