{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WM3NYSYVYNA4I4SY4VNFZROYT5","short_pith_number":"pith:WM3NYSYV","canonical_record":{"source":{"id":"1603.01326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-04T01:57:18Z","cross_cats_sorted":[],"title_canon_sha256":"5f1dc17ec3cf7b087899ea977bca1f80a06a5ae8de07bd0b3a4344fe2b110285","abstract_canon_sha256":"56dc6646b0215d21711219f884ffcbb3c9f8cec0e2318ff230cfcdf1640f4dae"},"schema_version":"1.0"},"canonical_sha256":"b336dc4b15c341c47258e55a5cc5d89f4c03475a73a0312975e4f5c822bf2c02","source":{"kind":"arxiv","id":"1603.01326","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01326","created_at":"2026-05-18T00:34:44Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01326v2","created_at":"2026-05-18T00:34:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01326","created_at":"2026-05-18T00:34:44Z"},{"alias_kind":"pith_short_12","alias_value":"WM3NYSYVYNA4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WM3NYSYVYNA4I4SY","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WM3NYSYV","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WM3NYSYVYNA4I4SY4VNFZROYT5","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-04T01:57:18Z","cross_cats_sorted":[],"title_canon_sha256":"5f1dc17ec3cf7b087899ea977bca1f80a06a5ae8de07bd0b3a4344fe2b110285","abstract_canon_sha256":"56dc6646b0215d21711219f884ffcbb3c9f8cec0e2318ff230cfcdf1640f4dae"},"schema_version":"1.0"},"canonical_sha256":"b336dc4b15c341c47258e55a5cc5d89f4c03475a73a0312975e4f5c822bf2c02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:44.910908Z","signature_b64":"ocuaWroiXmHLACdAHhHaQ6RJDTmBSUar0QbzELwzfuwz95Z1m2YnkwLR/twptE+eByVqfAJO9rwylkLawMuZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b336dc4b15c341c47258e55a5cc5d89f4c03475a73a0312975e4f5c822bf2c02","last_reissued_at":"2026-05-18T00:34:44.910138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:44.910138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01326","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkgblYJaKUzsyqlbKj/7iHSr/xabJdzJqlMjbFt0GnxjBqByj5sGZ14N8bwZhntYtRtUKog39r1YQ77Xogl/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:40:32.706648Z"},"content_sha256":"7e7fcbbf3596be0c1e4492a57c820ad7eb01a429cf06297934a019ef8bc8c0d3","schema_version":"1.0","event_id":"sha256:7e7fcbbf3596be0c1e4492a57c820ad7eb01a429cf06297934a019ef8bc8c0d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WM3NYSYVYNA4I4SY4VNFZROYT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of intertwining operators for vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kenichiro Tanabe","submitted_at":"2016-03-04T01:57:18Z","abstract_excerpt":"We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu algebras under some conditions on N-graded weak modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01326","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5AfdeGr62egxhWhe+lIWO+7eEErAogb7U9S1oWcXAr5vLooWAO6RbuYvb4+tmQJN8dvCGDonEN/DKwYW0X/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:40:32.707007Z"},"content_sha256":"da957adbf1b1df46cbc6ab8a502b9c388b1ef9aa613885424dbe71f86fbe62fb","schema_version":"1.0","event_id":"sha256:da957adbf1b1df46cbc6ab8a502b9c388b1ef9aa613885424dbe71f86fbe62fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WM3NYSYVYNA4I4SY4VNFZROYT5/bundle.json","state_url":"https://pith.science/pith/WM3NYSYVYNA4I4SY4VNFZROYT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WM3NYSYVYNA4I4SY4VNFZROYT5/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":"2026-06-22T23:40:32Z","links":{"resolver":"https://pith.science/pith/WM3NYSYVYNA4I4SY4VNFZROYT5","bundle":"https://pith.science/pith/WM3NYSYVYNA4I4SY4VNFZROYT5/bundle.json","state":"https://pith.science/pith/WM3NYSYVYNA4I4SY4VNFZROYT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WM3NYSYVYNA4I4SY4VNFZROYT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WM3NYSYVYNA4I4SY4VNFZROYT5","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":"56dc6646b0215d21711219f884ffcbb3c9f8cec0e2318ff230cfcdf1640f4dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-04T01:57:18Z","title_canon_sha256":"5f1dc17ec3cf7b087899ea977bca1f80a06a5ae8de07bd0b3a4344fe2b110285"},"schema_version":"1.0","source":{"id":"1603.01326","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01326","created_at":"2026-05-18T00:34:44Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01326v2","created_at":"2026-05-18T00:34:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01326","created_at":"2026-05-18T00:34:44Z"},{"alias_kind":"pith_short_12","alias_value":"WM3NYSYVYNA4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WM3NYSYVYNA4I4SY","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WM3NYSYV","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:da957adbf1b1df46cbc6ab8a502b9c388b1ef9aa613885424dbe71f86fbe62fb","target":"graph","created_at":"2026-05-18T00:34:44Z","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":"We generalize the notion of an intertwining operator to N-graded weak modules over a vertex operator algebra and study their properties. We show a formula for the dimensions of these intertwining operators in terms of modules over the Zhu algebras under some conditions on N-graded weak modules.","authors_text":"Kenichiro Tanabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-04T01:57:18Z","title":"A generalization of intertwining operators for vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01326","kind":"arxiv","version":2},"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":"sha256:7e7fcbbf3596be0c1e4492a57c820ad7eb01a429cf06297934a019ef8bc8c0d3","target":"record","created_at":"2026-05-18T00:34:44Z","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":"56dc6646b0215d21711219f884ffcbb3c9f8cec0e2318ff230cfcdf1640f4dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-03-04T01:57:18Z","title_canon_sha256":"5f1dc17ec3cf7b087899ea977bca1f80a06a5ae8de07bd0b3a4344fe2b110285"},"schema_version":"1.0","source":{"id":"1603.01326","kind":"arxiv","version":2}},"canonical_sha256":"b336dc4b15c341c47258e55a5cc5d89f4c03475a73a0312975e4f5c822bf2c02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b336dc4b15c341c47258e55a5cc5d89f4c03475a73a0312975e4f5c822bf2c02","first_computed_at":"2026-05-18T00:34:44.910138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:44.910138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ocuaWroiXmHLACdAHhHaQ6RJDTmBSUar0QbzELwzfuwz95Z1m2YnkwLR/twptE+eByVqfAJO9rwylkLawMuZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:44.910908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01326","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e7fcbbf3596be0c1e4492a57c820ad7eb01a429cf06297934a019ef8bc8c0d3","sha256:da957adbf1b1df46cbc6ab8a502b9c388b1ef9aa613885424dbe71f86fbe62fb"],"state_sha256":"d72cd1a02acb8d1f2dcbd1311255a3d9f364d410da0ec213b7ce4c68acb34205"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/1MH+AYE/n0WJ0CQ1Sv+bIONSKDlylfkGs/vvW/Dpcb+f3oLiqQkacREj81NmZ2CyZHI5FmRn0L5NQQ83P8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:40:32.708953Z","bundle_sha256":"c0e9984dc0d00e94f974c1b343b2f90a843ba2e8eb79252454aeccb9c9799c4d"}}