{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PCW6QVD4JCZVZN3YGUDQW3G4FJ","short_pith_number":"pith:PCW6QVD4","canonical_record":{"source":{"id":"1805.11031","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-25T17:26:14Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"2297e024603c4cf21a33fbeae5e37aedff0c7a03ba859b3c1cf980ea9e917264","abstract_canon_sha256":"f3aa330d2110b934b6b600ddd9bb640aacb8e48f212670371ac05fd35fd99d0a"},"schema_version":"1.0"},"canonical_sha256":"78ade8547c48b35cb77835070b6cdc2a4daf191dc925d561d8b4c422332b7f64","source":{"kind":"arxiv","id":"1805.11031","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11031","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11031v6","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11031","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"pith_short_12","alias_value":"PCW6QVD4JCZV","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"pith_short_16","alias_value":"PCW6QVD4JCZVZN3Y","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"pith_short_8","alias_value":"PCW6QVD4","created_at":"2026-07-05T01:02:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PCW6QVD4JCZVZN3YGUDQW3G4FJ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11031","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-25T17:26:14Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"2297e024603c4cf21a33fbeae5e37aedff0c7a03ba859b3c1cf980ea9e917264","abstract_canon_sha256":"f3aa330d2110b934b6b600ddd9bb640aacb8e48f212670371ac05fd35fd99d0a"},"schema_version":"1.0"},"canonical_sha256":"78ade8547c48b35cb77835070b6cdc2a4daf191dc925d561d8b4c422332b7f64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:02:38.564013Z","signature_b64":"tue/2QWqIFWs8jYd4g56NHOC6M1cBLVJ905qiwl5j+OkO9KmGXu/PAcbCaPwUryTu3DSWKqPfFJ470h5exuVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78ade8547c48b35cb77835070b6cdc2a4daf191dc925d561d8b4c422332b7f64","last_reissued_at":"2026-07-05T01:02:38.563623Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:02:38.563623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11031","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:02:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVUD9DqaKVA7ij6LJVaMjOh7eGi1AN2ocHcFPdVbAuhGRIQ3Pe1OH1shRcY4qV3DGfNascdbrCTbRb5MIk5KBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:39:17.074188Z"},"content_sha256":"3942bdb1c6f29f6c13d4018b24ae20475093fa09d0002dc1c71a0029aac4523a","schema_version":"1.0","event_id":"sha256:3942bdb1c6f29f6c13d4018b24ae20475093fa09d0002dc1c71a0029aac4523a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PCW6QVD4JCZVZN3YGUDQW3G4FJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal two-parameter even spin $\\mathcal{W}_{\\infty}$-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Shashank Kanade","submitted_at":"2018-05-25T17:26:14Z","abstract_excerpt":"We construct the unique two-parameter vertex algebra which is freely generated of type ${\\mathcal W}(2,4,6,\\dots)$, and generated by the weights $2$ and $4$ fields. Subject to some mild constraints, all vertex algebras of type ${\\mathcal W}(2,4,\\dots, 2N)$ for some $N$, can be obtained as quotients of this universal algebra. This includes the $B$ and $C$ type principal ${\\mathcal W}$-algebras, the $\\mathbb{Z}_2$-orbifolds of the $D$ type principal ${\\mathcal W}$-algebras, and many others which arise as cosets of affine vertex algebras inside larger structures. As an application, we classify al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11031","kind":"arxiv","version":6},"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/1805.11031/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":"2026-07-05T01:02:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0IbVCqYrmOJgEzQJmNSl0Y2El00KMI3R07xqxcEkIiYFi8Q4RsLjR6cKXuLR8wB1twtVfJBupNnTxcU4WMvNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:39:17.075135Z"},"content_sha256":"4f32bf4dc1404b6bbe4193b5724a92e7471d548eff8c9368fd9a2a5d11712bd4","schema_version":"1.0","event_id":"sha256:4f32bf4dc1404b6bbe4193b5724a92e7471d548eff8c9368fd9a2a5d11712bd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ/bundle.json","state_url":"https://pith.science/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ/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":"2026-08-16T19:39:17Z","links":{"resolver":"https://pith.science/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ","bundle":"https://pith.science/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ/bundle.json","state":"https://pith.science/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCW6QVD4JCZVZN3YGUDQW3G4FJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PCW6QVD4JCZVZN3YGUDQW3G4FJ","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":"f3aa330d2110b934b6b600ddd9bb640aacb8e48f212670371ac05fd35fd99d0a","cross_cats_sorted":["hep-th","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-25T17:26:14Z","title_canon_sha256":"2297e024603c4cf21a33fbeae5e37aedff0c7a03ba859b3c1cf980ea9e917264"},"schema_version":"1.0","source":{"id":"1805.11031","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11031","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11031v6","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11031","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"pith_short_12","alias_value":"PCW6QVD4JCZV","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"pith_short_16","alias_value":"PCW6QVD4JCZVZN3Y","created_at":"2026-07-05T01:02:38Z"},{"alias_kind":"pith_short_8","alias_value":"PCW6QVD4","created_at":"2026-07-05T01:02:38Z"}],"graph_snapshots":[{"event_id":"sha256:4f32bf4dc1404b6bbe4193b5724a92e7471d548eff8c9368fd9a2a5d11712bd4","target":"graph","created_at":"2026-07-05T01:02:38Z","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/1805.11031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct the unique two-parameter vertex algebra which is freely generated of type ${\\mathcal W}(2,4,6,\\dots)$, and generated by the weights $2$ and $4$ fields. Subject to some mild constraints, all vertex algebras of type ${\\mathcal W}(2,4,\\dots, 2N)$ for some $N$, can be obtained as quotients of this universal algebra. This includes the $B$ and $C$ type principal ${\\mathcal W}$-algebras, the $\\mathbb{Z}_2$-orbifolds of the $D$ type principal ${\\mathcal W}$-algebras, and many others which arise as cosets of affine vertex algebras inside larger structures. As an application, we classify al","authors_text":"Andrew R. Linshaw, Shashank Kanade","cross_cats":["hep-th","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-25T17:26:14Z","title":"Universal two-parameter even spin $\\mathcal{W}_{\\infty}$-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11031","kind":"arxiv","version":6},"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":"sha256:3942bdb1c6f29f6c13d4018b24ae20475093fa09d0002dc1c71a0029aac4523a","target":"record","created_at":"2026-07-05T01:02:38Z","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":"f3aa330d2110b934b6b600ddd9bb640aacb8e48f212670371ac05fd35fd99d0a","cross_cats_sorted":["hep-th","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-25T17:26:14Z","title_canon_sha256":"2297e024603c4cf21a33fbeae5e37aedff0c7a03ba859b3c1cf980ea9e917264"},"schema_version":"1.0","source":{"id":"1805.11031","kind":"arxiv","version":6}},"canonical_sha256":"78ade8547c48b35cb77835070b6cdc2a4daf191dc925d561d8b4c422332b7f64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78ade8547c48b35cb77835070b6cdc2a4daf191dc925d561d8b4c422332b7f64","first_computed_at":"2026-07-05T01:02:38.563623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:02:38.563623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tue/2QWqIFWs8jYd4g56NHOC6M1cBLVJ905qiwl5j+OkO9KmGXu/PAcbCaPwUryTu3DSWKqPfFJ470h5exuVAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:02:38.564013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11031","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3942bdb1c6f29f6c13d4018b24ae20475093fa09d0002dc1c71a0029aac4523a","sha256:4f32bf4dc1404b6bbe4193b5724a92e7471d548eff8c9368fd9a2a5d11712bd4"],"state_sha256":"67fc0ea4538c3c7756b8a2b81c05871bf78c4127d22e46074a044feec4292f8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dWlAZAGOj7yUaeqH3lY9j2RkA1/7/vcVTN7ch9cT9G59nysr27qnzXGzq8IskMzUA3H4j6yQ2SJeWcGLML6jBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:39:17.086634Z","bundle_sha256":"0d1253797a4d948a34491428c0d539a5b41003b8ad40f2db528fab2cb1411a8e"}}