{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:M7EKM6IVDJC4MRXGZGGSJ7GW3K","short_pith_number":"pith:M7EKM6IV","canonical_record":{"source":{"id":"1711.10804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-11-29T11:57:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ad1510eeffc63e73bafb142f1dc76fb4d7ebd638ff96a49bef2c77b8fc4bde4e","abstract_canon_sha256":"98c1ec514b8b6bbe093410fb8fa867a20e3563e460c379e9727b1c9d0f2f3d3b"},"schema_version":"1.0"},"canonical_sha256":"67c8a679151a45c646e6c98d24fcd6da9ed47d01a2acfcc487811072ebedd391","source":{"kind":"arxiv","id":"1711.10804","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10804","created_at":"2026-05-18T00:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10804v2","created_at":"2026-05-18T00:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10804","created_at":"2026-05-18T00:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"M7EKM6IVDJC4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"M7EKM6IVDJC4MRXG","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"M7EKM6IV","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:M7EKM6IVDJC4MRXGZGGSJ7GW3K","target":"record","payload":{"canonical_record":{"source":{"id":"1711.10804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-11-29T11:57:09Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ad1510eeffc63e73bafb142f1dc76fb4d7ebd638ff96a49bef2c77b8fc4bde4e","abstract_canon_sha256":"98c1ec514b8b6bbe093410fb8fa867a20e3563e460c379e9727b1c9d0f2f3d3b"},"schema_version":"1.0"},"canonical_sha256":"67c8a679151a45c646e6c98d24fcd6da9ed47d01a2acfcc487811072ebedd391","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:24.930813Z","signature_b64":"oiopB4XGiihqt/ilw2meeTgkdiKFV+t4c+sPyxikYXLUbseW9oVNqaNteIMgjG6y9mP8FqNY9C30zuRcMiZ0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67c8a679151a45c646e6c98d24fcd6da9ed47d01a2acfcc487811072ebedd391","last_reissued_at":"2026-05-18T00:19:24.930368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:24.930368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.10804","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":"2026-05-18T00:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EmDVaZJmebsz7RxQXiUXv2il/uQVDnmD7aOc41SFg/X6kXmmJpUvZX8FpBkzT5+8jDrdZPNp31oXNZ1yaCu0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:59:23.906552Z"},"content_sha256":"3893a9d3fa23507acc6c7ceffe9d67f3d875a1d990f10200d5ce9c7a380a9dfb","schema_version":"1.0","event_id":"sha256:3893a9d3fa23507acc6c7ceffe9d67f3d875a1d990f10200d5ce9c7a380a9dfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:M7EKM6IVDJC4MRXGZGGSJ7GW3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular vectors for the $W_N$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"David Ridout, Simon Wood, Steve Siu","submitted_at":"2017-11-29T11:57:09Z","abstract_excerpt":"In this paper, we use free field realisations of the A-type principal, or Casimir, $W_N$ algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10804","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":"2026-05-18T00:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MTB1GHKdvrlTmAAc6l/9MHYHSvxmVgtqXwoIrM8ndRJz1kwhneqx4iosXmNm7wrYvm/O6nvQ3hRPsjjuPeVsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:59:23.907234Z"},"content_sha256":"dd5801b7d2c6be4d3a5735930377969ff70b10b00b6a2d85b129947973f818ed","schema_version":"1.0","event_id":"sha256:dd5801b7d2c6be4d3a5735930377969ff70b10b00b6a2d85b129947973f818ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K/bundle.json","state_url":"https://pith.science/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K/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":"2026-05-26T20:59:23Z","links":{"resolver":"https://pith.science/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K","bundle":"https://pith.science/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K/bundle.json","state":"https://pith.science/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7EKM6IVDJC4MRXGZGGSJ7GW3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M7EKM6IVDJC4MRXGZGGSJ7GW3K","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":"98c1ec514b8b6bbe093410fb8fa867a20e3563e460c379e9727b1c9d0f2f3d3b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-11-29T11:57:09Z","title_canon_sha256":"ad1510eeffc63e73bafb142f1dc76fb4d7ebd638ff96a49bef2c77b8fc4bde4e"},"schema_version":"1.0","source":{"id":"1711.10804","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10804","created_at":"2026-05-18T00:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10804v2","created_at":"2026-05-18T00:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10804","created_at":"2026-05-18T00:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"M7EKM6IVDJC4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"M7EKM6IVDJC4MRXG","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"M7EKM6IV","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:dd5801b7d2c6be4d3a5735930377969ff70b10b00b6a2d85b129947973f818ed","target":"graph","created_at":"2026-05-18T00:19:24Z","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":"In this paper, we use free field realisations of the A-type principal, or Casimir, $W_N$ algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.","authors_text":"David Ridout, Simon Wood, Steve Siu","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-11-29T11:57:09Z","title":"Singular vectors for the $W_N$ algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10804","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":"sha256:3893a9d3fa23507acc6c7ceffe9d67f3d875a1d990f10200d5ce9c7a380a9dfb","target":"record","created_at":"2026-05-18T00:19:24Z","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":"98c1ec514b8b6bbe093410fb8fa867a20e3563e460c379e9727b1c9d0f2f3d3b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-11-29T11:57:09Z","title_canon_sha256":"ad1510eeffc63e73bafb142f1dc76fb4d7ebd638ff96a49bef2c77b8fc4bde4e"},"schema_version":"1.0","source":{"id":"1711.10804","kind":"arxiv","version":2}},"canonical_sha256":"67c8a679151a45c646e6c98d24fcd6da9ed47d01a2acfcc487811072ebedd391","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67c8a679151a45c646e6c98d24fcd6da9ed47d01a2acfcc487811072ebedd391","first_computed_at":"2026-05-18T00:19:24.930368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:24.930368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oiopB4XGiihqt/ilw2meeTgkdiKFV+t4c+sPyxikYXLUbseW9oVNqaNteIMgjG6y9mP8FqNY9C30zuRcMiZ0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:24.930813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10804","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3893a9d3fa23507acc6c7ceffe9d67f3d875a1d990f10200d5ce9c7a380a9dfb","sha256:dd5801b7d2c6be4d3a5735930377969ff70b10b00b6a2d85b129947973f818ed"],"state_sha256":"45db032608f0e830af72b539934027e1b14f6f5fc25d6b24657d5b5e5d3cb198"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdww4f+cvkKtV+aZjI56xC92kGeCFqgq2FtJaMGtFy0C9kZFoD5NCfvJkgDabGiZEFRH2E7RjMXBLN+gPyniAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:59:23.910751Z","bundle_sha256":"9a66e7bf4e2af446d496b0bc56c25d560022e214cbc437a827d66cc4caf3484b"}}