{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:APVC6HKBU76RQ4EBB6BOFPC54Y","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":"5ceef49c41533ae35b756e8679e4c14d80513bf8cfba4b1ed4962a7ea7c0edd0","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-04-30T17:08:50Z","title_canon_sha256":"e5fe8cc3fb0489b68726634e058706ee6faea5ecdf2682334d7db7a0504973ea"},"schema_version":"1.0","source":{"id":"1605.00138","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00138","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00138v2","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00138","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"APVC6HKBU76R","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"APVC6HKBU76RQ4EB","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"APVC6HKB","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:62b9902cac6490a2def4185fd5b84ae22b8e16a4dc6892a437458d5a03c9683e","target":"graph","created_at":"2026-05-18T00:50:52Z","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":"These are lecture notes from author's mini-course during Session 1: \"Vertex algebras, W-algebras, and application\" of INdAM Intensive research period \"Perspectives in Lie Theory\", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy. December 9, 2014 -- February 28, 2015.","authors_text":"Tomoyuki Arakawa","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-04-30T17:08:50Z","title":"Introduction to W-algebras and their representation theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00138","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":"sha256:8866d64546e033a19928a8c94753028336c52abbbed937a40d9a952336ea2522","target":"record","created_at":"2026-05-18T00:50:52Z","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":"5ceef49c41533ae35b756e8679e4c14d80513bf8cfba4b1ed4962a7ea7c0edd0","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-04-30T17:08:50Z","title_canon_sha256":"e5fe8cc3fb0489b68726634e058706ee6faea5ecdf2682334d7db7a0504973ea"},"schema_version":"1.0","source":{"id":"1605.00138","kind":"arxiv","version":2}},"canonical_sha256":"03ea2f1d41a7fd1870810f82e2bc5de6352a0d1bbeae7176591c7292d5555cf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03ea2f1d41a7fd1870810f82e2bc5de6352a0d1bbeae7176591c7292d5555cf0","first_computed_at":"2026-05-18T00:50:52.251495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:52.251495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKmr9D7dWttk/luc31cTSySANRx5E/IM/8hG3xZKcAF2ahtWLs4hXaBGbSo+xy2a28kEw71yyv5OEg82Z+iMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:52.252000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00138","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8866d64546e033a19928a8c94753028336c52abbbed937a40d9a952336ea2522","sha256:62b9902cac6490a2def4185fd5b84ae22b8e16a4dc6892a437458d5a03c9683e"],"state_sha256":"9753d0e9f65895f38984b25f2b204725eeb2440da16b24a741a9a2a95bc3852f"}