{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6RJ5BUAPHX3G7K5UXP4YTE4QPL","short_pith_number":"pith:6RJ5BUAP","canonical_record":{"source":{"id":"1810.06534","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T17:36:27Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"34b7142ff14ab061e78efdbca4d4f85e7335fbe6e9a0335a9fed37d9b64dc35b","abstract_canon_sha256":"19e226cb7009aa67d4f9861eb1122d062e30b3d034ac799d8934730e54d5992d"},"schema_version":"1.0"},"canonical_sha256":"f453d0d00f3df66fabb4bbf98993907ac0ec900337eb50860e3ced80e24efa9f","source":{"kind":"arxiv","id":"1810.06534","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06534","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06534v2","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06534","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"6RJ5BUAPHX3G","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6RJ5BUAPHX3G7K5U","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6RJ5BUAP","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6RJ5BUAPHX3G7K5UXP4YTE4QPL","target":"record","payload":{"canonical_record":{"source":{"id":"1810.06534","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T17:36:27Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"34b7142ff14ab061e78efdbca4d4f85e7335fbe6e9a0335a9fed37d9b64dc35b","abstract_canon_sha256":"19e226cb7009aa67d4f9861eb1122d062e30b3d034ac799d8934730e54d5992d"},"schema_version":"1.0"},"canonical_sha256":"f453d0d00f3df66fabb4bbf98993907ac0ec900337eb50860e3ced80e24efa9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:59.566782Z","signature_b64":"1mFj9C09mw++5btbUSH6kXLqBc/2mJ6yS2e2/Febv6tP0bGnd+iPYL6XBrKf08gKLrVI64GD/UhkCz0bLZtJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f453d0d00f3df66fabb4bbf98993907ac0ec900337eb50860e3ced80e24efa9f","last_reissued_at":"2026-05-17T23:49:59.566380Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:59.566380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.06534","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQRDkjxYw5hqPysGHAoGCkHTmAFo8lTnyl0S4VIrsSg1r/Uu6+Tdje1RrHdjbManrcxZEGtQ8EQYhlqXkM/RDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:59:08.031992Z"},"content_sha256":"79fedd5114af084d1a37278e3436c54253bc79bd5b3d8343c882a8a2769fc198","schema_version":"1.0","event_id":"sha256:79fedd5114af084d1a37278e3436c54253bc79bd5b3d8343c882a8a2769fc198"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6RJ5BUAPHX3G7K5UXP4YTE4QPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher Kac-Moody algebras and symmetries of holomorphic field theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.QA","authors_text":"Brian R. Williams, Owen Gwilliam","submitted_at":"2018-10-15T17:36:27Z","abstract_excerpt":"We introduce a higher dimensional generalization of the affine Kac-Moody algebra using the language of factorization algebras. In particular, on any complex manifold there is a factorization algebra of \"currents\" associated to any Lie algebra. We classify local cocycles of these current algebras, and compare them to central extensions of higher affine algebras recently proposed by Faonte-Hennion-Kapranov. A central goal of this paper is to witness higher Kac-Moody algebras as symmetries of a class of holomorphic quantum field theories. In particular, we prove a generalization of the free field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06534","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S6nY6FZtQ/1tWwuA7CF6JSW7N3Le2KfInjhd4Bt53KS4BMmCl8pIz7oa43mVn1Adp4Xv01zH18zPe8or3jpQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:59:08.032346Z"},"content_sha256":"4ca81450bbed07229adf4cbe3b660f21b0c66f309f40ce86f11c786c2e5c5d4a","schema_version":"1.0","event_id":"sha256:4ca81450bbed07229adf4cbe3b660f21b0c66f309f40ce86f11c786c2e5c5d4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL/bundle.json","state_url":"https://pith.science/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL/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":"2026-06-08T11:59:08Z","links":{"resolver":"https://pith.science/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL","bundle":"https://pith.science/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL/bundle.json","state":"https://pith.science/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6RJ5BUAPHX3G7K5UXP4YTE4QPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6RJ5BUAPHX3G7K5UXP4YTE4QPL","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":"19e226cb7009aa67d4f9861eb1122d062e30b3d034ac799d8934730e54d5992d","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T17:36:27Z","title_canon_sha256":"34b7142ff14ab061e78efdbca4d4f85e7335fbe6e9a0335a9fed37d9b64dc35b"},"schema_version":"1.0","source":{"id":"1810.06534","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06534","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06534v2","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06534","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"6RJ5BUAPHX3G","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6RJ5BUAPHX3G7K5U","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6RJ5BUAP","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:4ca81450bbed07229adf4cbe3b660f21b0c66f309f40ce86f11c786c2e5c5d4a","target":"graph","created_at":"2026-05-17T23:49:59Z","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 introduce a higher dimensional generalization of the affine Kac-Moody algebra using the language of factorization algebras. In particular, on any complex manifold there is a factorization algebra of \"currents\" associated to any Lie algebra. We classify local cocycles of these current algebras, and compare them to central extensions of higher affine algebras recently proposed by Faonte-Hennion-Kapranov. A central goal of this paper is to witness higher Kac-Moody algebras as symmetries of a class of holomorphic quantum field theories. In particular, we prove a generalization of the free field","authors_text":"Brian R. Williams, Owen Gwilliam","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T17:36:27Z","title":"Higher Kac-Moody algebras and symmetries of holomorphic field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06534","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":"sha256:79fedd5114af084d1a37278e3436c54253bc79bd5b3d8343c882a8a2769fc198","target":"record","created_at":"2026-05-17T23:49:59Z","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":"19e226cb7009aa67d4f9861eb1122d062e30b3d034ac799d8934730e54d5992d","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-15T17:36:27Z","title_canon_sha256":"34b7142ff14ab061e78efdbca4d4f85e7335fbe6e9a0335a9fed37d9b64dc35b"},"schema_version":"1.0","source":{"id":"1810.06534","kind":"arxiv","version":2}},"canonical_sha256":"f453d0d00f3df66fabb4bbf98993907ac0ec900337eb50860e3ced80e24efa9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f453d0d00f3df66fabb4bbf98993907ac0ec900337eb50860e3ced80e24efa9f","first_computed_at":"2026-05-17T23:49:59.566380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:59.566380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1mFj9C09mw++5btbUSH6kXLqBc/2mJ6yS2e2/Febv6tP0bGnd+iPYL6XBrKf08gKLrVI64GD/UhkCz0bLZtJAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:59.566782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06534","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79fedd5114af084d1a37278e3436c54253bc79bd5b3d8343c882a8a2769fc198","sha256:4ca81450bbed07229adf4cbe3b660f21b0c66f309f40ce86f11c786c2e5c5d4a"],"state_sha256":"4998ee6b8f7d1a585bd48560282ac216f38f9169ed1d2d1722b2c0228d41814d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYjChlysxyNUMqXVYCBXxpyO/A99XYQ0onyIlmFBUyZQBK/bK3Oy3OBEDuiZmWMaCP9ELBFpuz/a0JxrBss0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T11:59:08.034379Z","bundle_sha256":"7148b81bc341c7c8634e30829b9738731a8617f4f49fe3bec419b30df955ef04"}}