{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:F3EVFOWPCC2QN647HHYXFR5ANL","short_pith_number":"pith:F3EVFOWP","canonical_record":{"source":{"id":"1009.2245","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-12T16:25:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4a67193654311ace9266e4117f0cf68ab2ae99e229038556d13f345402af2494","abstract_canon_sha256":"11b4f4060bca36db13b9ba5d639a4b9b2b4b35945e7118651f9bcdce616c2a02"},"schema_version":"1.0"},"canonical_sha256":"2ec952bacf10b506fb9f39f172c7a06ac15cc48d43dc9f84d6f1e701f4ce6ace","source":{"kind":"arxiv","id":"1009.2245","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2245","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2245v2","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2245","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"F3EVFOWPCC2Q","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F3EVFOWPCC2QN647","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F3EVFOWP","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:F3EVFOWPCC2QN647HHYXFR5ANL","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2245","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-12T16:25:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4a67193654311ace9266e4117f0cf68ab2ae99e229038556d13f345402af2494","abstract_canon_sha256":"11b4f4060bca36db13b9ba5d639a4b9b2b4b35945e7118651f9bcdce616c2a02"},"schema_version":"1.0"},"canonical_sha256":"2ec952bacf10b506fb9f39f172c7a06ac15cc48d43dc9f84d6f1e701f4ce6ace","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:55.182147Z","signature_b64":"qwGdvYmq6knno2nwz9Dh1SMWffiWwZzXywIxLdQ8VZYA0M9jSF6cKyiJGod16kzi2wRBnO67d5Rf0wnDLGDpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ec952bacf10b506fb9f39f172c7a06ac15cc48d43dc9f84d6f1e701f4ce6ace","last_reissued_at":"2026-05-18T04:14:55.181716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:55.181716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2245","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":"2026-05-18T04:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BBPN74Wgq6fsMCFzjf4vXkhMyRk0dfydJxRrW43C90aCifrkFt4EqAxgCkyQ8sQ9ap4OUILZAQ9Uzm1drq4HBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:15:40.129610Z"},"content_sha256":"61c543a389e837b03b6960f63051bb1b80fc275d527b433afd4c8916a66bb2c9","schema_version":"1.0","event_id":"sha256:61c543a389e837b03b6960f63051bb1b80fc275d527b433afd4c8916a66bb2c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:F3EVFOWPCC2QN647HHYXFR5ANL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From WZW models to Modular Functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Eduard Looijenga","submitted_at":"2010-09-12T16:25:12Z","abstract_excerpt":"In this survey paper (which supersedes our earlier arXiv preprint math.AG/0507086) we give a relatively simple and coordinate free description of the WZW model as a local system whose base is a G_m-bundle on the moduli stack of pointed curves. We derive its main properties and show how it leads to a modular functor in the spirit of Graeme Segal (except for unitarity). The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichmueller theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2245","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":"2026-05-18T04:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WQK+dk+BOKk1Zm5azCN6im6UArok3iA8WCbYENIX24Agk9Se5QH5ZBpLGc0/weoQI5H7QPsTX7R994RGvGjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:15:40.130256Z"},"content_sha256":"c60cc197879e474f2913ef49b99e4d0a059f9caf693a7e9d3969f8b166557f40","schema_version":"1.0","event_id":"sha256:c60cc197879e474f2913ef49b99e4d0a059f9caf693a7e9d3969f8b166557f40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3EVFOWPCC2QN647HHYXFR5ANL/bundle.json","state_url":"https://pith.science/pith/F3EVFOWPCC2QN647HHYXFR5ANL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3EVFOWPCC2QN647HHYXFR5ANL/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":"2026-05-30T14:15:40Z","links":{"resolver":"https://pith.science/pith/F3EVFOWPCC2QN647HHYXFR5ANL","bundle":"https://pith.science/pith/F3EVFOWPCC2QN647HHYXFR5ANL/bundle.json","state":"https://pith.science/pith/F3EVFOWPCC2QN647HHYXFR5ANL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3EVFOWPCC2QN647HHYXFR5ANL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F3EVFOWPCC2QN647HHYXFR5ANL","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":"11b4f4060bca36db13b9ba5d639a4b9b2b4b35945e7118651f9bcdce616c2a02","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-12T16:25:12Z","title_canon_sha256":"4a67193654311ace9266e4117f0cf68ab2ae99e229038556d13f345402af2494"},"schema_version":"1.0","source":{"id":"1009.2245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2245","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2245v2","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2245","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"F3EVFOWPCC2Q","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F3EVFOWPCC2QN647","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F3EVFOWP","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:c60cc197879e474f2913ef49b99e4d0a059f9caf693a7e9d3969f8b166557f40","target":"graph","created_at":"2026-05-18T04:14:55Z","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 survey paper (which supersedes our earlier arXiv preprint math.AG/0507086) we give a relatively simple and coordinate free description of the WZW model as a local system whose base is a G_m-bundle on the moduli stack of pointed curves. We derive its main properties and show how it leads to a modular functor in the spirit of Graeme Segal (except for unitarity). The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichmueller theory.","authors_text":"Eduard Looijenga","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-12T16:25:12Z","title":"From WZW models to Modular Functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2245","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":"sha256:61c543a389e837b03b6960f63051bb1b80fc275d527b433afd4c8916a66bb2c9","target":"record","created_at":"2026-05-18T04:14:55Z","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":"11b4f4060bca36db13b9ba5d639a4b9b2b4b35945e7118651f9bcdce616c2a02","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-12T16:25:12Z","title_canon_sha256":"4a67193654311ace9266e4117f0cf68ab2ae99e229038556d13f345402af2494"},"schema_version":"1.0","source":{"id":"1009.2245","kind":"arxiv","version":2}},"canonical_sha256":"2ec952bacf10b506fb9f39f172c7a06ac15cc48d43dc9f84d6f1e701f4ce6ace","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ec952bacf10b506fb9f39f172c7a06ac15cc48d43dc9f84d6f1e701f4ce6ace","first_computed_at":"2026-05-18T04:14:55.181716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:55.181716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwGdvYmq6knno2nwz9Dh1SMWffiWwZzXywIxLdQ8VZYA0M9jSF6cKyiJGod16kzi2wRBnO67d5Rf0wnDLGDpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:55.182147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61c543a389e837b03b6960f63051bb1b80fc275d527b433afd4c8916a66bb2c9","sha256:c60cc197879e474f2913ef49b99e4d0a059f9caf693a7e9d3969f8b166557f40"],"state_sha256":"ffed116e7d957a992380992eb015d81d4ae91c436eba86f992b177844e7521e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMH5tcjWHsek5XmcTXJWAUIf7A9ApwL+5ijjJJDQ+wJnT0xls5Q9hYHCdh/A5hQvKG/LWbyBQbbNZF21k2wMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:15:40.136734Z","bundle_sha256":"1246860930e9581006f5432ef4119b3b8c59a716845c7678b0bd2d76993a352c"}}