{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:DWCDUX3JLJB7NYCGA6E5EQC4QN","short_pith_number":"pith:DWCDUX3J","canonical_record":{"source":{"id":"math/0603065","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-03-03T01:40:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"66dcaf7a81b4f20bd57561bad8b106a32005d2a43e6d669ec9cb0461561fed24","abstract_canon_sha256":"e24094e5faa002eea68dcc6d5f58ebcd0783bf2fb968a06be99c6e485f46887d"},"schema_version":"1.0"},"canonical_sha256":"1d843a5f695a43f6e0460789d2405c837e1ce90c5fdf8ddb48670249371e2e04","source":{"kind":"arxiv","id":"math/0603065","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603065","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603065v3","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603065","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"DWCDUX3JLJB7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DWCDUX3JLJB7NYCG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DWCDUX3J","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:DWCDUX3JLJB7NYCGA6E5EQC4QN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0603065","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-03-03T01:40:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"66dcaf7a81b4f20bd57561bad8b106a32005d2a43e6d669ec9cb0461561fed24","abstract_canon_sha256":"e24094e5faa002eea68dcc6d5f58ebcd0783bf2fb968a06be99c6e485f46887d"},"schema_version":"1.0"},"canonical_sha256":"1d843a5f695a43f6e0460789d2405c837e1ce90c5fdf8ddb48670249371e2e04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:44.263638Z","signature_b64":"TCvXRaEU0qRR3Yr/ArWd1u4cwLqjsUzOidKV75x2DCoEm/G88btHdjoEJqwKmKpVVKfatk4j3zDIn4ACmVKNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d843a5f695a43f6e0460789d2405c837e1ce90c5fdf8ddb48670249371e2e04","last_reissued_at":"2026-05-18T04:24:44.263239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:44.263239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0603065","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GCP2T29OJ3APTA0f1GWPt6PzgDVyC0FLkMBA1br4kqnchbSpXlem1GJaFgenvYqZPovhW5VpANWY+2jfZohnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:01:45.502984Z"},"content_sha256":"6282b4cba871a18c883b13189d712284122bb97c4dc0f91dae96bff8f62192a4","schema_version":"1.0","event_id":"sha256:6282b4cba871a18c883b13189d712284122bb97c4dc0f91dae96bff8f62192a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:DWCDUX3JLJB7NYCGA6E5EQC4QN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full field algebras, operads and tensor categories","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Liang Kong","submitted_at":"2006-03-03T01:40:51Z","abstract_excerpt":"We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted $\\R\\times \\R$-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over $V^L\\otimes V^R$, where V^L and V^R are two vertex operator algebras satisfying certain finiteness and reductivity conditions. We also study the geometry interpretation of conformal full field algebras over $V^L\\otimes V^R$ equipped with a nondeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603065","kind":"arxiv","version":3},"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":"2026-05-18T04:24:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YmUMQRNhqiSraNumK1nauWTeNDhQbcBDRTYAjnx8CUoEsBJ6zBvOiBME2odMIKzBY26X0uZcwQ0yoKdZSil2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:01:45.503806Z"},"content_sha256":"352462f8d098523c504e4b52734748f727388fa3e9c8da91629ca75c16992059","schema_version":"1.0","event_id":"sha256:352462f8d098523c504e4b52734748f727388fa3e9c8da91629ca75c16992059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN/bundle.json","state_url":"https://pith.science/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN/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":"2026-08-10T13:01:45Z","links":{"resolver":"https://pith.science/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN","bundle":"https://pith.science/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN/bundle.json","state":"https://pith.science/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWCDUX3JLJB7NYCGA6E5EQC4QN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DWCDUX3JLJB7NYCGA6E5EQC4QN","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":"e24094e5faa002eea68dcc6d5f58ebcd0783bf2fb968a06be99c6e485f46887d","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.QA","submitted_at":"2006-03-03T01:40:51Z","title_canon_sha256":"66dcaf7a81b4f20bd57561bad8b106a32005d2a43e6d669ec9cb0461561fed24"},"schema_version":"1.0","source":{"id":"math/0603065","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603065","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603065v3","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603065","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"DWCDUX3JLJB7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DWCDUX3JLJB7NYCG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DWCDUX3J","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:352462f8d098523c504e4b52734748f727388fa3e9c8da91629ca75c16992059","target":"graph","created_at":"2026-05-18T04:24:44Z","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 study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted $\\R\\times \\R$-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over $V^L\\otimes V^R$, where V^L and V^R are two vertex operator algebras satisfying certain finiteness and reductivity conditions. We also study the geometry interpretation of conformal full field algebras over $V^L\\otimes V^R$ equipped with a nondeg","authors_text":"Liang Kong","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2006-03-03T01:40:51Z","title":"Full field algebras, operads and tensor categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603065","kind":"arxiv","version":3},"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":"sha256:6282b4cba871a18c883b13189d712284122bb97c4dc0f91dae96bff8f62192a4","target":"record","created_at":"2026-05-18T04:24:44Z","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":"e24094e5faa002eea68dcc6d5f58ebcd0783bf2fb968a06be99c6e485f46887d","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.QA","submitted_at":"2006-03-03T01:40:51Z","title_canon_sha256":"66dcaf7a81b4f20bd57561bad8b106a32005d2a43e6d669ec9cb0461561fed24"},"schema_version":"1.0","source":{"id":"math/0603065","kind":"arxiv","version":3}},"canonical_sha256":"1d843a5f695a43f6e0460789d2405c837e1ce90c5fdf8ddb48670249371e2e04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d843a5f695a43f6e0460789d2405c837e1ce90c5fdf8ddb48670249371e2e04","first_computed_at":"2026-05-18T04:24:44.263239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:44.263239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TCvXRaEU0qRR3Yr/ArWd1u4cwLqjsUzOidKV75x2DCoEm/G88btHdjoEJqwKmKpVVKfatk4j3zDIn4ACmVKNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:44.263638Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0603065","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6282b4cba871a18c883b13189d712284122bb97c4dc0f91dae96bff8f62192a4","sha256:352462f8d098523c504e4b52734748f727388fa3e9c8da91629ca75c16992059"],"state_sha256":"1663aa1f18e66442ace056408e4259d23080e761c4ad43b6d0c839e49f743ff9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kbvatRXV9W1YZrxktNfRjTbYPY2cywuXHkS6nEddp3omXEYATPkislRD28wrTl8Bbt2z8eXe3H6jQdsMB30jDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T13:01:45.512518Z","bundle_sha256":"b9e8c3b8931525b9b1f23f9058720f5e33daf833232aa434cf098e1c881a65d8"}}