{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CWQPRHAFVEB6W7BJL4GV35DPBW","short_pith_number":"pith:CWQPRHAF","canonical_record":{"source":{"id":"1708.07361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-24T11:51:25Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"29183601e5fde1eb2e9e290d75af660e8fe75094c62f0246af4d0d69cbfc0ab8","abstract_canon_sha256":"87aaf9fb594bf8850a05daf19c779c8ecf65e74ef84dda2986e3e56df9686668"},"schema_version":"1.0"},"canonical_sha256":"15a0f89c05a903eb7c295f0d5df46f0db433dccaddcf67790641560488efeefd","source":{"kind":"arxiv","id":"1708.07361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07361","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07361v2","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07361","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"CWQPRHAFVEB6","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CWQPRHAFVEB6W7BJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CWQPRHAF","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CWQPRHAFVEB6W7BJL4GV35DPBW","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-24T11:51:25Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"29183601e5fde1eb2e9e290d75af660e8fe75094c62f0246af4d0d69cbfc0ab8","abstract_canon_sha256":"87aaf9fb594bf8850a05daf19c779c8ecf65e74ef84dda2986e3e56df9686668"},"schema_version":"1.0"},"canonical_sha256":"15a0f89c05a903eb7c295f0d5df46f0db433dccaddcf67790641560488efeefd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:34.795395Z","signature_b64":"/iF9HhtZLwCeWgbHM2pwmdLYVJz4/B42eTl12gVeOSDCWJCBv+iVStTUqcXXuaOvQmw9XYprq5pu6DNeoXMiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15a0f89c05a903eb7c295f0d5df46f0db433dccaddcf67790641560488efeefd","last_reissued_at":"2026-05-18T00:21:34.794648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:34.794648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07361","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":"2026-05-18T00:21:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PAba//UCGvYBssTHBUiasVKB0ikmVUv9P/l8Ot0UMM3YHVCLJevxxTJvuxFUCl2rD6PaWH67AYTNaiHsAkMxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T22:53:43.859023Z"},"content_sha256":"4d1d001a2e801bec9f8f406a5679a02fac487368d999fa739e41ccb7cb498c6d","schema_version":"1.0","event_id":"sha256:4d1d001a2e801bec9f8f406a5679a02fac487368d999fa739e41ccb7cb498c6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CWQPRHAFVEB6W7BJL4GV35DPBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculus of conformal fields on a compact Riemann surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Nam-Gyu Kang, Nikolai G. Makarov","submitted_at":"2017-08-24T11:51:25Z","abstract_excerpt":"We present analytical implementation of conformal field theory on a compact Riemann surface. We consider statistical fields constructed from background charge modifications of the Gaussian free field and derive Ward identities which represent the Lie derivative operators in terms of the Virasoro fields and the puncture operators associated with the background charges. As applications, we derive Eguchi-Ooguri's version of Ward's equations and certain types of BPZ equations on a torus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07361","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":"2026-05-18T00:21:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"poI/XHzcBRcodI828pcgfinM8ZRIeAPoPaMpp+0bnyFSupRA3X9A9kXOYS5dzqsgfdvPMAtv9KFYZ+IYD0WHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T22:53:43.859368Z"},"content_sha256":"1b4209b433862ab230ef926d5be5a7967647340df389b0115e9ea419ced77113","schema_version":"1.0","event_id":"sha256:1b4209b433862ab230ef926d5be5a7967647340df389b0115e9ea419ced77113"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWQPRHAFVEB6W7BJL4GV35DPBW/bundle.json","state_url":"https://pith.science/pith/CWQPRHAFVEB6W7BJL4GV35DPBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWQPRHAFVEB6W7BJL4GV35DPBW/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":"2026-06-28T22:53:43Z","links":{"resolver":"https://pith.science/pith/CWQPRHAFVEB6W7BJL4GV35DPBW","bundle":"https://pith.science/pith/CWQPRHAFVEB6W7BJL4GV35DPBW/bundle.json","state":"https://pith.science/pith/CWQPRHAFVEB6W7BJL4GV35DPBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWQPRHAFVEB6W7BJL4GV35DPBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CWQPRHAFVEB6W7BJL4GV35DPBW","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":"87aaf9fb594bf8850a05daf19c779c8ecf65e74ef84dda2986e3e56df9686668","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-24T11:51:25Z","title_canon_sha256":"29183601e5fde1eb2e9e290d75af660e8fe75094c62f0246af4d0d69cbfc0ab8"},"schema_version":"1.0","source":{"id":"1708.07361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07361","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07361v2","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07361","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"CWQPRHAFVEB6","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CWQPRHAFVEB6W7BJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CWQPRHAF","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:1b4209b433862ab230ef926d5be5a7967647340df389b0115e9ea419ced77113","target":"graph","created_at":"2026-05-18T00:21:34Z","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 present analytical implementation of conformal field theory on a compact Riemann surface. We consider statistical fields constructed from background charge modifications of the Gaussian free field and derive Ward identities which represent the Lie derivative operators in terms of the Virasoro fields and the puncture operators associated with the background charges. As applications, we derive Eguchi-Ooguri's version of Ward's equations and certain types of BPZ equations on a torus.","authors_text":"Nam-Gyu Kang, Nikolai G. Makarov","cross_cats":["math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-24T11:51:25Z","title":"Calculus of conformal fields on a compact Riemann surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07361","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":"sha256:4d1d001a2e801bec9f8f406a5679a02fac487368d999fa739e41ccb7cb498c6d","target":"record","created_at":"2026-05-18T00:21:34Z","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":"87aaf9fb594bf8850a05daf19c779c8ecf65e74ef84dda2986e3e56df9686668","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-24T11:51:25Z","title_canon_sha256":"29183601e5fde1eb2e9e290d75af660e8fe75094c62f0246af4d0d69cbfc0ab8"},"schema_version":"1.0","source":{"id":"1708.07361","kind":"arxiv","version":2}},"canonical_sha256":"15a0f89c05a903eb7c295f0d5df46f0db433dccaddcf67790641560488efeefd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15a0f89c05a903eb7c295f0d5df46f0db433dccaddcf67790641560488efeefd","first_computed_at":"2026-05-18T00:21:34.794648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:34.794648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/iF9HhtZLwCeWgbHM2pwmdLYVJz4/B42eTl12gVeOSDCWJCBv+iVStTUqcXXuaOvQmw9XYprq5pu6DNeoXMiAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:34.795395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1d001a2e801bec9f8f406a5679a02fac487368d999fa739e41ccb7cb498c6d","sha256:1b4209b433862ab230ef926d5be5a7967647340df389b0115e9ea419ced77113"],"state_sha256":"a08739d244ec07e48f42babd073b3ccf7170792860c2aefdc67ec8ea666d0c26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oglGB3E/53ekoY7WgxXbeaq+Yp87pTRHzebDaYe9NSb4LmkfbmP9wZz6Ht5Ga/HjP47bpiTp23OkML+5jQXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T22:53:43.861160Z","bundle_sha256":"9ffd2882e3d0c21f086ca57fe4d8a4dd3b0ea6b82040c0e09823db423faaec3c"}}