{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:BX4YMK3SU4B57QUL6GNFMNIVA7","short_pith_number":"pith:BX4YMK3S","canonical_record":{"source":{"id":"math/0502169","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-02-08T16:17:41Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"960dd5a2f7f82de0e84c147c41f6f640ea015b3f10d03f7622ce25a496c95bb5","abstract_canon_sha256":"4dfba1eb694826994c1237a5416f0310922842e94080da7e09cf376c13f80f77"},"schema_version":"1.0"},"canonical_sha256":"0df9862b72a703dfc28bf19a56351507d8c4751b49502eb11bf78b897a651d85","source":{"kind":"arxiv","id":"math/0502169","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502169","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502169v2","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502169","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"BX4YMK3SU4B5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BX4YMK3SU4B57QUL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BX4YMK3S","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:BX4YMK3SU4B57QUL6GNFMNIVA7","target":"record","payload":{"canonical_record":{"source":{"id":"math/0502169","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-02-08T16:17:41Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"960dd5a2f7f82de0e84c147c41f6f640ea015b3f10d03f7622ce25a496c95bb5","abstract_canon_sha256":"4dfba1eb694826994c1237a5416f0310922842e94080da7e09cf376c13f80f77"},"schema_version":"1.0"},"canonical_sha256":"0df9862b72a703dfc28bf19a56351507d8c4751b49502eb11bf78b897a651d85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:23.765029Z","signature_b64":"/j+jhI6Fo9bO0zKF/b/ZmkViXZWzhO8XmhhPEAHiPbJHsL58pPhSU6ufceJKzGq4iwUhA4vH0KDyyoZ4b4knDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df9862b72a703dfc28bf19a56351507d8c4751b49502eb11bf78b897a651d85","last_reissued_at":"2026-05-18T01:05:23.764471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:23.764471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0502169","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":"2026-05-18T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHp5LAP+Q31yi978EtxzMgSsU2sfoLqHranZxu+CD512tzGIkBy579Hs2yzMcmUn1LQI9d933rGBmwwD925WCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:48:12.443370Z"},"content_sha256":"357f060a60f168f1608c0c014cdd8ff71d5ed5948ef3db46bae3f38ad7bda7f3","schema_version":"1.0","event_id":"sha256:357f060a60f168f1608c0c014cdd8ff71d5ed5948ef3db46bae3f38ad7bda7f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:BX4YMK3SU4B57QUL6GNFMNIVA7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex Counterpart of Chern-Simons-Witten Theory and Holomorphic Linking","license":"","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.AG","authors_text":"Andrey Todorov, Igor Frenkel","submitted_at":"2005-02-08T16:17:41Z","abstract_excerpt":"In this paper we are begining to explore the complex counterpart of the Chern-Simon-Witten theory. We define the complex analogue of the Gauss linking number for complex curves embedded in a Calabi-Yau threefold using the formal path integral that leads to a rigorous mathematical expression. We give an analytic and geometric interpretation of our holomorphic linking following the parallel with the real case. We show in particular that the Green kernel that appears in the explicit integral for the Gauss linking number is replaced by the Bochner-Martinelli kernel. We also find canonical expressi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502169","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":"2026-05-18T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/zT/sxEQmjnQ5PPSwtDueaV6FVEPMsVt5Jgw4i/MCpFET/HqoXcy1N5vjEQ9CewdEa+23p6J7TfQ7Y8UK6mAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:48:12.443715Z"},"content_sha256":"d75b61bb66e062a44d6b88e397f3c48b943ec12dc3c24772ce174bf76a7e42e4","schema_version":"1.0","event_id":"sha256:d75b61bb66e062a44d6b88e397f3c48b943ec12dc3c24772ce174bf76a7e42e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BX4YMK3SU4B57QUL6GNFMNIVA7/bundle.json","state_url":"https://pith.science/pith/BX4YMK3SU4B57QUL6GNFMNIVA7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BX4YMK3SU4B57QUL6GNFMNIVA7/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":"2026-06-23T10:48:12Z","links":{"resolver":"https://pith.science/pith/BX4YMK3SU4B57QUL6GNFMNIVA7","bundle":"https://pith.science/pith/BX4YMK3SU4B57QUL6GNFMNIVA7/bundle.json","state":"https://pith.science/pith/BX4YMK3SU4B57QUL6GNFMNIVA7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BX4YMK3SU4B57QUL6GNFMNIVA7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:BX4YMK3SU4B57QUL6GNFMNIVA7","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":"4dfba1eb694826994c1237a5416f0310922842e94080da7e09cf376c13f80f77","cross_cats_sorted":["hep-th","math.SG"],"license":"","primary_cat":"math.AG","submitted_at":"2005-02-08T16:17:41Z","title_canon_sha256":"960dd5a2f7f82de0e84c147c41f6f640ea015b3f10d03f7622ce25a496c95bb5"},"schema_version":"1.0","source":{"id":"math/0502169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502169","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502169v2","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502169","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"BX4YMK3SU4B5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BX4YMK3SU4B57QUL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BX4YMK3S","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d75b61bb66e062a44d6b88e397f3c48b943ec12dc3c24772ce174bf76a7e42e4","target":"graph","created_at":"2026-05-18T01:05:23Z","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 paper we are begining to explore the complex counterpart of the Chern-Simon-Witten theory. We define the complex analogue of the Gauss linking number for complex curves embedded in a Calabi-Yau threefold using the formal path integral that leads to a rigorous mathematical expression. We give an analytic and geometric interpretation of our holomorphic linking following the parallel with the real case. We show in particular that the Green kernel that appears in the explicit integral for the Gauss linking number is replaced by the Bochner-Martinelli kernel. We also find canonical expressi","authors_text":"Andrey Todorov, Igor Frenkel","cross_cats":["hep-th","math.SG"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-02-08T16:17:41Z","title":"Complex Counterpart of Chern-Simons-Witten Theory and Holomorphic Linking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502169","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":"sha256:357f060a60f168f1608c0c014cdd8ff71d5ed5948ef3db46bae3f38ad7bda7f3","target":"record","created_at":"2026-05-18T01:05:23Z","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":"4dfba1eb694826994c1237a5416f0310922842e94080da7e09cf376c13f80f77","cross_cats_sorted":["hep-th","math.SG"],"license":"","primary_cat":"math.AG","submitted_at":"2005-02-08T16:17:41Z","title_canon_sha256":"960dd5a2f7f82de0e84c147c41f6f640ea015b3f10d03f7622ce25a496c95bb5"},"schema_version":"1.0","source":{"id":"math/0502169","kind":"arxiv","version":2}},"canonical_sha256":"0df9862b72a703dfc28bf19a56351507d8c4751b49502eb11bf78b897a651d85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0df9862b72a703dfc28bf19a56351507d8c4751b49502eb11bf78b897a651d85","first_computed_at":"2026-05-18T01:05:23.764471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.764471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/j+jhI6Fo9bO0zKF/b/ZmkViXZWzhO8XmhhPEAHiPbJHsL58pPhSU6ufceJKzGq4iwUhA4vH0KDyyoZ4b4knDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.765029Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:357f060a60f168f1608c0c014cdd8ff71d5ed5948ef3db46bae3f38ad7bda7f3","sha256:d75b61bb66e062a44d6b88e397f3c48b943ec12dc3c24772ce174bf76a7e42e4"],"state_sha256":"a5ba5f47675e0345e4e915e9faef269b380c190b6be2b71e73b7138e5f70cd22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TcfsLkB604gwdmhX3FiGS7PMCMaEReOhHnoL+ahS2RWoCMQkDPt/qCqx+cVG8WT1zFLmdfc6k9WaPV7LIwNZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:48:12.445729Z","bundle_sha256":"618026d5e0422b23f312682a329053271b4b247a2d92cd553814a7f72f463bb1"}}