{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JDCDXUH3NDU4MMUJRDARL7GDQM","short_pith_number":"pith:JDCDXUH3","canonical_record":{"source":{"id":"1509.06006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-20T12:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"44d7c1e31686c7e506c908176b50c1d2b6860b4f8dd80622f7e3058d56b432a6","abstract_canon_sha256":"a4ba7898af128370f8e80ab15b764469aeff4af18c144b3f6ae06f322701277d"},"schema_version":"1.0"},"canonical_sha256":"48c43bd0fb68e9c6328988c115fcc3832da22c25d9f55794f7753bcf3790f2b5","source":{"kind":"arxiv","id":"1509.06006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06006","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06006v1","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06006","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"JDCDXUH3NDU4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JDCDXUH3NDU4MMUJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JDCDXUH3","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JDCDXUH3NDU4MMUJRDARL7GDQM","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-20T12:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"44d7c1e31686c7e506c908176b50c1d2b6860b4f8dd80622f7e3058d56b432a6","abstract_canon_sha256":"a4ba7898af128370f8e80ab15b764469aeff4af18c144b3f6ae06f322701277d"},"schema_version":"1.0"},"canonical_sha256":"48c43bd0fb68e9c6328988c115fcc3832da22c25d9f55794f7753bcf3790f2b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:36.113967Z","signature_b64":"AO8Tu3ORNIVhM3bTWAQ1CK5r7D7ZMa9228p7T0fN2xFRsSBKkTFU6BzL30YjVLPIdLq9DVcq1PRAWzhX5YpkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48c43bd0fb68e9c6328988c115fcc3832da22c25d9f55794f7753bcf3790f2b5","last_reissued_at":"2026-05-18T01:32:36.113361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:36.113361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06006","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tEWuWdnq70XhETSaZRoXyPD+FMsEeksYdPbin1kNDhazBOcuu0syWt5YvWRfLQXgCdbGFnHDGRzWAkkl3HWHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:32:51.058722Z"},"content_sha256":"3d80f516206e0e58b79c6f1cbb0697fd706941480e402224f411bfd67efd2716","schema_version":"1.0","event_id":"sha256:3d80f516206e0e58b79c6f1cbb0697fd706941480e402224f411bfd67efd2716"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JDCDXUH3NDU4MMUJRDARL7GDQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Krichever-Novikov Vertex Algebras on Compact Riemann Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Lu Ding, Shikun Wang","submitted_at":"2015-09-20T12:27:45Z","abstract_excerpt":"We give a notation of Krichever-Novikov vertex algebras on compact Riemann surfaces which is a bit weaker, but quite similar to vertex algebras. As example, we construct Krichever-Novikov vertex algebras of generalized Heisenberg algebras on arbitrary compact Riemann surfaces, which are reduced to be Heisenberg vertex algebra when restricted on Riemann spheres."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06006","kind":"arxiv","version":1},"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":"2026-05-18T01:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Db5Xy8UkZd3ZYxyEVjbkYCbtcrQSnIQdmCnkL5v++I90aR0GsHZXk9wEGIpXwHoPDt90ZMZochmQknIc0nNQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:32:51.059382Z"},"content_sha256":"3c6e4c6fe4a57cceee689b9691c03dafcc4d8b517938e56891798d12adf161c0","schema_version":"1.0","event_id":"sha256:3c6e4c6fe4a57cceee689b9691c03dafcc4d8b517938e56891798d12adf161c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDCDXUH3NDU4MMUJRDARL7GDQM/bundle.json","state_url":"https://pith.science/pith/JDCDXUH3NDU4MMUJRDARL7GDQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDCDXUH3NDU4MMUJRDARL7GDQM/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":"2026-06-05T18:32:51Z","links":{"resolver":"https://pith.science/pith/JDCDXUH3NDU4MMUJRDARL7GDQM","bundle":"https://pith.science/pith/JDCDXUH3NDU4MMUJRDARL7GDQM/bundle.json","state":"https://pith.science/pith/JDCDXUH3NDU4MMUJRDARL7GDQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDCDXUH3NDU4MMUJRDARL7GDQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JDCDXUH3NDU4MMUJRDARL7GDQM","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":"a4ba7898af128370f8e80ab15b764469aeff4af18c144b3f6ae06f322701277d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-20T12:27:45Z","title_canon_sha256":"44d7c1e31686c7e506c908176b50c1d2b6860b4f8dd80622f7e3058d56b432a6"},"schema_version":"1.0","source":{"id":"1509.06006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06006","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06006v1","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06006","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"JDCDXUH3NDU4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JDCDXUH3NDU4MMUJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JDCDXUH3","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:3c6e4c6fe4a57cceee689b9691c03dafcc4d8b517938e56891798d12adf161c0","target":"graph","created_at":"2026-05-18T01:32:36Z","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 give a notation of Krichever-Novikov vertex algebras on compact Riemann surfaces which is a bit weaker, but quite similar to vertex algebras. As example, we construct Krichever-Novikov vertex algebras of generalized Heisenberg algebras on arbitrary compact Riemann surfaces, which are reduced to be Heisenberg vertex algebra when restricted on Riemann spheres.","authors_text":"Lu Ding, Shikun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-20T12:27:45Z","title":"Krichever-Novikov Vertex Algebras on Compact Riemann Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06006","kind":"arxiv","version":1},"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":"sha256:3d80f516206e0e58b79c6f1cbb0697fd706941480e402224f411bfd67efd2716","target":"record","created_at":"2026-05-18T01:32:36Z","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":"a4ba7898af128370f8e80ab15b764469aeff4af18c144b3f6ae06f322701277d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-20T12:27:45Z","title_canon_sha256":"44d7c1e31686c7e506c908176b50c1d2b6860b4f8dd80622f7e3058d56b432a6"},"schema_version":"1.0","source":{"id":"1509.06006","kind":"arxiv","version":1}},"canonical_sha256":"48c43bd0fb68e9c6328988c115fcc3832da22c25d9f55794f7753bcf3790f2b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48c43bd0fb68e9c6328988c115fcc3832da22c25d9f55794f7753bcf3790f2b5","first_computed_at":"2026-05-18T01:32:36.113361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:36.113361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AO8Tu3ORNIVhM3bTWAQ1CK5r7D7ZMa9228p7T0fN2xFRsSBKkTFU6BzL30YjVLPIdLq9DVcq1PRAWzhX5YpkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:36.113967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d80f516206e0e58b79c6f1cbb0697fd706941480e402224f411bfd67efd2716","sha256:3c6e4c6fe4a57cceee689b9691c03dafcc4d8b517938e56891798d12adf161c0"],"state_sha256":"70cdd682849d3f1f3a95d033982c08d4ea89b1676cdebeb1ab7dd959dc214822"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IXX9tgeFlyl1VlbnplMmadSORvBopfoWL7p5pHgQp+1aLHjreUmQYx7I0Tk2ZqSzr+MlmOkINT09Z0WmvSmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:32:51.062661Z","bundle_sha256":"5952870fd8f5446b8ab6f3b0e6dd3d78e5d1896623a56c9ee2ac9849ed156c17"}}