{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:K54HE2XWIUHSTXK2X4LIXXUBRK","short_pith_number":"pith:K54HE2XW","canonical_record":{"source":{"id":"1706.07596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-23T08:28:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4442f1ece32d54a411c20aa4fa65e6dd3270ffedacd87fb6e8a4522de16f41c9","abstract_canon_sha256":"b839ca931b60d270cf610c36fe6380b2c6437ab4029dfc4fb6c3787330c302e7"},"schema_version":"1.0"},"canonical_sha256":"5778726af6450f29dd5abf168bde818a8fb92017bef3f4abe9bd4fd0481299b8","source":{"kind":"arxiv","id":"1706.07596","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07596","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07596v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07596","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"K54HE2XWIUHS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K54HE2XWIUHSTXK2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K54HE2XW","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:K54HE2XWIUHSTXK2X4LIXXUBRK","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-23T08:28:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4442f1ece32d54a411c20aa4fa65e6dd3270ffedacd87fb6e8a4522de16f41c9","abstract_canon_sha256":"b839ca931b60d270cf610c36fe6380b2c6437ab4029dfc4fb6c3787330c302e7"},"schema_version":"1.0"},"canonical_sha256":"5778726af6450f29dd5abf168bde818a8fb92017bef3f4abe9bd4fd0481299b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:48.682223Z","signature_b64":"wDYZmeets74XEgWB/R7VxN3t+Oq7iVIG88dk3QjJCCxp42+kn27CGeuXiAcHd/giZkmB/fwSRMGRnq3XTdQDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5778726af6450f29dd5abf168bde818a8fb92017bef3f4abe9bd4fd0481299b8","last_reissued_at":"2026-05-18T00:41:48.681583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:48.681583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07596","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":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zveHISlmT9WldtW6WKRKZwc5FZxV1RBP9raZMsWWCGlhTq9AwtF82MXS4DqF+0Nz7EkPgiYT9dGQU3ge9J38Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:15.711900Z"},"content_sha256":"db2e9f4e6f5ea8955d3e63d27457128857db9cc22b5d75888e23346d15d30fd8","schema_version":"1.0","event_id":"sha256:db2e9f4e6f5ea8955d3e63d27457128857db9cc22b5d75888e23346d15d30fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:K54HE2XWIUHSTXK2X4LIXXUBRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zhu reduction for Jacobi $n$-point functions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.QA","authors_text":"Kathrin Bringmann, Matthew Krauel, Michael P. Tuite","submitted_at":"2017-06-23T08:28:51Z","abstract_excerpt":"We establish precise Zhu reduction formulas for Jacobi $n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply the reduction formulas to the Fermion model in order to create polynomials of quasi-Jacobi forms which are Jacobi forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07596","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":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y58ImQi1ggARA5se+Jr4tw2l/n6r2kCwKJQucNoA3k2l5JEQWpPXJX81sa9gD6TFziYPmsOHqZkTATUUbTdPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:15.712238Z"},"content_sha256":"d0052345dd96057dbfab127340bc8c4eb0c8a72ad61717d8576d8859d9c3782c","schema_version":"1.0","event_id":"sha256:d0052345dd96057dbfab127340bc8c4eb0c8a72ad61717d8576d8859d9c3782c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K54HE2XWIUHSTXK2X4LIXXUBRK/bundle.json","state_url":"https://pith.science/pith/K54HE2XWIUHSTXK2X4LIXXUBRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K54HE2XWIUHSTXK2X4LIXXUBRK/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":"2026-06-02T22:19:15Z","links":{"resolver":"https://pith.science/pith/K54HE2XWIUHSTXK2X4LIXXUBRK","bundle":"https://pith.science/pith/K54HE2XWIUHSTXK2X4LIXXUBRK/bundle.json","state":"https://pith.science/pith/K54HE2XWIUHSTXK2X4LIXXUBRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K54HE2XWIUHSTXK2X4LIXXUBRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K54HE2XWIUHSTXK2X4LIXXUBRK","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":"b839ca931b60d270cf610c36fe6380b2c6437ab4029dfc4fb6c3787330c302e7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-23T08:28:51Z","title_canon_sha256":"4442f1ece32d54a411c20aa4fa65e6dd3270ffedacd87fb6e8a4522de16f41c9"},"schema_version":"1.0","source":{"id":"1706.07596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07596","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07596v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07596","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"K54HE2XWIUHS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K54HE2XWIUHSTXK2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K54HE2XW","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:d0052345dd96057dbfab127340bc8c4eb0c8a72ad61717d8576d8859d9c3782c","target":"graph","created_at":"2026-05-18T00:41:48Z","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 establish precise Zhu reduction formulas for Jacobi $n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply the reduction formulas to the Fermion model in order to create polynomials of quasi-Jacobi forms which are Jacobi forms.","authors_text":"Kathrin Bringmann, Matthew Krauel, Michael P. Tuite","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-23T08:28:51Z","title":"Zhu reduction for Jacobi $n$-point functions and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07596","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:db2e9f4e6f5ea8955d3e63d27457128857db9cc22b5d75888e23346d15d30fd8","target":"record","created_at":"2026-05-18T00:41:48Z","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":"b839ca931b60d270cf610c36fe6380b2c6437ab4029dfc4fb6c3787330c302e7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-06-23T08:28:51Z","title_canon_sha256":"4442f1ece32d54a411c20aa4fa65e6dd3270ffedacd87fb6e8a4522de16f41c9"},"schema_version":"1.0","source":{"id":"1706.07596","kind":"arxiv","version":1}},"canonical_sha256":"5778726af6450f29dd5abf168bde818a8fb92017bef3f4abe9bd4fd0481299b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5778726af6450f29dd5abf168bde818a8fb92017bef3f4abe9bd4fd0481299b8","first_computed_at":"2026-05-18T00:41:48.681583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:48.681583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wDYZmeets74XEgWB/R7VxN3t+Oq7iVIG88dk3QjJCCxp42+kn27CGeuXiAcHd/giZkmB/fwSRMGRnq3XTdQDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:48.682223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db2e9f4e6f5ea8955d3e63d27457128857db9cc22b5d75888e23346d15d30fd8","sha256:d0052345dd96057dbfab127340bc8c4eb0c8a72ad61717d8576d8859d9c3782c"],"state_sha256":"8c153aca81b878d4b0b88a84d6b02f4169aa3b3714a8cf1b75fd9e5072ecab94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p/E32pK8rf0NQIrYjeYGhwW/NsmjdMM5yoquQz4JAkyphYeSa2a9bUXiV01+T2XM86QIyJFhRpjPTfOJpeaLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:19:15.714120Z","bundle_sha256":"3c792ad16ade6f1e1bf8a6a6177da5b4b2c817b7a0a5435527306804194c3d93"}}