{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZWRDI3UWOOVOYPZ7SSXS2WGCIA","short_pith_number":"pith:ZWRDI3UW","canonical_record":{"source":{"id":"1501.00124","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-31T12:46:47Z","cross_cats_sorted":[],"title_canon_sha256":"a42f19b3316ede570f2ac9875695acfcbe85123a11497b4a1aec418a15c734df","abstract_canon_sha256":"92684c3fae1074509d2a91f59f27311d60b9b11015d69683b712956533b19d89"},"schema_version":"1.0"},"canonical_sha256":"cda2346e9673aaec3f3f94af2d58c2401416793141c253126bf71f94f5c8a859","source":{"kind":"arxiv","id":"1501.00124","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00124","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00124v2","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00124","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZWRDI3UWOOVO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZWRDI3UWOOVOYPZ7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZWRDI3UW","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZWRDI3UWOOVOYPZ7SSXS2WGCIA","target":"record","payload":{"canonical_record":{"source":{"id":"1501.00124","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-31T12:46:47Z","cross_cats_sorted":[],"title_canon_sha256":"a42f19b3316ede570f2ac9875695acfcbe85123a11497b4a1aec418a15c734df","abstract_canon_sha256":"92684c3fae1074509d2a91f59f27311d60b9b11015d69683b712956533b19d89"},"schema_version":"1.0"},"canonical_sha256":"cda2346e9673aaec3f3f94af2d58c2401416793141c253126bf71f94f5c8a859","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:45.422026Z","signature_b64":"eFMD5nYiMWZ98P7u1QmFsb+8/QWjLLPL+zb8uev1tas5e2E4/AjgtLGAp7uoh3Cu0sCeCXwrowJWbqNtYh8iAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cda2346e9673aaec3f3f94af2d58c2401416793141c253126bf71f94f5c8a859","last_reissued_at":"2026-05-18T01:34:45.421444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:45.421444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.00124","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":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OykxjpCuQlxi9b00S14wQ6Zxmu1XelU6idYeqW9VVuTFksJFcNFMrBnbJpeQWJnazrDC2PZWKLnKcjYHsrupAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:45:44.975084Z"},"content_sha256":"88cf17b91cf439cd42f3879670ab10edfc82e5dcca0051326fc5ec8b45d92779","schema_version":"1.0","event_id":"sha256:88cf17b91cf439cd42f3879670ab10edfc82e5dcca0051326fc5ec8b45d92779"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZWRDI3UWOOVOYPZ7SSXS2WGCIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A modular invariance property of multivariable trace functions for regular vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Masahiko Miyamoto, Matthew Krauel","submitted_at":"2014-12-31T12:46:47Z","abstract_excerpt":"We prove an $\\text{SL}_2 (\\mathbb{Z})$-invariance property of multivariable trace functions on modules for a regular VOA. Applying this result, we provide a proof of the inversion transformation formula for Siegel theta series. As another application, we show that if $V$ is a regular VOA containing a regular subVOA $U$ whose commutant $U^c$ is regular and satisfies $(U^c)^c =U$, then all simple $U$-modules appear in some simple $V$-module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00124","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":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MfpoSxcb4OSlmILL6KeybqfZ/8hXRlkpulIRJIV2/Iiets4Tf1PaRz4zD76Iumc7Jqq78bElVLilAh0LSAWKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:45:44.975435Z"},"content_sha256":"e88b1fc8a0574302b5bb5763c0ab54e1abf473b1f8a8a003cf142df4f7e9d664","schema_version":"1.0","event_id":"sha256:e88b1fc8a0574302b5bb5763c0ab54e1abf473b1f8a8a003cf142df4f7e9d664"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA/bundle.json","state_url":"https://pith.science/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA/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":"2026-06-29T00:45:44Z","links":{"resolver":"https://pith.science/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA","bundle":"https://pith.science/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA/bundle.json","state":"https://pith.science/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWRDI3UWOOVOYPZ7SSXS2WGCIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZWRDI3UWOOVOYPZ7SSXS2WGCIA","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":"92684c3fae1074509d2a91f59f27311d60b9b11015d69683b712956533b19d89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-31T12:46:47Z","title_canon_sha256":"a42f19b3316ede570f2ac9875695acfcbe85123a11497b4a1aec418a15c734df"},"schema_version":"1.0","source":{"id":"1501.00124","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00124","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00124v2","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00124","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZWRDI3UWOOVO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZWRDI3UWOOVOYPZ7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZWRDI3UW","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:e88b1fc8a0574302b5bb5763c0ab54e1abf473b1f8a8a003cf142df4f7e9d664","target":"graph","created_at":"2026-05-18T01:34:45Z","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 prove an $\\text{SL}_2 (\\mathbb{Z})$-invariance property of multivariable trace functions on modules for a regular VOA. Applying this result, we provide a proof of the inversion transformation formula for Siegel theta series. As another application, we show that if $V$ is a regular VOA containing a regular subVOA $U$ whose commutant $U^c$ is regular and satisfies $(U^c)^c =U$, then all simple $U$-modules appear in some simple $V$-module.","authors_text":"Masahiko Miyamoto, Matthew Krauel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-31T12:46:47Z","title":"A modular invariance property of multivariable trace functions for regular vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00124","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":"sha256:88cf17b91cf439cd42f3879670ab10edfc82e5dcca0051326fc5ec8b45d92779","target":"record","created_at":"2026-05-18T01:34:45Z","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":"92684c3fae1074509d2a91f59f27311d60b9b11015d69683b712956533b19d89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-31T12:46:47Z","title_canon_sha256":"a42f19b3316ede570f2ac9875695acfcbe85123a11497b4a1aec418a15c734df"},"schema_version":"1.0","source":{"id":"1501.00124","kind":"arxiv","version":2}},"canonical_sha256":"cda2346e9673aaec3f3f94af2d58c2401416793141c253126bf71f94f5c8a859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cda2346e9673aaec3f3f94af2d58c2401416793141c253126bf71f94f5c8a859","first_computed_at":"2026-05-18T01:34:45.421444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:45.421444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eFMD5nYiMWZ98P7u1QmFsb+8/QWjLLPL+zb8uev1tas5e2E4/AjgtLGAp7uoh3Cu0sCeCXwrowJWbqNtYh8iAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:45.422026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00124","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88cf17b91cf439cd42f3879670ab10edfc82e5dcca0051326fc5ec8b45d92779","sha256:e88b1fc8a0574302b5bb5763c0ab54e1abf473b1f8a8a003cf142df4f7e9d664"],"state_sha256":"e051fd06e2391c7f138698d458e2d2f8a7d3a136724c5e413cb7c9ff67f0a140"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/Xpv8picNvOjarHNmpXAxIAvcUBNb5DUKhDRGaHikfb1vDq9PjsL8zOmCP5HyZu7lNpLYKW40XqZ1TGOwJPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T00:45:44.977330Z","bundle_sha256":"5eb771fb1bb1c0b4ed94ffef5bfe6efba5f56a0f9367a8012fb123d8e3111bc8"}}