{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BNQG4UEEZMDCJP2EGFW7WIJ3EU","short_pith_number":"pith:BNQG4UEE","canonical_record":{"source":{"id":"1504.06381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-24T03:13:23Z","cross_cats_sorted":[],"title_canon_sha256":"226e6ae51847fb81e6d0fbe566f858d1caad3eb6d664df232e71436db6429f4c","abstract_canon_sha256":"e7cb1ed9f33fe28372eee95a1a27a0a5ee6a5cbf26aa1e767105fe1ab451ad0f"},"schema_version":"1.0"},"canonical_sha256":"0b606e5084cb0624bf44316dfb213b251a3e23d17094e20c035a1e913a3f76ae","source":{"kind":"arxiv","id":"1504.06381","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06381","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06381v1","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06381","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"BNQG4UEEZMDC","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BNQG4UEEZMDCJP2E","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BNQG4UEE","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BNQG4UEEZMDCJP2EGFW7WIJ3EU","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-24T03:13:23Z","cross_cats_sorted":[],"title_canon_sha256":"226e6ae51847fb81e6d0fbe566f858d1caad3eb6d664df232e71436db6429f4c","abstract_canon_sha256":"e7cb1ed9f33fe28372eee95a1a27a0a5ee6a5cbf26aa1e767105fe1ab451ad0f"},"schema_version":"1.0"},"canonical_sha256":"0b606e5084cb0624bf44316dfb213b251a3e23d17094e20c035a1e913a3f76ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:22.899200Z","signature_b64":"N1mmkKm7+gRFco06zRCCmknKM387wYKtFTJnObNXjP306ajX7wlSDUhFyggASrML2SkHTwYGRx/cas2XIr0lCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b606e5084cb0624bf44316dfb213b251a3e23d17094e20c035a1e913a3f76ae","last_reissued_at":"2026-05-18T01:12:22.898750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:22.898750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06381","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":"2026-05-18T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4wCIQp5At605rSGO/ILH0+EnbNTyit5vWPCeBOufwHfI4X+aMmDCrSKUW9kXVyIsErRVGMEJhXaszkf5YORJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:57:11.000354Z"},"content_sha256":"d7f18a3cc10914e9a8949495d1ace6e1f6f913d2fdf6abc958b9a45fbd036a3a","schema_version":"1.0","event_id":"sha256:d7f18a3cc10914e9a8949495d1ace6e1f6f913d2fdf6abc958b9a45fbd036a3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BNQG4UEEZMDCJP2EGFW7WIJ3EU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted logarithmic modules of vertex algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bojko Bakalov","submitted_at":"2015-04-24T03:13:23Z","abstract_excerpt":"Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted fields involve the logarithm of the formal variable. We develop the theory of such twisted modules and, in particular, derive a Borcherds identity and commutator formula for them. We investigate in detail the examples of affine and Heisenberg vertex algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06381","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":"2026-05-18T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3c3oy9yJoWIW4kbfDMsiQjke/pWe8CwTdJ0+KXukutJwo7cZ8UV2M/WwBnFKMlnKvoFE6hReOPk5AzdZ9iZmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:57:11.000885Z"},"content_sha256":"8e86d198735b5375df1098ce5969b3fa8f40a5d9fdf7be1ee3c97ec3db0acaa0","schema_version":"1.0","event_id":"sha256:8e86d198735b5375df1098ce5969b3fa8f40a5d9fdf7be1ee3c97ec3db0acaa0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU/bundle.json","state_url":"https://pith.science/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU/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":"2026-05-30T23:57:11Z","links":{"resolver":"https://pith.science/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU","bundle":"https://pith.science/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU/bundle.json","state":"https://pith.science/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNQG4UEEZMDCJP2EGFW7WIJ3EU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BNQG4UEEZMDCJP2EGFW7WIJ3EU","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":"e7cb1ed9f33fe28372eee95a1a27a0a5ee6a5cbf26aa1e767105fe1ab451ad0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-24T03:13:23Z","title_canon_sha256":"226e6ae51847fb81e6d0fbe566f858d1caad3eb6d664df232e71436db6429f4c"},"schema_version":"1.0","source":{"id":"1504.06381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06381","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06381v1","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06381","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"BNQG4UEEZMDC","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BNQG4UEEZMDCJP2E","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BNQG4UEE","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:8e86d198735b5375df1098ce5969b3fa8f40a5d9fdf7be1ee3c97ec3db0acaa0","target":"graph","created_at":"2026-05-18T01:12:22Z","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":"Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted fields involve the logarithm of the formal variable. We develop the theory of such twisted modules and, in particular, derive a Borcherds identity and commutator formula for them. We investigate in detail the examples of affine and Heisenberg vertex algebras.","authors_text":"Bojko Bakalov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-24T03:13:23Z","title":"Twisted logarithmic modules of vertex algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06381","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:d7f18a3cc10914e9a8949495d1ace6e1f6f913d2fdf6abc958b9a45fbd036a3a","target":"record","created_at":"2026-05-18T01:12:22Z","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":"e7cb1ed9f33fe28372eee95a1a27a0a5ee6a5cbf26aa1e767105fe1ab451ad0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-24T03:13:23Z","title_canon_sha256":"226e6ae51847fb81e6d0fbe566f858d1caad3eb6d664df232e71436db6429f4c"},"schema_version":"1.0","source":{"id":"1504.06381","kind":"arxiv","version":1}},"canonical_sha256":"0b606e5084cb0624bf44316dfb213b251a3e23d17094e20c035a1e913a3f76ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b606e5084cb0624bf44316dfb213b251a3e23d17094e20c035a1e913a3f76ae","first_computed_at":"2026-05-18T01:12:22.898750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:22.898750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N1mmkKm7+gRFco06zRCCmknKM387wYKtFTJnObNXjP306ajX7wlSDUhFyggASrML2SkHTwYGRx/cas2XIr0lCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:22.899200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7f18a3cc10914e9a8949495d1ace6e1f6f913d2fdf6abc958b9a45fbd036a3a","sha256:8e86d198735b5375df1098ce5969b3fa8f40a5d9fdf7be1ee3c97ec3db0acaa0"],"state_sha256":"82a0c356d4dcb70716291cfafa26588a125549666dba45a534ebe732193089e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+4lQAKNqPgmmm/lntf67OyTlk6OBKQQmuftkjiYBcAW1LG5z09TwR7U5kV3SdtVt9iJBYpiWTTfHLwXZ5rnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:57:11.004592Z","bundle_sha256":"523edd1aea1f311963504c63783b596c2050b647179b4f817c4bdd4ea80e2033"}}