{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:I3UW3ELWLXPGP2EB3J7X4KLTGD","short_pith_number":"pith:I3UW3ELW","canonical_record":{"source":{"id":"1112.5361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-22T16:06:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a79ab06c12d9484ce4db96a5c6ba0b1e8249bb6fb366660f2aaf9cdd02e7bc9a","abstract_canon_sha256":"b599656ef66b283bd510301a656935d624aa25232b8f06e8efd7224c7cbc33a9"},"schema_version":"1.0"},"canonical_sha256":"46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b","source":{"kind":"arxiv","id":"1112.5361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5361","created_at":"2026-05-18T01:59:03Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5361v1","created_at":"2026-05-18T01:59:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5361","created_at":"2026-05-18T01:59:03Z"},{"alias_kind":"pith_short_12","alias_value":"I3UW3ELWLXPG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I3UW3ELWLXPGP2EB","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I3UW3ELW","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:I3UW3ELWLXPGP2EB3J7X4KLTGD","target":"record","payload":{"canonical_record":{"source":{"id":"1112.5361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-22T16:06:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a79ab06c12d9484ce4db96a5c6ba0b1e8249bb6fb366660f2aaf9cdd02e7bc9a","abstract_canon_sha256":"b599656ef66b283bd510301a656935d624aa25232b8f06e8efd7224c7cbc33a9"},"schema_version":"1.0"},"canonical_sha256":"46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:03.108629Z","signature_b64":"hgm7cHhsz2iM2qaAZ6rfDwXaaqcMJ5giqFQQHrNgc+GldZoiaQmH5xSF1+nCPTKtcT2h2D0v3sJzBsPwCttzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b","last_reissued_at":"2026-05-18T01:59:03.107920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:03.107920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.5361","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":"2026-05-18T01:59:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyDyZ+vC4Rvtoobeadz2YCUl+orttpSgdKx9IsWVDu+LsMuijp8l9wBoaXOdPjP5HIpZeafmt+spQXfmabVXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:38:03.656405Z"},"content_sha256":"4c22851b3dea66b7772952a60d35db0b6373e5a5023e24b6d041532e92328d1e","schema_version":"1.0","event_id":"sha256:4c22851b3dea66b7772952a60d35db0b6373e5a5023e24b6d041532e92328d1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:I3UW3ELWLXPGP2EB3J7X4KLTGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virasoro action on Imaginary Verma modules and the operator form of the KZ-equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Ben Cox, Renato Martins, Vyacheslav Futorny","submitted_at":"2011-12-22T16:06:13Z","abstract_excerpt":"We define the Virasoro algebra action on imaginary Verma modules for affine sl(2) and construct the analogs of Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a free field realization of imaginary Verma modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5361","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":"2026-05-18T01:59:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YICDNNOh2tcEQGxF1evd1cTRmWflDJfxrkFoIF+eiOHMyRmgM8R7IowF3p7UDa8c6Ue9DUPD4l9IkUU0XnBeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:38:03.657257Z"},"content_sha256":"c4ec714e31e848b6e7c4cf473efe9723687eeccea9b7a25d9db15bf13b56f4c8","schema_version":"1.0","event_id":"sha256:c4ec714e31e848b6e7c4cf473efe9723687eeccea9b7a25d9db15bf13b56f4c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD/bundle.json","state_url":"https://pith.science/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD/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":"2026-05-30T21:38:03Z","links":{"resolver":"https://pith.science/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD","bundle":"https://pith.science/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD/bundle.json","state":"https://pith.science/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3UW3ELWLXPGP2EB3J7X4KLTGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:I3UW3ELWLXPGP2EB3J7X4KLTGD","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":"b599656ef66b283bd510301a656935d624aa25232b8f06e8efd7224c7cbc33a9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-22T16:06:13Z","title_canon_sha256":"a79ab06c12d9484ce4db96a5c6ba0b1e8249bb6fb366660f2aaf9cdd02e7bc9a"},"schema_version":"1.0","source":{"id":"1112.5361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5361","created_at":"2026-05-18T01:59:03Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5361v1","created_at":"2026-05-18T01:59:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5361","created_at":"2026-05-18T01:59:03Z"},{"alias_kind":"pith_short_12","alias_value":"I3UW3ELWLXPG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I3UW3ELWLXPGP2EB","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I3UW3ELW","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:c4ec714e31e848b6e7c4cf473efe9723687eeccea9b7a25d9db15bf13b56f4c8","target":"graph","created_at":"2026-05-18T01:59:03Z","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 define the Virasoro algebra action on imaginary Verma modules for affine sl(2) and construct the analogs of Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a free field realization of imaginary Verma modules.","authors_text":"Ben Cox, Renato Martins, Vyacheslav Futorny","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-22T16:06:13Z","title":"Virasoro action on Imaginary Verma modules and the operator form of the KZ-equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5361","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":"sha256:4c22851b3dea66b7772952a60d35db0b6373e5a5023e24b6d041532e92328d1e","target":"record","created_at":"2026-05-18T01:59:03Z","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":"b599656ef66b283bd510301a656935d624aa25232b8f06e8efd7224c7cbc33a9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-22T16:06:13Z","title_canon_sha256":"a79ab06c12d9484ce4db96a5c6ba0b1e8249bb6fb366660f2aaf9cdd02e7bc9a"},"schema_version":"1.0","source":{"id":"1112.5361","kind":"arxiv","version":1}},"canonical_sha256":"46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e96d91765dde67e881da7f7e297330fd9ad4b6e9e6d1d2597ddde3b897288b","first_computed_at":"2026-05-18T01:59:03.107920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:03.107920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hgm7cHhsz2iM2qaAZ6rfDwXaaqcMJ5giqFQQHrNgc+GldZoiaQmH5xSF1+nCPTKtcT2h2D0v3sJzBsPwCttzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:03.108629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c22851b3dea66b7772952a60d35db0b6373e5a5023e24b6d041532e92328d1e","sha256:c4ec714e31e848b6e7c4cf473efe9723687eeccea9b7a25d9db15bf13b56f4c8"],"state_sha256":"d70247f53c408cf3f05134125baffff6d48387053c52e3d5e27a5a67e756b73a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bc+WZI0tCV7dKco6GNw37XQ2GCnKag8WLE4jrIfwvPnpzVrIZhgRTHKJh4cD0VLXH69pdZolLOt/m+keNWT5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:38:03.660950Z","bundle_sha256":"f2ddf5d3051ea8e3637f40a2b2444d33399463b083c2db10021dfa298b3b7873"}}