{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:WUT33A3OQRQVMCIGNGAPVBC6MW","short_pith_number":"pith:WUT33A3O","canonical_record":{"source":{"id":"nlin/0004015","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2000-04-10T08:44:24Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"c4119df27002561692e7ff342a78d792adbdb9a4a57f8b08a48efd60c45fd345","abstract_canon_sha256":"89d74388ef3b1c8599bc5744de8e8bcdeee87fa8d64ba435e596d189a6b60741"},"schema_version":"1.0"},"canonical_sha256":"b527bd836e84615609066980fa845e65b4755fe9e37bd15a4bb3d88884583491","source":{"kind":"arxiv","id":"nlin/0004015","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0004015","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0004015v4","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0004015","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"WUT33A3OQRQV","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"pith_short_16","alias_value":"WUT33A3OQRQVMCIG","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"pith_short_8","alias_value":"WUT33A3O","created_at":"2026-07-04T14:41:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:WUT33A3OQRQVMCIGNGAPVBC6MW","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0004015","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2000-04-10T08:44:24Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"c4119df27002561692e7ff342a78d792adbdb9a4a57f8b08a48efd60c45fd345","abstract_canon_sha256":"89d74388ef3b1c8599bc5744de8e8bcdeee87fa8d64ba435e596d189a6b60741"},"schema_version":"1.0"},"canonical_sha256":"b527bd836e84615609066980fa845e65b4755fe9e37bd15a4bb3d88884583491","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:34.661447Z","signature_b64":"14tRZNWhurs1Qc1f8OvxwUjIHea+kO51CyVeOMIrrs37HbECg3kJOmraQ/1Jd4WvPsG297wJTTSZZmdaZZBMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b527bd836e84615609066980fa845e65b4755fe9e37bd15a4bb3d88884583491","last_reissued_at":"2026-07-04T14:41:34.661019Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:34.661019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0004015","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:41:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTnby6iaS1cxP5ofzImj5nFgPklN9gZHHVkiSJGpjArQFuifmL1jfLS39i4wapqrMII2y2NllSVGUo3nx7pFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:07:34.305506Z"},"content_sha256":"5aee2fb8a337edb84eb30b959cc31411c309411ac00d701a1d70e24170645206","schema_version":"1.0","event_id":"sha256:5aee2fb8a337edb84eb30b959cc31411c309411ac00d701a1d70e24170645206"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:WUT33A3OQRQVMCIGNGAPVBC6MW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"nlin.SI","authors_text":"K. Takasaki, T. Ikeda","submitted_at":"2000-04-10T08:44:24Z","abstract_excerpt":"We introduce an extension of the \\ell-reduced KP hierarchy, which we call the \\ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of \\ell=2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl_\\ell^{tor}. This reproduces essentially the same Hirota bilinear equations as those recently introduced by Billig and Iohara et al. We can further derive these Hirota bilinear equation from a Lax formalism of the hierarchy.This Lax formalism also enables us to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0004015","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/nlin/0004015/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:41:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0MpukIXc/QPlpZPFwP9UJLA944I7yQXHVdeekv5LVHlFx8gljrqi6y8ciSuZmQwBZ4OrEXTsMZQVQneagdJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:07:34.306109Z"},"content_sha256":"747f505f81778167383cacd2297a96a1f456140802108d53264d3a1b2c8b3f3f","schema_version":"1.0","event_id":"sha256:747f505f81778167383cacd2297a96a1f456140802108d53264d3a1b2c8b3f3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUT33A3OQRQVMCIGNGAPVBC6MW/bundle.json","state_url":"https://pith.science/pith/WUT33A3OQRQVMCIGNGAPVBC6MW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUT33A3OQRQVMCIGNGAPVBC6MW/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":"2026-08-11T22:07:34Z","links":{"resolver":"https://pith.science/pith/WUT33A3OQRQVMCIGNGAPVBC6MW","bundle":"https://pith.science/pith/WUT33A3OQRQVMCIGNGAPVBC6MW/bundle.json","state":"https://pith.science/pith/WUT33A3OQRQVMCIGNGAPVBC6MW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUT33A3OQRQVMCIGNGAPVBC6MW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:WUT33A3OQRQVMCIGNGAPVBC6MW","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":"89d74388ef3b1c8599bc5744de8e8bcdeee87fa8d64ba435e596d189a6b60741","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"nlin.SI","submitted_at":"2000-04-10T08:44:24Z","title_canon_sha256":"c4119df27002561692e7ff342a78d792adbdb9a4a57f8b08a48efd60c45fd345"},"schema_version":"1.0","source":{"id":"nlin/0004015","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0004015","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0004015v4","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0004015","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"WUT33A3OQRQV","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"pith_short_16","alias_value":"WUT33A3OQRQVMCIG","created_at":"2026-07-04T14:41:34Z"},{"alias_kind":"pith_short_8","alias_value":"WUT33A3O","created_at":"2026-07-04T14:41:34Z"}],"graph_snapshots":[{"event_id":"sha256:747f505f81778167383cacd2297a96a1f456140802108d53264d3a1b2c8b3f3f","target":"graph","created_at":"2026-07-04T14:41:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/nlin/0004015/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce an extension of the \\ell-reduced KP hierarchy, which we call the \\ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of \\ell=2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl_\\ell^{tor}. This reproduces essentially the same Hirota bilinear equations as those recently introduced by Billig and Iohara et al. We can further derive these Hirota bilinear equation from a Lax formalism of the hierarchy.This Lax formalism also enables us to ","authors_text":"K. Takasaki, T. Ikeda","cross_cats":["hep-th","math.QA"],"headline":"","license":"","primary_cat":"nlin.SI","submitted_at":"2000-04-10T08:44:24Z","title":"Toroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0004015","kind":"arxiv","version":4},"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":"sha256:5aee2fb8a337edb84eb30b959cc31411c309411ac00d701a1d70e24170645206","target":"record","created_at":"2026-07-04T14:41:34Z","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":"89d74388ef3b1c8599bc5744de8e8bcdeee87fa8d64ba435e596d189a6b60741","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"nlin.SI","submitted_at":"2000-04-10T08:44:24Z","title_canon_sha256":"c4119df27002561692e7ff342a78d792adbdb9a4a57f8b08a48efd60c45fd345"},"schema_version":"1.0","source":{"id":"nlin/0004015","kind":"arxiv","version":4}},"canonical_sha256":"b527bd836e84615609066980fa845e65b4755fe9e37bd15a4bb3d88884583491","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b527bd836e84615609066980fa845e65b4755fe9e37bd15a4bb3d88884583491","first_computed_at":"2026-07-04T14:41:34.661019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:34.661019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"14tRZNWhurs1Qc1f8OvxwUjIHea+kO51CyVeOMIrrs37HbECg3kJOmraQ/1Jd4WvPsG297wJTTSZZmdaZZBMDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:34.661447Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0004015","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aee2fb8a337edb84eb30b959cc31411c309411ac00d701a1d70e24170645206","sha256:747f505f81778167383cacd2297a96a1f456140802108d53264d3a1b2c8b3f3f"],"state_sha256":"a8abec127060368b60bfe7931f73e6c8ea791ea38c2e103e81ac87b3cef9940a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MMDQcgELEcfTG5fnGzDryU5PmmLgsUMo4g5WGj8uX1nX2QvfxXc+j4HnU6ZGgJ0cfiZ+VMQVRHbqnDHfB8shDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T22:07:34.309477Z","bundle_sha256":"730c3b5648ea636348b3744c5443dae3e755fb5077fd9fa39b93df7cd81253dc"}}