{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:UA4MEO2VBQOLCGUWIEEDXO5XIO","short_pith_number":"pith:UA4MEO2V","canonical_record":{"source":{"id":"2104.06123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2021-04-13T11:55:14Z","cross_cats_sorted":[],"title_canon_sha256":"23624b56d5bc0e76bdec063cee7b4d994e8238ecc239eb206c90033a2f76c1ec","abstract_canon_sha256":"72da3bb5a58805a174d4e22af037ef9074737816b9d84187b7d3b8747d1aa140"},"schema_version":"1.0"},"canonical_sha256":"a038c23b550c1cb11a9641083bbbb743a60a3a51fd7013046f422821f8ad96d2","source":{"kind":"arxiv","id":"2104.06123","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.06123","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"2104.06123v2","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.06123","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"UA4MEO2VBQOL","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"pith_short_16","alias_value":"UA4MEO2VBQOLCGUW","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"pith_short_8","alias_value":"UA4MEO2V","created_at":"2026-07-05T02:58:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:UA4MEO2VBQOLCGUWIEEDXO5XIO","target":"record","payload":{"canonical_record":{"source":{"id":"2104.06123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2021-04-13T11:55:14Z","cross_cats_sorted":[],"title_canon_sha256":"23624b56d5bc0e76bdec063cee7b4d994e8238ecc239eb206c90033a2f76c1ec","abstract_canon_sha256":"72da3bb5a58805a174d4e22af037ef9074737816b9d84187b7d3b8747d1aa140"},"schema_version":"1.0"},"canonical_sha256":"a038c23b550c1cb11a9641083bbbb743a60a3a51fd7013046f422821f8ad96d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:58:41.368232Z","signature_b64":"NIG2EKbV4xZ5ImR1tzEJpk27BvWbPzIeKKC08d6xrxCXC7BkGM1RYY1arV2QX+zKLRmCoDM7Nv/kniH1aD7NBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a038c23b550c1cb11a9641083bbbb743a60a3a51fd7013046f422821f8ad96d2","last_reissued_at":"2026-07-05T02:58:41.367778Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:58:41.367778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.06123","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":"2026-07-05T02:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmNmo8/xdQNFYSvgL1J/qYl3S+qqlo0Ax+5glX3hL0NvCJAQAlUx2AQUteZqLMOjUp1pVBADX7a9PPSeXNLwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:10:53.603124Z"},"content_sha256":"6926b0e91f13028a7f309e311d5fb0a51627fc0bfc03fef3f4c96aec78e359b8","schema_version":"1.0","event_id":"sha256:6926b0e91f13028a7f309e311d5fb0a51627fc0bfc03fef3f4c96aec78e359b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:UA4MEO2VBQOLCGUWIEEDXO5XIO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear integral equations and two-dimensional Toda systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Wei Fu, Yue Yin","submitted_at":"2021-04-13T11:55:14Z","abstract_excerpt":"The direct linearisation framework is presented for the two-dimensional Toda equations associated with the infinite-dimensional Lie algebras $A_\\infty$, $B_\\infty$ and $C_\\infty$, as well as the Kac--Moody algebras $A_{r}^{(1)}$, $A_{2r}^{(2)}$, $C_{r}^{(1)}$ and $D_{r+1}^{(2)}$ for arbitrary integers $r\\in\\mathbb{Z}^+$, from the aspect of a set of linear integral equations in a certain form. Such a scheme not only provides a unified perspective to understand the underlying integrability structure, but also induces the direct linearising type solution potentially leading to the universal solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.06123","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.06123/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":"2026-07-05T02:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4fh0PXXDO2N36oSg1whY0bgZm4JohL8dbd6aWGdh5+JzVhk3d+nvzrYUwj0VxHtdLzqOS4GfaLRBPPGZul9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:10:53.603940Z"},"content_sha256":"1981f9f74703eacb739bd5c959ba23a0a9a2df569acbfc9df9bd78126dada1ec","schema_version":"1.0","event_id":"sha256:1981f9f74703eacb739bd5c959ba23a0a9a2df569acbfc9df9bd78126dada1ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO/bundle.json","state_url":"https://pith.science/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO/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":"2026-08-05T02:10:53Z","links":{"resolver":"https://pith.science/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO","bundle":"https://pith.science/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO/bundle.json","state":"https://pith.science/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UA4MEO2VBQOLCGUWIEEDXO5XIO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:UA4MEO2VBQOLCGUWIEEDXO5XIO","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":"72da3bb5a58805a174d4e22af037ef9074737816b9d84187b7d3b8747d1aa140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2021-04-13T11:55:14Z","title_canon_sha256":"23624b56d5bc0e76bdec063cee7b4d994e8238ecc239eb206c90033a2f76c1ec"},"schema_version":"1.0","source":{"id":"2104.06123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.06123","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"2104.06123v2","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.06123","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"UA4MEO2VBQOL","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"pith_short_16","alias_value":"UA4MEO2VBQOLCGUW","created_at":"2026-07-05T02:58:41Z"},{"alias_kind":"pith_short_8","alias_value":"UA4MEO2V","created_at":"2026-07-05T02:58:41Z"}],"graph_snapshots":[{"event_id":"sha256:1981f9f74703eacb739bd5c959ba23a0a9a2df569acbfc9df9bd78126dada1ec","target":"graph","created_at":"2026-07-05T02:58:41Z","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/2104.06123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The direct linearisation framework is presented for the two-dimensional Toda equations associated with the infinite-dimensional Lie algebras $A_\\infty$, $B_\\infty$ and $C_\\infty$, as well as the Kac--Moody algebras $A_{r}^{(1)}$, $A_{2r}^{(2)}$, $C_{r}^{(1)}$ and $D_{r+1}^{(2)}$ for arbitrary integers $r\\in\\mathbb{Z}^+$, from the aspect of a set of linear integral equations in a certain form. Such a scheme not only provides a unified perspective to understand the underlying integrability structure, but also induces the direct linearising type solution potentially leading to the universal solut","authors_text":"Wei Fu, Yue Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2021-04-13T11:55:14Z","title":"Linear integral equations and two-dimensional Toda systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.06123","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":"sha256:6926b0e91f13028a7f309e311d5fb0a51627fc0bfc03fef3f4c96aec78e359b8","target":"record","created_at":"2026-07-05T02:58:41Z","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":"72da3bb5a58805a174d4e22af037ef9074737816b9d84187b7d3b8747d1aa140","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2021-04-13T11:55:14Z","title_canon_sha256":"23624b56d5bc0e76bdec063cee7b4d994e8238ecc239eb206c90033a2f76c1ec"},"schema_version":"1.0","source":{"id":"2104.06123","kind":"arxiv","version":2}},"canonical_sha256":"a038c23b550c1cb11a9641083bbbb743a60a3a51fd7013046f422821f8ad96d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a038c23b550c1cb11a9641083bbbb743a60a3a51fd7013046f422821f8ad96d2","first_computed_at":"2026-07-05T02:58:41.367778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:58:41.367778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NIG2EKbV4xZ5ImR1tzEJpk27BvWbPzIeKKC08d6xrxCXC7BkGM1RYY1arV2QX+zKLRmCoDM7Nv/kniH1aD7NBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:58:41.368232Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.06123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6926b0e91f13028a7f309e311d5fb0a51627fc0bfc03fef3f4c96aec78e359b8","sha256:1981f9f74703eacb739bd5c959ba23a0a9a2df569acbfc9df9bd78126dada1ec"],"state_sha256":"a5f1de2270755893e6406b15f927e1e91a60b6e8afc3c4638806699c76dd8c0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"an7CubFlP9mLQYY2XepQnLNFyedcXWvz1EFhekQh8/6cL4+frl+Z0OThXSDnKHXclH79VJxZkrzC7ejN0jwmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:10:53.610762Z","bundle_sha256":"9928dfebd07271fdfb4100f720059badf976941433e2ee35b85587a4f57ae13f"}}