{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S2C3OKLJPSSDVFGLIXH4JVP3F5","short_pith_number":"pith:S2C3OKLJ","canonical_record":{"source":{"id":"1802.06452","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-02-18T21:38:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bb0722cfe5570c29a8d09b2649b00742b89d0fc95d8bf3c5442203bec1192242","abstract_canon_sha256":"e1d22f93437736c283b74495c221222de137bc8345f13a450a06a7f2b6971347"},"schema_version":"1.0"},"canonical_sha256":"9685b729697ca43a94cb45cfc4d5fb2f79c24408e203e284663346b6e20093ec","source":{"kind":"arxiv","id":"1802.06452","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06452","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06452v3","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06452","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"S2C3OKLJPSSD","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S2C3OKLJPSSDVFGL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S2C3OKLJ","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S2C3OKLJPSSDVFGLIXH4JVP3F5","target":"record","payload":{"canonical_record":{"source":{"id":"1802.06452","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-02-18T21:38:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bb0722cfe5570c29a8d09b2649b00742b89d0fc95d8bf3c5442203bec1192242","abstract_canon_sha256":"e1d22f93437736c283b74495c221222de137bc8345f13a450a06a7f2b6971347"},"schema_version":"1.0"},"canonical_sha256":"9685b729697ca43a94cb45cfc4d5fb2f79c24408e203e284663346b6e20093ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:17.848605Z","signature_b64":"glN/LWjS3+pzvNgQc4bnVyBzxPJAbVJ/oTV46tt5b74v79gJQDPdZPFTskCZDNdvXUI8r29n9aeX2FizgmmNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9685b729697ca43a94cb45cfc4d5fb2f79c24408e203e284663346b6e20093ec","last_reissued_at":"2026-05-18T00:11:17.847903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:17.847903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.06452","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOhAOHbq6RK70DuZ/KlFiLuiULSCcWp03uw5ve2r6wMdzN+6zsiEkDeiW9njokc7Bwz+z45W+ExKlQ9dfk7WDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:52:08.706166Z"},"content_sha256":"db49d22b02566861ed1541a7d1e52641e3827bc40a88765dde618d3c30bd6491","schema_version":"1.0","event_id":"sha256:db49d22b02566861ed1541a7d1e52641e3827bc40a88765dde618d3c30bd6491"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S2C3OKLJPSSDVFGLIXH4JVP3F5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Direct linearisation of the discrete-time two-dimensional Toda lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Wei Fu","submitted_at":"2018-02-18T21:38:51Z","abstract_excerpt":"The discrete-time two-dimensional Toda lattice of $A_\\infty$-type is studied within the direct linearisation framework, which allows us to deal with several nonlinear equations in this class simultaneously and to construct more general solutions of these equations. The periodic reductions of this model are also considered, giving rise to the discrete-time two-dimensional Toda lattices of $A_{r-1}^{(1)}$-type for $r\\geq 2$ (which amount to the negative flows of members in the discrete Gel'fand--Dikii hierarchy) and their integrability properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06452","kind":"arxiv","version":3},"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":"2026-05-18T00:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l17Ay1IPGeW6/nE0Yzxy0mOL8tsm1E+9uA3C3d+6OycHHKRgIDGPcmBVtsF6tY/jdw3HUf+NWrDQgBQRCEDGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:52:08.706535Z"},"content_sha256":"3871b8b5a61711a719472f435c30a180d65926ae951105f0381c333454ceb965","schema_version":"1.0","event_id":"sha256:3871b8b5a61711a719472f435c30a180d65926ae951105f0381c333454ceb965"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5/bundle.json","state_url":"https://pith.science/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5/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":"2026-06-02T16:52:08Z","links":{"resolver":"https://pith.science/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5","bundle":"https://pith.science/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5/bundle.json","state":"https://pith.science/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2C3OKLJPSSDVFGLIXH4JVP3F5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S2C3OKLJPSSDVFGLIXH4JVP3F5","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":"e1d22f93437736c283b74495c221222de137bc8345f13a450a06a7f2b6971347","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-02-18T21:38:51Z","title_canon_sha256":"bb0722cfe5570c29a8d09b2649b00742b89d0fc95d8bf3c5442203bec1192242"},"schema_version":"1.0","source":{"id":"1802.06452","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06452","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06452v3","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06452","created_at":"2026-05-18T00:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"S2C3OKLJPSSD","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S2C3OKLJPSSDVFGL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S2C3OKLJ","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:3871b8b5a61711a719472f435c30a180d65926ae951105f0381c333454ceb965","target":"graph","created_at":"2026-05-18T00:11:17Z","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":"The discrete-time two-dimensional Toda lattice of $A_\\infty$-type is studied within the direct linearisation framework, which allows us to deal with several nonlinear equations in this class simultaneously and to construct more general solutions of these equations. The periodic reductions of this model are also considered, giving rise to the discrete-time two-dimensional Toda lattices of $A_{r-1}^{(1)}$-type for $r\\geq 2$ (which amount to the negative flows of members in the discrete Gel'fand--Dikii hierarchy) and their integrability properties.","authors_text":"Wei Fu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-02-18T21:38:51Z","title":"Direct linearisation of the discrete-time two-dimensional Toda lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06452","kind":"arxiv","version":3},"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:db49d22b02566861ed1541a7d1e52641e3827bc40a88765dde618d3c30bd6491","target":"record","created_at":"2026-05-18T00:11:17Z","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":"e1d22f93437736c283b74495c221222de137bc8345f13a450a06a7f2b6971347","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2018-02-18T21:38:51Z","title_canon_sha256":"bb0722cfe5570c29a8d09b2649b00742b89d0fc95d8bf3c5442203bec1192242"},"schema_version":"1.0","source":{"id":"1802.06452","kind":"arxiv","version":3}},"canonical_sha256":"9685b729697ca43a94cb45cfc4d5fb2f79c24408e203e284663346b6e20093ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9685b729697ca43a94cb45cfc4d5fb2f79c24408e203e284663346b6e20093ec","first_computed_at":"2026-05-18T00:11:17.847903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:17.847903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"glN/LWjS3+pzvNgQc4bnVyBzxPJAbVJ/oTV46tt5b74v79gJQDPdZPFTskCZDNdvXUI8r29n9aeX2FizgmmNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:17.848605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06452","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db49d22b02566861ed1541a7d1e52641e3827bc40a88765dde618d3c30bd6491","sha256:3871b8b5a61711a719472f435c30a180d65926ae951105f0381c333454ceb965"],"state_sha256":"88ddef934ffd0884918f05e895136a0345f6ab53392221093342a92d0a621e7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agDH/zx2TtwCTsoc8sVPC/slDLUbRs3w0bhvT+vYZic9DQ+SJJQ6+Vuz1HSxxTStZgzD+nT/3qtVSojpszySAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:52:08.708476Z","bundle_sha256":"333946d1c56bc04f78cfd8bc5ea617b27f6bf593f8d1bdce8e4f07cb37c7589e"}}