{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Y7OEC5IWQC4UMOGZQ5L62QNGZC","short_pith_number":"pith:Y7OEC5IW","canonical_record":{"source":{"id":"1404.2593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-09T09:56:48Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"5eea467d3bb9d2bb187c7474b7d5f853ca2aa5fd7c4425c7175b926fc1fb3095","abstract_canon_sha256":"535f6737d1f043ca962e3de5a2beec94003807b33c2f3c4d129693f4ff5be3f4"},"schema_version":"1.0"},"canonical_sha256":"c7dc41751680b94638d98757ed41a6c89f2f81319425e1e3484b6343aee30580","source":{"kind":"arxiv","id":"1404.2593","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2593","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2593v1","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2593","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"Y7OEC5IWQC4U","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y7OEC5IWQC4UMOGZ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y7OEC5IW","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Y7OEC5IWQC4UMOGZQ5L62QNGZC","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-09T09:56:48Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"5eea467d3bb9d2bb187c7474b7d5f853ca2aa5fd7c4425c7175b926fc1fb3095","abstract_canon_sha256":"535f6737d1f043ca962e3de5a2beec94003807b33c2f3c4d129693f4ff5be3f4"},"schema_version":"1.0"},"canonical_sha256":"c7dc41751680b94638d98757ed41a6c89f2f81319425e1e3484b6343aee30580","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:30.046551Z","signature_b64":"5VpE/xrBQ0O7u+OL27SAUVW8gwX6Mjn8TRYnybeTxDxnFE1ZoYbL+NMU1HSj58hGg2a3Ng76qjXc6PE6uD+7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7dc41751680b94638d98757ed41a6c89f2f81319425e1e3484b6343aee30580","last_reissued_at":"2026-05-18T02:54:30.045873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:30.045873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2593","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":"2026-05-18T02:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkYFnIGTqu029ZLhZoxNtSXRvbUtZZgUCc3GhHbrApZrgVh1IBJBaFD7V0Vd8o7H4SwdZaF05t8wLPcQ3DtZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:43:32.085748Z"},"content_sha256":"7b35c076f4528de221fdef7118f43057e8d77ef2269b200962a04e8f5b9cfc9c","schema_version":"1.0","event_id":"sha256:7b35c076f4528de221fdef7118f43057e8d77ef2269b200962a04e8f5b9cfc9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Y7OEC5IWQC4UMOGZQ5L62QNGZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical study of the long wavelength limit of the Toda lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"C. Klein, K. Roidot","submitted_at":"2014-04-09T09:56:48Z","abstract_excerpt":"We present the first detailed numerical study of the Toda equations in $2+1$ dimensions in the limit of long wavelengths, both for the hyperbolic and elliptic case. We first study the formal dispersionless limit of the Toda equations and solve initial value problems for the resulting system up to the point of gradient catastrophe.\n  It is shown that the break-up of the solution in the hyperbolic case is similar to the shock formation in the Hopf equation, a $1+1$ dimensional singularity. In the elliptic case, it is found that the break-up is given by a cusp as for the semiclassical system of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2593","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":"2026-05-18T02:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NP2QMfPJL6Hu7LZvnXGAYks1nw8Yc9WH0oReMATCIDQ0YcISXHU+coMZCKqTJHaCJA1SYuWfGYpGIbAiq9YDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:43:32.086468Z"},"content_sha256":"8f81d5cddc854c680b88c49feb522f88881237115c26a7da0de0a38135ce2a00","schema_version":"1.0","event_id":"sha256:8f81d5cddc854c680b88c49feb522f88881237115c26a7da0de0a38135ce2a00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC/bundle.json","state_url":"https://pith.science/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC/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":"2026-06-06T15:43:32Z","links":{"resolver":"https://pith.science/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC","bundle":"https://pith.science/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC/bundle.json","state":"https://pith.science/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y7OEC5IWQC4UMOGZQ5L62QNGZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Y7OEC5IWQC4UMOGZQ5L62QNGZC","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":"535f6737d1f043ca962e3de5a2beec94003807b33c2f3c4d129693f4ff5be3f4","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-09T09:56:48Z","title_canon_sha256":"5eea467d3bb9d2bb187c7474b7d5f853ca2aa5fd7c4425c7175b926fc1fb3095"},"schema_version":"1.0","source":{"id":"1404.2593","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2593","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2593v1","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2593","created_at":"2026-05-18T02:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"Y7OEC5IWQC4U","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y7OEC5IWQC4UMOGZ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y7OEC5IW","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:8f81d5cddc854c680b88c49feb522f88881237115c26a7da0de0a38135ce2a00","target":"graph","created_at":"2026-05-18T02:54:30Z","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 present the first detailed numerical study of the Toda equations in $2+1$ dimensions in the limit of long wavelengths, both for the hyperbolic and elliptic case. We first study the formal dispersionless limit of the Toda equations and solve initial value problems for the resulting system up to the point of gradient catastrophe.\n  It is shown that the break-up of the solution in the hyperbolic case is similar to the shock formation in the Hopf equation, a $1+1$ dimensional singularity. In the elliptic case, it is found that the break-up is given by a cusp as for the semiclassical system of t","authors_text":"C. Klein, K. Roidot","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-09T09:56:48Z","title":"Numerical study of the long wavelength limit of the Toda lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2593","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":"sha256:7b35c076f4528de221fdef7118f43057e8d77ef2269b200962a04e8f5b9cfc9c","target":"record","created_at":"2026-05-18T02:54:30Z","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":"535f6737d1f043ca962e3de5a2beec94003807b33c2f3c4d129693f4ff5be3f4","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-09T09:56:48Z","title_canon_sha256":"5eea467d3bb9d2bb187c7474b7d5f853ca2aa5fd7c4425c7175b926fc1fb3095"},"schema_version":"1.0","source":{"id":"1404.2593","kind":"arxiv","version":1}},"canonical_sha256":"c7dc41751680b94638d98757ed41a6c89f2f81319425e1e3484b6343aee30580","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7dc41751680b94638d98757ed41a6c89f2f81319425e1e3484b6343aee30580","first_computed_at":"2026-05-18T02:54:30.045873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:30.045873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VpE/xrBQ0O7u+OL27SAUVW8gwX6Mjn8TRYnybeTxDxnFE1ZoYbL+NMU1HSj58hGg2a3Ng76qjXc6PE6uD+7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:30.046551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2593","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b35c076f4528de221fdef7118f43057e8d77ef2269b200962a04e8f5b9cfc9c","sha256:8f81d5cddc854c680b88c49feb522f88881237115c26a7da0de0a38135ce2a00"],"state_sha256":"d79911894caf9bbc6fe24c4751c47041bcc7b74a06b0760fd54b4d44f778cd6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L5BglVoEt4cp48YwXnxSOOYbMDVvvaXyxYtGuJ5bu8bYciVi8dgUoRj4H2Xts9pNJnFRlkleI2iLlsNPL7BqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:43:32.090739Z","bundle_sha256":"c5e4ba540fdb05919affabae1240835976e616b11902bfb6b4c23e3ea6513f15"}}