{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7HF5P2I6DYMQXCYHRFZS67I4DZ","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":"637126bd8800dda0bdf0478689ff38600b3f77c5f3254e73479d3a377bc21b3c","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-24T06:41:35Z","title_canon_sha256":"3a6c24ccd004cc69ac727fcae23eccf1ee7136e6dd064bd86aa144cb3730f50b"},"schema_version":"1.0","source":{"id":"1204.5278","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5278","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5278v2","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5278","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"7HF5P2I6DYMQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7HF5P2I6DYMQXCYH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7HF5P2I6","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:1e7e3a8b962813cd26dd16940fa3703ad9027b696289dfa365a4c7a1c3035836","target":"graph","created_at":"2026-05-18T03:48:13Z","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 establish locality estimates, known as Lieb-Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb-Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems.","authors_text":"Gerald Teschl, Robert Sims, Umar Islambekov","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-24T06:41:35Z","title":"Lieb-Robinson Bounds for the Toda Lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5278","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:de133af47a8befb3901af1498227b26cd5fafcfa924170fd75e841d24a81067a","target":"record","created_at":"2026-05-18T03:48:13Z","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":"637126bd8800dda0bdf0478689ff38600b3f77c5f3254e73479d3a377bc21b3c","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-24T06:41:35Z","title_canon_sha256":"3a6c24ccd004cc69ac727fcae23eccf1ee7136e6dd064bd86aa144cb3730f50b"},"schema_version":"1.0","source":{"id":"1204.5278","kind":"arxiv","version":2}},"canonical_sha256":"f9cbd7e91e1e190b8b0789732f7d1c1e5abced1e17a500f23fca43c9be8ed9af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9cbd7e91e1e190b8b0789732f7d1c1e5abced1e17a500f23fca43c9be8ed9af","first_computed_at":"2026-05-18T03:48:13.384125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:13.384125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dA8J69UOTWdX3/YKB29Dhg1Gd9GtdF0pMsRXMaoz71oCOK0eXnQqyoAy7GpKwtIiW6kGwhi5K+2RPKxR9mTHAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:13.384827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5278","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de133af47a8befb3901af1498227b26cd5fafcfa924170fd75e841d24a81067a","sha256:1e7e3a8b962813cd26dd16940fa3703ad9027b696289dfa365a4c7a1c3035836"],"state_sha256":"0c349824fe06d0949da65d37725aed3ca4b522191c56069d315e22d640206754"}