{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GYOVBZP7RWLYF7YZSRH6RGRFHU","short_pith_number":"pith:GYOVBZP7","canonical_record":{"source":{"id":"1508.01788","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-08-07T19:40:48Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"c2108819b70a4e9ec39130e2ff3410e549a02499291647f57519e7982ed158ba","abstract_canon_sha256":"ec36f0f64c8fc75fb95bcf2113d7f72eac918ccc4261b19c793a1852437d31a7"},"schema_version":"1.0"},"canonical_sha256":"361d50e5ff8d9782ff19944fe89a253d101b2c7ea24d05a931c71e9fa99de2e1","source":{"kind":"arxiv","id":"1508.01788","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01788","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01788v4","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01788","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"GYOVBZP7RWLY","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GYOVBZP7RWLYF7YZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GYOVBZP7","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GYOVBZP7RWLYF7YZSRH6RGRFHU","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01788","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-08-07T19:40:48Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"c2108819b70a4e9ec39130e2ff3410e549a02499291647f57519e7982ed158ba","abstract_canon_sha256":"ec36f0f64c8fc75fb95bcf2113d7f72eac918ccc4261b19c793a1852437d31a7"},"schema_version":"1.0"},"canonical_sha256":"361d50e5ff8d9782ff19944fe89a253d101b2c7ea24d05a931c71e9fa99de2e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:44.403289Z","signature_b64":"mAR2rpjC4bBqPzysrI5HZ1CnUk2M6Pb9fzhNoYOO8yuFuC4JxG5M5NAerGt38dG7K5ls/i6JIxKrw4s48AtkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"361d50e5ff8d9782ff19944fe89a253d101b2c7ea24d05a931c71e9fa99de2e1","last_reissued_at":"2026-05-18T01:03:44.402904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:44.402904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01788","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":"2026-05-18T01:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XDR/wWlUHla8k7y0qf6s5l7ILgH/9TJLmEstVyXlzfLmNXIPch25gyat2SRCqJDPKsURnQKiJXiM/EmS+FcWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:31:39.358305Z"},"content_sha256":"3c99f8af8413c6cb3093843fb537746d2ea25f928d9fc08159a46406df7f4a57","schema_version":"1.0","event_id":"sha256:3c99f8af8413c6cb3093843fb537746d2ea25f928d9fc08159a46406df7f4a57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GYOVBZP7RWLYF7YZSRH6RGRFHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Inverse Scattering for the Toda Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"nlin.SI","authors_text":"Deniz Bilman, Thomas Trogdon","submitted_at":"2015-08-07T19:40:48Z","abstract_excerpt":"We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in $\\mathcal O(1)$ operations for arbitrary points in the $(n,t)$-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because $(n,t)$ appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01788","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":""},"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":"2026-05-18T01:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QzTtFpLw3v1ji/vLJ9okM0rtNjeSsOrF4yfRY/iOYLJ7LBkvw4eyAVoOLUbwdlPAGT9GiUzYuPVd4xjKteyoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:31:39.358678Z"},"content_sha256":"b80b0515ef6dc06fa3d85f2d20ae97e61fb6434294dd35cbb2931299f1845906","schema_version":"1.0","event_id":"sha256:b80b0515ef6dc06fa3d85f2d20ae97e61fb6434294dd35cbb2931299f1845906"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU/bundle.json","state_url":"https://pith.science/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU/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":"2026-06-12T08:31:39Z","links":{"resolver":"https://pith.science/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU","bundle":"https://pith.science/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU/bundle.json","state":"https://pith.science/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYOVBZP7RWLYF7YZSRH6RGRFHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GYOVBZP7RWLYF7YZSRH6RGRFHU","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":"ec36f0f64c8fc75fb95bcf2113d7f72eac918ccc4261b19c793a1852437d31a7","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-08-07T19:40:48Z","title_canon_sha256":"c2108819b70a4e9ec39130e2ff3410e549a02499291647f57519e7982ed158ba"},"schema_version":"1.0","source":{"id":"1508.01788","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01788","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01788v4","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01788","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"GYOVBZP7RWLY","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GYOVBZP7RWLYF7YZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GYOVBZP7","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:b80b0515ef6dc06fa3d85f2d20ae97e61fb6434294dd35cbb2931299f1845906","target":"graph","created_at":"2026-05-18T01:03:44Z","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 a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in $\\mathcal O(1)$ operations for arbitrary points in the $(n,t)$-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because $(n,t)$ appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigor","authors_text":"Deniz Bilman, Thomas Trogdon","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-08-07T19:40:48Z","title":"Numerical Inverse Scattering for the Toda Lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01788","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":"sha256:3c99f8af8413c6cb3093843fb537746d2ea25f928d9fc08159a46406df7f4a57","target":"record","created_at":"2026-05-18T01:03:44Z","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":"ec36f0f64c8fc75fb95bcf2113d7f72eac918ccc4261b19c793a1852437d31a7","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-08-07T19:40:48Z","title_canon_sha256":"c2108819b70a4e9ec39130e2ff3410e549a02499291647f57519e7982ed158ba"},"schema_version":"1.0","source":{"id":"1508.01788","kind":"arxiv","version":4}},"canonical_sha256":"361d50e5ff8d9782ff19944fe89a253d101b2c7ea24d05a931c71e9fa99de2e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"361d50e5ff8d9782ff19944fe89a253d101b2c7ea24d05a931c71e9fa99de2e1","first_computed_at":"2026-05-18T01:03:44.402904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:44.402904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mAR2rpjC4bBqPzysrI5HZ1CnUk2M6Pb9fzhNoYOO8yuFuC4JxG5M5NAerGt38dG7K5ls/i6JIxKrw4s48AtkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:44.403289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01788","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c99f8af8413c6cb3093843fb537746d2ea25f928d9fc08159a46406df7f4a57","sha256:b80b0515ef6dc06fa3d85f2d20ae97e61fb6434294dd35cbb2931299f1845906"],"state_sha256":"719f223b72ddf13784972b77ffa168589713950ff6e51ab37dec0dc8f7a3b676"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOOEwIKqTMVDpVCH8g7aSuUsaIZq+JM+WzAY1mNgY9qB/z3aCzvSu0/FpjSddNuBoSDnU390axGlUPfUps1sDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:31:39.361078Z","bundle_sha256":"50b8c5ff7b3338e07d06ebad165308f01db52ceb9bc0b1293fe89ac64fae39df"}}