{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:MZ6HB4SFZT7EXIO6IBQTRLL27B","short_pith_number":"pith:MZ6HB4SF","canonical_record":{"source":{"id":"nlin/0508007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2005-08-01T17:25:42Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"14b098659b31604c9af600e9a7477e96e1899e0d9278b6198350848b2ffe6195","abstract_canon_sha256":"11a9f6e4c444f6ffa0caac6236c93222c016cc2745ee9a6a5be388f65f4b7600"},"schema_version":"1.0"},"canonical_sha256":"667c70f245ccfe4ba1de406138ad7af87a8c14a3767e371056ff56e57ea0657f","source":{"kind":"arxiv","id":"nlin/0508007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0508007","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0508007v1","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0508007","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"MZ6HB4SFZT7E","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MZ6HB4SFZT7EXIO6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MZ6HB4SF","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:MZ6HB4SFZT7EXIO6IBQTRLL27B","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0508007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2005-08-01T17:25:42Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"14b098659b31604c9af600e9a7477e96e1899e0d9278b6198350848b2ffe6195","abstract_canon_sha256":"11a9f6e4c444f6ffa0caac6236c93222c016cc2745ee9a6a5be388f65f4b7600"},"schema_version":"1.0"},"canonical_sha256":"667c70f245ccfe4ba1de406138ad7af87a8c14a3767e371056ff56e57ea0657f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:21.729845Z","signature_b64":"UlkS6FixNuW0PsRG0ldRSJRH89Z1XA/23MFg3CYr4lWlGm/cCPlwEIcmBsQplQn86pCrrFoME/PUNabgPzY/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"667c70f245ccfe4ba1de406138ad7af87a8c14a3767e371056ff56e57ea0657f","last_reissued_at":"2026-05-18T01:05:21.729297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:21.729297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0508007","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":"2026-05-18T01:05:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hSgDf4ifKl1jVLNPw6Y4KYyO4TtsaTgzuqmOEPFaeYFjK/4u5tOeRBBlLmbxtPps3NrJMbX3Aoz+3RKXmIg/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:35:31.792420Z"},"content_sha256":"d0e074fad26fe77785ab53570f2b0f729f4cc8c22d021b219e183182c3aa62b0","schema_version":"1.0","event_id":"sha256:d0e074fad26fe77785ab53570f2b0f729f4cc8c22d021b219e183182c3aa62b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:MZ6HB4SFZT7EXIO6IBQTRLL27B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The N-soliton of the focusing nonlinear Schroedinger equation for N large","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"nlin.SI","authors_text":"Gregory Lyng, Peter D. Miller","submitted_at":"2005-08-01T17:25:42Z","abstract_excerpt":"We present a detailed analysis of the solution of the focusing nonlinear Schr\\\"odinger equation with initial condition $\\psi(x,0)=N {\\rm sech}(x)$ in the limit $N\\to\\infty$. We begin by presenting new and more accurate numerical reconstructions of the $N$-soliton by inverse scattering (numerical linear algebra) for N=5, 10, 20, and 40. We then recast the inverse-scattering problem as a Riemann-Hilbert problem and provide a rigorous asymptotic analysis of this problem in the large-N limit. For those $(x,t)$ where results have been obtained by other authors, we improve the error estimates from $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0508007","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":"2026-05-18T01:05:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2VlOiOhbAlWVuwIKf6fIxwWPKZmnriiTtfAdadcf8hmTQWgx8k0tPhx+kfc9Eh+DQ6x0qTJ4ES+KqzwHMB6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:35:31.792850Z"},"content_sha256":"623eedf51f88e5a58fcc2b7024c58f5068072287cf48d192b44cce75278f2517","schema_version":"1.0","event_id":"sha256:623eedf51f88e5a58fcc2b7024c58f5068072287cf48d192b44cce75278f2517"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B/bundle.json","state_url":"https://pith.science/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B/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":"2026-06-01T02:35:31Z","links":{"resolver":"https://pith.science/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B","bundle":"https://pith.science/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B/bundle.json","state":"https://pith.science/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZ6HB4SFZT7EXIO6IBQTRLL27B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:MZ6HB4SFZT7EXIO6IBQTRLL27B","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":"11a9f6e4c444f6ffa0caac6236c93222c016cc2745ee9a6a5be388f65f4b7600","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"nlin.SI","submitted_at":"2005-08-01T17:25:42Z","title_canon_sha256":"14b098659b31604c9af600e9a7477e96e1899e0d9278b6198350848b2ffe6195"},"schema_version":"1.0","source":{"id":"nlin/0508007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0508007","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0508007v1","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0508007","created_at":"2026-05-18T01:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"MZ6HB4SFZT7E","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MZ6HB4SFZT7EXIO6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MZ6HB4SF","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:623eedf51f88e5a58fcc2b7024c58f5068072287cf48d192b44cce75278f2517","target":"graph","created_at":"2026-05-18T01:05:21Z","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 detailed analysis of the solution of the focusing nonlinear Schr\\\"odinger equation with initial condition $\\psi(x,0)=N {\\rm sech}(x)$ in the limit $N\\to\\infty$. We begin by presenting new and more accurate numerical reconstructions of the $N$-soliton by inverse scattering (numerical linear algebra) for N=5, 10, 20, and 40. We then recast the inverse-scattering problem as a Riemann-Hilbert problem and provide a rigorous asymptotic analysis of this problem in the large-N limit. For those $(x,t)$ where results have been obtained by other authors, we improve the error estimates from $","authors_text":"Gregory Lyng, Peter D. Miller","cross_cats":["math.CA"],"headline":"","license":"","primary_cat":"nlin.SI","submitted_at":"2005-08-01T17:25:42Z","title":"The N-soliton of the focusing nonlinear Schroedinger equation for N large"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0508007","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:d0e074fad26fe77785ab53570f2b0f729f4cc8c22d021b219e183182c3aa62b0","target":"record","created_at":"2026-05-18T01:05:21Z","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":"11a9f6e4c444f6ffa0caac6236c93222c016cc2745ee9a6a5be388f65f4b7600","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"nlin.SI","submitted_at":"2005-08-01T17:25:42Z","title_canon_sha256":"14b098659b31604c9af600e9a7477e96e1899e0d9278b6198350848b2ffe6195"},"schema_version":"1.0","source":{"id":"nlin/0508007","kind":"arxiv","version":1}},"canonical_sha256":"667c70f245ccfe4ba1de406138ad7af87a8c14a3767e371056ff56e57ea0657f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"667c70f245ccfe4ba1de406138ad7af87a8c14a3767e371056ff56e57ea0657f","first_computed_at":"2026-05-18T01:05:21.729297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:21.729297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UlkS6FixNuW0PsRG0ldRSJRH89Z1XA/23MFg3CYr4lWlGm/cCPlwEIcmBsQplQn86pCrrFoME/PUNabgPzY/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:21.729845Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0508007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0e074fad26fe77785ab53570f2b0f729f4cc8c22d021b219e183182c3aa62b0","sha256:623eedf51f88e5a58fcc2b7024c58f5068072287cf48d192b44cce75278f2517"],"state_sha256":"3aab89f09122d6a450d99e7c91e6c75c5b03dd05026f6a7c192b9f1bdd498b1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLJdOuWZQr6gtGxBJAm6me7OtWz/aN6NT/Kv/VNHfEdzRlGQX6f4bGDGMGtZlC7gvrQ8rMXO8ybNNNYNXG3gAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:35:31.796147Z","bundle_sha256":"ddf62ac7e4f95ff9934ebcf0c169c7554d9f5b0e25057fb2f2661d93a46dc628"}}