{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3ITVWADZNEN2QWCZTHZQG6GGC2","short_pith_number":"pith:3ITVWADZ","canonical_record":{"source":{"id":"1505.05635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-21T07:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"f4786d4ddf20ac023ba1091a6327d11f03e351c816926f2ae23422049cc63bb5","abstract_canon_sha256":"916cad25239f4728ed578061d1028aeec3d44d8acf55731b5c611fa0ed353a72"},"schema_version":"1.0"},"canonical_sha256":"da275b0079691ba8585999f30378c616a484d21ceb984d407d42060fbf47070d","source":{"kind":"arxiv","id":"1505.05635","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05635","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05635v1","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05635","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"3ITVWADZNEN2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3ITVWADZNEN2QWCZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3ITVWADZ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3ITVWADZNEN2QWCZTHZQG6GGC2","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-21T07:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"f4786d4ddf20ac023ba1091a6327d11f03e351c816926f2ae23422049cc63bb5","abstract_canon_sha256":"916cad25239f4728ed578061d1028aeec3d44d8acf55731b5c611fa0ed353a72"},"schema_version":"1.0"},"canonical_sha256":"da275b0079691ba8585999f30378c616a484d21ceb984d407d42060fbf47070d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:53.953190Z","signature_b64":"lpQxG1E+6/Dr9cuMGMqrgCxR4xKsnS5KanGGxV7FxKEwkQ1/qgOsVSxRDYNcoDj/YvNmHxMG5UceZheN8cnuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da275b0079691ba8585999f30378c616a484d21ceb984d407d42060fbf47070d","last_reissued_at":"2026-05-18T02:03:53.952615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:53.952615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05635","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":"2026-05-18T02:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z4iCCBNzlLHsJRkzE0Z+rOZILVVAHUKKAeOlkslUSNsIXCnIVO/ZgVMfAk4jrJML+e7Lnz7/sK2chbeWXcqGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:42:17.951709Z"},"content_sha256":"4a95b6862def1aba526643f05fc7ec027fdf869e607e9d2f4d3bb346e9a2ac98","schema_version":"1.0","event_id":"sha256:4a95b6862def1aba526643f05fc7ec027fdf869e607e9d2f4d3bb346e9a2ac98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3ITVWADZNEN2QWCZTHZQG6GGC2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"A. Duran, J. Alvarez","submitted_at":"2015-05-21T07:57:33Z","abstract_excerpt":"Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and solves several drawbacks of some previous algorithms proposed in the literature. The method is illustrated with the numerical generation of periodic traveling waves of fractional KdV type equations and some extended Boussinesq systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05635","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":"2026-05-18T02:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUcYvbIExw+4NzlxAdzzMARvzOaYefKI82HS9Bw2LzRB8/t570tJr+Dyg0xyOSzwP7PRE8rUY6War6jOKiTNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:42:17.952052Z"},"content_sha256":"36516522f41b018f36114c1223cd1c09d03aeb4d959ae84e374e8ea483e72101","schema_version":"1.0","event_id":"sha256:36516522f41b018f36114c1223cd1c09d03aeb4d959ae84e374e8ea483e72101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ITVWADZNEN2QWCZTHZQG6GGC2/bundle.json","state_url":"https://pith.science/pith/3ITVWADZNEN2QWCZTHZQG6GGC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ITVWADZNEN2QWCZTHZQG6GGC2/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":"2026-06-05T16:42:17Z","links":{"resolver":"https://pith.science/pith/3ITVWADZNEN2QWCZTHZQG6GGC2","bundle":"https://pith.science/pith/3ITVWADZNEN2QWCZTHZQG6GGC2/bundle.json","state":"https://pith.science/pith/3ITVWADZNEN2QWCZTHZQG6GGC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ITVWADZNEN2QWCZTHZQG6GGC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3ITVWADZNEN2QWCZTHZQG6GGC2","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":"916cad25239f4728ed578061d1028aeec3d44d8acf55731b5c611fa0ed353a72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-21T07:57:33Z","title_canon_sha256":"f4786d4ddf20ac023ba1091a6327d11f03e351c816926f2ae23422049cc63bb5"},"schema_version":"1.0","source":{"id":"1505.05635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05635","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05635v1","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05635","created_at":"2026-05-18T02:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"3ITVWADZNEN2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3ITVWADZNEN2QWCZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3ITVWADZ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:36516522f41b018f36114c1223cd1c09d03aeb4d959ae84e374e8ea483e72101","target":"graph","created_at":"2026-05-18T02:03:53Z","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":"Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and solves several drawbacks of some previous algorithms proposed in the literature. The method is illustrated with the numerical generation of periodic traveling waves of fractional KdV type equations and some extended Boussinesq systems.","authors_text":"A. Duran, J. Alvarez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-21T07:57:33Z","title":"Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05635","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":"sha256:4a95b6862def1aba526643f05fc7ec027fdf869e607e9d2f4d3bb346e9a2ac98","target":"record","created_at":"2026-05-18T02:03:53Z","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":"916cad25239f4728ed578061d1028aeec3d44d8acf55731b5c611fa0ed353a72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-21T07:57:33Z","title_canon_sha256":"f4786d4ddf20ac023ba1091a6327d11f03e351c816926f2ae23422049cc63bb5"},"schema_version":"1.0","source":{"id":"1505.05635","kind":"arxiv","version":1}},"canonical_sha256":"da275b0079691ba8585999f30378c616a484d21ceb984d407d42060fbf47070d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da275b0079691ba8585999f30378c616a484d21ceb984d407d42060fbf47070d","first_computed_at":"2026-05-18T02:03:53.952615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:53.952615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lpQxG1E+6/Dr9cuMGMqrgCxR4xKsnS5KanGGxV7FxKEwkQ1/qgOsVSxRDYNcoDj/YvNmHxMG5UceZheN8cnuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:53.953190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a95b6862def1aba526643f05fc7ec027fdf869e607e9d2f4d3bb346e9a2ac98","sha256:36516522f41b018f36114c1223cd1c09d03aeb4d959ae84e374e8ea483e72101"],"state_sha256":"362cac5b7bbb32cb7184ccd65d603f6cdedff41d0b8b35a0d4bc333409683433"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCdtS6VDtsxTLXj94nsSYhjuAupFuZ/amEe73xcUV3QlePBPZnF2905GvKVDFgJAP/IdQaz7XSA9Axj/sGyqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:42:17.954075Z","bundle_sha256":"883af9cad96e3b49c6f0d6748c1c3ab4a463c7d7875a5ffec5eac48bcb37ce91"}}