{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QFF756KN5BJLSMO6GNLHYYSSID","short_pith_number":"pith:QFF756KN","schema_version":"1.0","canonical_sha256":"814bfef94de852b931de33567c625240d8b8e5f503facc6b5515393f305b964a","source":{"kind":"arxiv","id":"1409.3214","version":1},"attestation_state":"computed","paper":{"title":"The Initial Value Problem for Weakly Nonlinear PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Richard S. Palais","submitted_at":"2014-09-10T19:55:17Z","abstract_excerpt":"We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem. Our generalization of their algorithm can be used to solve initial value problems for a wide class of evolution equations that are \"weakly nonlinear\" in a sense that we will make precise. This class includes in particular the other classical soliton equations (SGE and NLS). As well as being very simple to implement, this method exhibits remarkable speed and stability, making it ideal for use with visualization tools where it m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.3214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-10T19:55:17Z","cross_cats_sorted":[],"title_canon_sha256":"88b15bf373d4aaac8067ecc11b070d03939c20ada3e3209e71acd5d8cb47e86a","abstract_canon_sha256":"a33a40ce9596fd629031a095059356d8832282a83e39d8a99baa105104355203"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:02.882555Z","signature_b64":"S9O0h6T233HTri9f4HfXAvotuv4DU27c5C2nfW3iyPh+DBVz9a/FkNygia4O7XmZBTaCGIm3HGALESXvYl6oBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"814bfef94de852b931de33567c625240d8b8e5f503facc6b5515393f305b964a","last_reissued_at":"2026-05-18T02:43:02.882019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:02.882019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Initial Value Problem for Weakly Nonlinear PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Richard S. Palais","submitted_at":"2014-09-10T19:55:17Z","abstract_excerpt":"We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem. Our generalization of their algorithm can be used to solve initial value problems for a wide class of evolution equations that are \"weakly nonlinear\" in a sense that we will make precise. This class includes in particular the other classical soliton equations (SGE and NLS). As well as being very simple to implement, this method exhibits remarkable speed and stability, making it ideal for use with visualization tools where it m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3214","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.3214","created_at":"2026-05-18T02:43:02.882096+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3214v1","created_at":"2026-05-18T02:43:02.882096+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3214","created_at":"2026-05-18T02:43:02.882096+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFF756KN5BJL","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFF756KN5BJLSMO6","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFF756KN","created_at":"2026-05-18T12:28:43.426989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID","json":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID.json","graph_json":"https://pith.science/api/pith-number/QFF756KN5BJLSMO6GNLHYYSSID/graph.json","events_json":"https://pith.science/api/pith-number/QFF756KN5BJLSMO6GNLHYYSSID/events.json","paper":"https://pith.science/paper/QFF756KN"},"agent_actions":{"view_html":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID","download_json":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID.json","view_paper":"https://pith.science/paper/QFF756KN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3214&json=true","fetch_graph":"https://pith.science/api/pith-number/QFF756KN5BJLSMO6GNLHYYSSID/graph.json","fetch_events":"https://pith.science/api/pith-number/QFF756KN5BJLSMO6GNLHYYSSID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID/action/storage_attestation","attest_author":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID/action/author_attestation","sign_citation":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID/action/citation_signature","submit_replication":"https://pith.science/pith/QFF756KN5BJLSMO6GNLHYYSSID/action/replication_record"}},"created_at":"2026-05-18T02:43:02.882096+00:00","updated_at":"2026-05-18T02:43:02.882096+00:00"}