{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:PGASK52I7U5ZESIYIVQ6AGIUO3","short_pith_number":"pith:PGASK52I","schema_version":"1.0","canonical_sha256":"7981257748fd3b9249184561e0191476f3f54df2b0152bf448555fae55df4bb0","source":{"kind":"arxiv","id":"0801.2326","version":1},"attestation_state":"computed","paper":{"title":"Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Tamara Grava, Tom Claeys","submitted_at":"2008-01-15T15:38:34Z","abstract_excerpt":"We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\n  The sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent "},"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":"0801.2326","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2008-01-15T15:38:34Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"cb713f90b0cb9885f84bbde2fdf6b5556deefc599fe60dc2e9d8b6844687f7af","abstract_canon_sha256":"1918048119a8f97e7e0f3199e1d6ba9bf46576effcd06b9c5f5c2158686f8960"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:04.260782Z","signature_b64":"NP6RPU0c0s5BLY7frQouUhQkQES5qfRVr2q2cIeVtyR2rA9vnKShhGLsa1xGwG5z1Jg5ABbojgp9KOqCYn+qCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7981257748fd3b9249184561e0191476f3f54df2b0152bf448555fae55df4bb0","last_reissued_at":"2026-05-18T01:31:04.259943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:04.259943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Tamara Grava, Tom Claeys","submitted_at":"2008-01-15T15:38:34Z","abstract_excerpt":"We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\n  The sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2326","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":"0801.2326","created_at":"2026-05-18T01:31:04.260051+00:00"},{"alias_kind":"arxiv_version","alias_value":"0801.2326v1","created_at":"2026-05-18T01:31:04.260051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.2326","created_at":"2026-05-18T01:31:04.260051+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGASK52I7U5Z","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGASK52I7U5ZESIY","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGASK52I","created_at":"2026-05-18T12:25:57.157939+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/PGASK52I7U5ZESIYIVQ6AGIUO3","json":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3.json","graph_json":"https://pith.science/api/pith-number/PGASK52I7U5ZESIYIVQ6AGIUO3/graph.json","events_json":"https://pith.science/api/pith-number/PGASK52I7U5ZESIYIVQ6AGIUO3/events.json","paper":"https://pith.science/paper/PGASK52I"},"agent_actions":{"view_html":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3","download_json":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3.json","view_paper":"https://pith.science/paper/PGASK52I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0801.2326&json=true","fetch_graph":"https://pith.science/api/pith-number/PGASK52I7U5ZESIYIVQ6AGIUO3/graph.json","fetch_events":"https://pith.science/api/pith-number/PGASK52I7U5ZESIYIVQ6AGIUO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3/action/storage_attestation","attest_author":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3/action/author_attestation","sign_citation":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3/action/citation_signature","submit_replication":"https://pith.science/pith/PGASK52I7U5ZESIYIVQ6AGIUO3/action/replication_record"}},"created_at":"2026-05-18T01:31:04.260051+00:00","updated_at":"2026-05-18T01:31:04.260051+00:00"}