{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VNCF3BN67S3VZTL6YT4WI2DQDQ","short_pith_number":"pith:VNCF3BN6","schema_version":"1.0","canonical_sha256":"ab445d85befcb75ccd7ec4f96468701c1ffe518d93fa36e8fee2dacc5fedf1bc","source":{"kind":"arxiv","id":"1101.2602","version":1},"attestation_state":"computed","paper":{"title":"The KdV hierarchy: universality and a Painleve transcendent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"T. Claeys, T. Grava","submitted_at":"2011-01-13T16:10:45Z","abstract_excerpt":"We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\\e\\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbatio"},"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":"1101.2602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-13T16:10:45Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"54ff2923ca97f6c7985554d022650d091849a6e5d6a8133a506f80b3a2ef185f","abstract_canon_sha256":"39e062e6ca53b8474ccff924a7f49edfeb37da965413b54da80c69f1a061bf64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:57.863569Z","signature_b64":"4ws7nCGHxncz6qHTveyNbf2jw35psRFJAu3XwaRiutKnZ2wyHDHXZ+98LBGycKsqtDRcMs87rdBB04c8FfvJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab445d85befcb75ccd7ec4f96468701c1ffe518d93fa36e8fee2dacc5fedf1bc","last_reissued_at":"2026-05-18T02:22:57.863039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:57.863039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The KdV hierarchy: universality and a Painleve transcendent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"T. Claeys, T. Grava","submitted_at":"2011-01-13T16:10:45Z","abstract_excerpt":"We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\\e\\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2602","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":"1101.2602","created_at":"2026-05-18T02:22:57.863124+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.2602v1","created_at":"2026-05-18T02:22:57.863124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2602","created_at":"2026-05-18T02:22:57.863124+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNCF3BN67S3V","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNCF3BN67S3VZTL6","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNCF3BN6","created_at":"2026-05-18T12:26:44.992195+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/VNCF3BN67S3VZTL6YT4WI2DQDQ","json":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ.json","graph_json":"https://pith.science/api/pith-number/VNCF3BN67S3VZTL6YT4WI2DQDQ/graph.json","events_json":"https://pith.science/api/pith-number/VNCF3BN67S3VZTL6YT4WI2DQDQ/events.json","paper":"https://pith.science/paper/VNCF3BN6"},"agent_actions":{"view_html":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ","download_json":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ.json","view_paper":"https://pith.science/paper/VNCF3BN6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.2602&json=true","fetch_graph":"https://pith.science/api/pith-number/VNCF3BN67S3VZTL6YT4WI2DQDQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VNCF3BN67S3VZTL6YT4WI2DQDQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ/action/storage_attestation","attest_author":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ/action/author_attestation","sign_citation":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ/action/citation_signature","submit_replication":"https://pith.science/pith/VNCF3BN67S3VZTL6YT4WI2DQDQ/action/replication_record"}},"created_at":"2026-05-18T02:22:57.863124+00:00","updated_at":"2026-05-18T02:22:57.863124+00:00"}