{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:JSDDOTLJ2GP43DIJ3Q263RJMVK","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":"aecbfa32563406578b378f4bf0b5f4255afe10a89a957559e3b6ac96587bf139","cross_cats_sorted":["math.CA","math.CV","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-04-20T13:29:54Z","title_canon_sha256":"680bbdfdb374a65160436b4e3a66adca50c5921ce6b09d985e53088fba55f9e4"},"schema_version":"1.0","source":{"id":"math-ph/0604046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0604046","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0604046v1","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0604046","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"JSDDOTLJ2GP4","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"JSDDOTLJ2GP43DIJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"JSDDOTLJ","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:81733eb03cdf163b617e4cd8b3fe7bc2cc67e89ee45587ebbb08b6eaf479fc82","target":"graph","created_at":"2026-05-18T01:38:32Z","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 establish the existence of a real solution y(x,T) with no poles on the real line of the following fourth order analogue of the Painleve I equation, x=Ty-({1/6}y^3+{1/24}(y_x^2+2yy_{xx})+{1/240}y_{xxxx}). This proves the existence part of a conjecture posed by Dubrovin. We obtain our result by proving the solvability of an associated Riemann-Hilbert problem through the approach of a vanishing lemma. In addition, by applying the Deift/Zhou steepest-descent method to this Riemann-Hilbert problem, we obtain the asymptotics for y(x,T) as x\\to\\pm\\infty.","authors_text":"M. Vanlessen, T. Claeys","cross_cats":["math.CA","math.CV","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-04-20T13:29:54Z","title":"The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0604046","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":"sha256:1cc0f3bb4fffcb8a2f91bf07c6c9ab79d1b791c602176526ad5b6cc806c06399","target":"record","created_at":"2026-05-18T01:38:32Z","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":"aecbfa32563406578b378f4bf0b5f4255afe10a89a957559e3b6ac96587bf139","cross_cats_sorted":["math.CA","math.CV","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-04-20T13:29:54Z","title_canon_sha256":"680bbdfdb374a65160436b4e3a66adca50c5921ce6b09d985e53088fba55f9e4"},"schema_version":"1.0","source":{"id":"math-ph/0604046","kind":"arxiv","version":1}},"canonical_sha256":"4c86374d69d19fcd8d09dc35edc52caa96f687205fa34f708d64303d83b09f9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c86374d69d19fcd8d09dc35edc52caa96f687205fa34f708d64303d83b09f9a","first_computed_at":"2026-05-18T01:38:32.900915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:32.900915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"we8S3dIBmTjiMHtmVSSp4saTIU3FWcqj7i+QP5XyOaNnE8oCagH3NSrcfTwv0PnZEVVVJwkV1pIvUDlApOa5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:32.901411Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0604046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cc0f3bb4fffcb8a2f91bf07c6c9ab79d1b791c602176526ad5b6cc806c06399","sha256:81733eb03cdf163b617e4cd8b3fe7bc2cc67e89ee45587ebbb08b6eaf479fc82"],"state_sha256":"fd0ccf4c9fdff4d28dc694279c44d5a2058d181d574487f25bb7990e506ffee2"}