{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6RMY22C7RDRVZ6F3I3JEDA4EG5","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":"e96b5962678a88a376079a7d2d960d9dd51559e01446ea270439500ce6c8196f","cross_cats_sorted":["math.CA","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-01T12:55:04Z","title_canon_sha256":"3576e6d4505a607ffcef75c7a0b6e816c683fa64ae1b7c080e83adc175516a49"},"schema_version":"1.0","source":{"id":"1107.0214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0214","created_at":"2026-05-18T02:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0214v1","created_at":"2026-05-18T02:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0214","created_at":"2026-05-18T02:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"6RMY22C7RDRV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6RMY22C7RDRVZ6F3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6RMY22C7","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:1fe27d00c6c6b2ae0592b519d0271361cfce84a2967993ea36262ffa74d2e3dd","target":"graph","created_at":"2026-05-18T02:01:25Z","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 real pole-free solutions to all even members of the Painlev\\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the description of critical asymptotic behavior of solutions to the KdV equation in the small dispersion limit. This was understood in the case of a generic critical point, and we generalize it here to the case of non-generic critical points.","authors_text":"Tom Claeys","cross_cats":["math.CA","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-01T12:55:04Z","title":"Pole-free solutions of the first Painlev\\'e hierarchy and non-generic critical behavior for the KdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0214","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":"sha256:20446f2752629bf8225d5753b2c861e2c8e81cceeda0abd4b601512a53cd163a","target":"record","created_at":"2026-05-18T02:01:25Z","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":"e96b5962678a88a376079a7d2d960d9dd51559e01446ea270439500ce6c8196f","cross_cats_sorted":["math.CA","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-01T12:55:04Z","title_canon_sha256":"3576e6d4505a607ffcef75c7a0b6e816c683fa64ae1b7c080e83adc175516a49"},"schema_version":"1.0","source":{"id":"1107.0214","kind":"arxiv","version":1}},"canonical_sha256":"f4598d685f88e35cf8bb46d2418384374b659293991ea29b989106cec7718f26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4598d685f88e35cf8bb46d2418384374b659293991ea29b989106cec7718f26","first_computed_at":"2026-05-18T02:01:25.919662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:25.919662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sk/l51B3655qP/eC9bpWz5A8cAsPh3vt0ItiX7YWCC97aLFDHi/2NNJnS01cgSPhTtEdHYT+3gUGn1ihfk7DBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:25.920308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20446f2752629bf8225d5753b2c861e2c8e81cceeda0abd4b601512a53cd163a","sha256:1fe27d00c6c6b2ae0592b519d0271361cfce84a2967993ea36262ffa74d2e3dd"],"state_sha256":"13a4ae69f879824124088f1c15b019c4c87d1b19c783a0710573e005ff29786a"}