{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KIGTOVJ6VP7S6AJOJINH3JGJTK","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":"81e984fe8bcd30f607d8f6a86cc8c89f39ebe0ae708991ee9cc46542428789dd","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T13:10:54Z","title_canon_sha256":"8e0b92e3676e8ea6c7b3cb39d95e7c0fe32d5dc0adeca5545347b04175d16261"},"schema_version":"1.0","source":{"id":"1707.01361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01361","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01361v1","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01361","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"KIGTOVJ6VP7S","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KIGTOVJ6VP7S6AJO","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KIGTOVJ6","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:a2a1132bef410af0ee298a9fb70745fbce32b15aa90e3802b871cf5a841d3c39","target":"graph","created_at":"2026-05-18T00:40:52Z","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 study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is the continuation of a precedent work by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.","authors_text":"Alberto Lastra, St\\'ephane Malek","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T13:10:54Z","title":"Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01361","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":"sha256:03396c764c6880468c8c12e8b64911ad9a50715cc9c3545bbc16e0b8b7da63ff","target":"record","created_at":"2026-05-18T00:40:52Z","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":"81e984fe8bcd30f607d8f6a86cc8c89f39ebe0ae708991ee9cc46542428789dd","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T13:10:54Z","title_canon_sha256":"8e0b92e3676e8ea6c7b3cb39d95e7c0fe32d5dc0adeca5545347b04175d16261"},"schema_version":"1.0","source":{"id":"1707.01361","kind":"arxiv","version":1}},"canonical_sha256":"520d37553eabff2f012e4a1a7da4c99aa8355cbb89e58fa22b32d5fe34f5ede3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"520d37553eabff2f012e4a1a7da4c99aa8355cbb89e58fa22b32d5fe34f5ede3","first_computed_at":"2026-05-18T00:40:52.511327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:52.511327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09JFiAwRySYpmWJCwtgVGfeYhcab3P/sxf+U0fxifMLkUZLNylI3hDMdbuOJIYzN5lfKsCSEeQOvLcmvgKTPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:52.511976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03396c764c6880468c8c12e8b64911ad9a50715cc9c3545bbc16e0b8b7da63ff","sha256:a2a1132bef410af0ee298a9fb70745fbce32b15aa90e3802b871cf5a841d3c39"],"state_sha256":"3bce1f07976472f98f8a4ebb54da214d8b466d1e6928dfb26603f4e7ef9f8cfe"}