{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QCME3K323TTJQBMLBSP5EZCNXP","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":"32cfc4d907f0ae67a005e4f8a607fdec0a9d4b6f8c6e466239fb5d823b085c9a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-26T12:58:23Z","title_canon_sha256":"09d4ef51a70a1454f62f28194717b019871097f1ce61692390d8d3c10277b5a7"},"schema_version":"1.0","source":{"id":"1802.09279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09279","created_at":"2026-05-18T00:22:34Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09279v1","created_at":"2026-05-18T00:22:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09279","created_at":"2026-05-18T00:22:34Z"},{"alias_kind":"pith_short_12","alias_value":"QCME3K323TTJ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QCME3K323TTJQBML","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QCME3K32","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:bcd73e3bb8b0f470b56adef22d0b8626cff7ff18d71f9192cffd29ebe132b01c","target":"graph","created_at":"2026-05-18T00:22:34Z","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 consider a family of linear singularly perturbed Cauchy problems which combines partial differential operators and linear fractional transforms. We construct a collection of holomorphic solutions on a full covering by sectors of a neighborhood of the origin in $\\mathbb{C}$ with respect to the perturbation parameter $\\epsilon$. This set is built up through classical and special Laplace transforms along piecewise linear paths of functions which possess exponential or super exponential growth/decay on horizontal strips. A fine structure which entails two levels of Gevrey asymptotics of order 1","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":"2018-02-26T12:58:23Z","title":"On parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09279","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:b252f488ea9acaf20fd8023b4d5f79debb1bfc65ff87f6894203561b5a7bd06e","target":"record","created_at":"2026-05-18T00:22:34Z","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":"32cfc4d907f0ae67a005e4f8a607fdec0a9d4b6f8c6e466239fb5d823b085c9a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-26T12:58:23Z","title_canon_sha256":"09d4ef51a70a1454f62f28194717b019871097f1ce61692390d8d3c10277b5a7"},"schema_version":"1.0","source":{"id":"1802.09279","kind":"arxiv","version":1}},"canonical_sha256":"80984dab7adce698058b0c9fd2644dbbc96f31ab6918e7295ce63ee8fd7f6c4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80984dab7adce698058b0c9fd2644dbbc96f31ab6918e7295ce63ee8fd7f6c4d","first_computed_at":"2026-05-18T00:22:34.214051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:34.214051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kVmNuz9JA/by1uQtSTwFwBTA+Dmff2kC4rJFIZ8yTkHyLsaBle+CCT9DzRvHnGKjHau+sXU7ZjSjNYeF7GWHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:34.214733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b252f488ea9acaf20fd8023b4d5f79debb1bfc65ff87f6894203561b5a7bd06e","sha256:bcd73e3bb8b0f470b56adef22d0b8626cff7ff18d71f9192cffd29ebe132b01c"],"state_sha256":"b181c4a0e9ee47c8b0f4a9c6ae340d7604be35942d7259ae921556d7e997bff4"}