{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CEZ3W4GTPOU37ZFGFRREI4N5YT","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":"79928f8e995ea1eef1976a2d63311bdf7c87af0c856dd1601391f83fb4272761","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:29:02Z","title_canon_sha256":"b181449ef34bcb37b8822a3e83a02f130402867cd468468f83d4012ebb3aee00"},"schema_version":"1.0","source":{"id":"1607.01986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01986","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01986v1","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01986","created_at":"2026-05-18T01:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"CEZ3W4GTPOU3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CEZ3W4GTPOU37ZFG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CEZ3W4GT","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:ec1ecd50037945555e047de2225017fdac2461883e5c2518ce31afc1f1f9f8df","target":"graph","created_at":"2026-05-18T01:11:22Z","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 the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey and q-Gevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution.\n  The proof leans on a two level novel version of Ramis-Sibuya theorem under Gevrey and q-Gevrey orders.","authors_text":"Alberto Lastra, Stephane Malek","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:29:02Z","title":"On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01986","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:b18d77f41350704abb69bcf6b444c89783ad9537af2482ccc817548fc5c6db85","target":"record","created_at":"2026-05-18T01:11:22Z","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":"79928f8e995ea1eef1976a2d63311bdf7c87af0c856dd1601391f83fb4272761","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-07T12:29:02Z","title_canon_sha256":"b181449ef34bcb37b8822a3e83a02f130402867cd468468f83d4012ebb3aee00"},"schema_version":"1.0","source":{"id":"1607.01986","kind":"arxiv","version":1}},"canonical_sha256":"1133bb70d37ba9bfe4a62c624471bdc4d8ef5ed3f465fd046750043ac382db9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1133bb70d37ba9bfe4a62c624471bdc4d8ef5ed3f465fd046750043ac382db9c","first_computed_at":"2026-05-18T01:11:22.870346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:22.870346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JOmmZSinHU/SycJGkPFPEEMuf3YjRErKVkV+0wvMnDcYV67VRN6m3S+Sa3OAOvj+Uk4w3TiUNjWc2feI8SQaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:22.870875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b18d77f41350704abb69bcf6b444c89783ad9537af2482ccc817548fc5c6db85","sha256:ec1ecd50037945555e047de2225017fdac2461883e5c2518ce31afc1f1f9f8df"],"state_sha256":"d0c672a8e0691c47f76c26909d788e38345299ee8727eace4b50974fb22a600d"}