{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BA2ZXQEMMW2PXJRGECZABTVTC5","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":"534a7fc7884f9b8c28a772295dc9d0fd9807490a43fec5aee5940a874c1b92c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-10T21:06:01Z","title_canon_sha256":"5a9f0a552aada332b4635c770378d4df1e80abe4202a0c4a5567935e12cf9f1a"},"schema_version":"1.0","source":{"id":"0902.1758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1758","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1758v2","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1758","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"pith_short_12","alias_value":"BA2ZXQEMMW2P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BA2ZXQEMMW2PXJRG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BA2ZXQEM","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f569c40c13df558fbe5a291a46dce85c66318a92032b0a64c2f09d8eb3343499","target":"graph","created_at":"2026-05-18T04:15:17Z","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 differential equations $F(y,...,y^{(n)})=0$ where $F(Y_0,...,Y_n)$ is a formal series in $Y_0,...,Y_n$ with coefficients in some field of \\emph{generalized power series} $\\mathds{K}_r$ with finite rank $r\\in\\mathbb{N}^*$. Our purpose is to understand the connection between the set of exponents of the coefficients of the equation $\\textrm{Supp} F$ and the set $\\textrm{Supp} y_0$ of exponents of the elements $y_0\\in\\mathds{K}_r$ that are solutions.","authors_text":"Mickael Matusinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-10T21:06:01Z","title":"Differential Puiseux theorem in generalized series fields of finite rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1758","kind":"arxiv","version":2},"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:de2923a84d2c41dff409d150bb412084ef45e2d26cad0fcb0e53e3557dff830b","target":"record","created_at":"2026-05-18T04:15:17Z","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":"534a7fc7884f9b8c28a772295dc9d0fd9807490a43fec5aee5940a874c1b92c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-10T21:06:01Z","title_canon_sha256":"5a9f0a552aada332b4635c770378d4df1e80abe4202a0c4a5567935e12cf9f1a"},"schema_version":"1.0","source":{"id":"0902.1758","kind":"arxiv","version":2}},"canonical_sha256":"08359bc08c65b4fba62620b200ceb31769a422e76bf94ca6afd9380d8f08c409","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08359bc08c65b4fba62620b200ceb31769a422e76bf94ca6afd9380d8f08c409","first_computed_at":"2026-05-18T04:15:17.164074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:17.164074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OQPfjX8Dfmp3u+vHcCxcarmXYm8nsxUk5RU8r7esmENC9DT14jTiVZ0Jk/Fijw606wHuVL2KlgTlJRXrOWsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:17.164771Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de2923a84d2c41dff409d150bb412084ef45e2d26cad0fcb0e53e3557dff830b","sha256:f569c40c13df558fbe5a291a46dce85c66318a92032b0a64c2f09d8eb3343499"],"state_sha256":"75614afebffb37a84a83c7fc41387254a557ec557e0a2769044cc14f8307102d"}