{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:PQD6PVHNSIVJCCNEYZ2BOHWNMZ","short_pith_number":"pith:PQD6PVHN","schema_version":"1.0","canonical_sha256":"7c07e7d4ed922a9109a4c674171ecd6667c7cbfecdbe5bee40089c1c95cdedd9","source":{"kind":"arxiv","id":"math/0608290","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear evolution PDEs in R^+ \\times C^d: existence and uniqueness of solutions, asymptotic and Borel summability","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"O. Costin, S. Tanveer","submitted_at":"2006-08-11T17:50:38Z","abstract_excerpt":"We consider a system of $n$-th order nonlinear quasilinear partial differential equations of the form\n  $${\\bf u}_t + \\mathcal{P}(\\partial_{\\bf x}^{\\bf j}){\\bf u}+{\\bf g} \\left( {\\bf x}, t, \\{\\partial_{\\bf x}^{{\\bf j}} {\\bf u}\\}) =0; {\\bf {u}}({\\bf x}, 0) = {\\bf {u}}_I({\\bf x})$$\n with $\\mathbf{u}\\in\\CC^{r}$, for $ t\\in (0,T)$ and large $|{\\bf x}|$ in a poly-sector $S$ in $\\mathbb{C}^d$ ($\\partial_{\\bf x}^{\\bf j} \\equiv \\partial_{x_1}^{j_1} \\partial_{x_2}^{j_2} ...\\partial_{x_d}^{j_d}$ and $j_1+...+j_d\\le n$). The principal part of the constant coefficient $n$-th order differential operator $\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0608290","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-08-11T17:50:38Z","cross_cats_sorted":[],"title_canon_sha256":"9e8d722954f5bbfebf1d62e74f1af9069b399801c0ff1d5cd8fe5dc16cc0fb3a","abstract_canon_sha256":"db885affd42b7c3682f98f83f94fb2c00ef27cca95607f327c5957b537a1e912"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:23.868932Z","signature_b64":"KhRjkTMgMzEGuPHiKD/2TsdRuwGZmBISN7fkLOLaNpRO3b2WgO69bJwxazPMBdDo5HxXZgEmuOAYekM2P2JLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c07e7d4ed922a9109a4c674171ecd6667c7cbfecdbe5bee40089c1c95cdedd9","last_reissued_at":"2026-05-18T01:38:23.868269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:23.868269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear evolution PDEs in R^+ \\times C^d: existence and uniqueness of solutions, asymptotic and Borel summability","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"O. Costin, S. Tanveer","submitted_at":"2006-08-11T17:50:38Z","abstract_excerpt":"We consider a system of $n$-th order nonlinear quasilinear partial differential equations of the form\n  $${\\bf u}_t + \\mathcal{P}(\\partial_{\\bf x}^{\\bf j}){\\bf u}+{\\bf g} \\left( {\\bf x}, t, \\{\\partial_{\\bf x}^{{\\bf j}} {\\bf u}\\}) =0; {\\bf {u}}({\\bf x}, 0) = {\\bf {u}}_I({\\bf x})$$\n with $\\mathbf{u}\\in\\CC^{r}$, for $ t\\in (0,T)$ and large $|{\\bf x}|$ in a poly-sector $S$ in $\\mathbb{C}^d$ ($\\partial_{\\bf x}^{\\bf j} \\equiv \\partial_{x_1}^{j_1} \\partial_{x_2}^{j_2} ...\\partial_{x_d}^{j_d}$ and $j_1+...+j_d\\le n$). The principal part of the constant coefficient $n$-th order differential operator $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608290","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0608290","created_at":"2026-05-18T01:38:23.868373+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608290v1","created_at":"2026-05-18T01:38:23.868373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608290","created_at":"2026-05-18T01:38:23.868373+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQD6PVHNSIVJ","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQD6PVHNSIVJCCNE","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQD6PVHN","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ","json":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ.json","graph_json":"https://pith.science/api/pith-number/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/graph.json","events_json":"https://pith.science/api/pith-number/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/events.json","paper":"https://pith.science/paper/PQD6PVHN"},"agent_actions":{"view_html":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ","download_json":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ.json","view_paper":"https://pith.science/paper/PQD6PVHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608290&json=true","fetch_graph":"https://pith.science/api/pith-number/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/action/storage_attestation","attest_author":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/action/author_attestation","sign_citation":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/action/citation_signature","submit_replication":"https://pith.science/pith/PQD6PVHNSIVJCCNEYZ2BOHWNMZ/action/replication_record"}},"created_at":"2026-05-18T01:38:23.868373+00:00","updated_at":"2026-05-18T01:38:23.868373+00:00"}