{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5KYPMR46DAJCNRMG2BM74UFJ5T","short_pith_number":"pith:5KYPMR46","schema_version":"1.0","canonical_sha256":"eab0f6479e181226c586d059fe50a9ece627ca97a2cd00e03726ede3b92786c1","source":{"kind":"arxiv","id":"1706.06903","version":1},"attestation_state":"computed","paper":{"title":"Global well-posedness of partially periodic KP-I equation in the energy space and application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Robert","submitted_at":"2017-06-21T13:43:28Z","abstract_excerpt":"In this article, we address the Cauchy problem for the KP-I equation \\[\\partial_t u + \\partial_x^3 u -\\partial_x^{-1}\\partial_y^2u + u\\partial_x u = 0\\] for functions periodic in $y$. We prove global well-posedness of this problem for any data in the energy space $\\mathbb{E} = \\left\\{u\\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right),~\\partial_x u \\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right),~\\partial_x^{-1}\\partial_y u \\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right)\\right\\}$. We then prove that the KdV line soliton, seen as a special solution of KP-I equation, is orbitally stable under this flo"},"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":"1706.06903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-21T13:43:28Z","cross_cats_sorted":[],"title_canon_sha256":"be99de6456f7f1df8b27264199a759849694f01540b53d61faec5e1ebed2bb61","abstract_canon_sha256":"eef113bd50a4ff24f9edca660b1f49768f4f6b6bba0c4b4a20602ca81883337a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:56.561306Z","signature_b64":"u89K+eAmHI6n+Gkpnm6VL27SpKVCxbauPrM3+NfYbfTbuNJzcXyGdET+7yUrE26SGd79rdgH2/m+y9srB6OgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eab0f6479e181226c586d059fe50a9ece627ca97a2cd00e03726ede3b92786c1","last_reissued_at":"2026-05-18T00:41:56.560609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:56.560609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global well-posedness of partially periodic KP-I equation in the energy space and application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Robert","submitted_at":"2017-06-21T13:43:28Z","abstract_excerpt":"In this article, we address the Cauchy problem for the KP-I equation \\[\\partial_t u + \\partial_x^3 u -\\partial_x^{-1}\\partial_y^2u + u\\partial_x u = 0\\] for functions periodic in $y$. We prove global well-posedness of this problem for any data in the energy space $\\mathbb{E} = \\left\\{u\\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right),~\\partial_x u \\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right),~\\partial_x^{-1}\\partial_y u \\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right)\\right\\}$. We then prove that the KdV line soliton, seen as a special solution of KP-I equation, is orbitally stable under this flo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06903","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":"1706.06903","created_at":"2026-05-18T00:41:56.560727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06903v1","created_at":"2026-05-18T00:41:56.560727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06903","created_at":"2026-05-18T00:41:56.560727+00:00"},{"alias_kind":"pith_short_12","alias_value":"5KYPMR46DAJC","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5KYPMR46DAJCNRMG","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5KYPMR46","created_at":"2026-05-18T12:31:00.734936+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/5KYPMR46DAJCNRMG2BM74UFJ5T","json":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T.json","graph_json":"https://pith.science/api/pith-number/5KYPMR46DAJCNRMG2BM74UFJ5T/graph.json","events_json":"https://pith.science/api/pith-number/5KYPMR46DAJCNRMG2BM74UFJ5T/events.json","paper":"https://pith.science/paper/5KYPMR46"},"agent_actions":{"view_html":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T","download_json":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T.json","view_paper":"https://pith.science/paper/5KYPMR46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06903&json=true","fetch_graph":"https://pith.science/api/pith-number/5KYPMR46DAJCNRMG2BM74UFJ5T/graph.json","fetch_events":"https://pith.science/api/pith-number/5KYPMR46DAJCNRMG2BM74UFJ5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T/action/storage_attestation","attest_author":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T/action/author_attestation","sign_citation":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T/action/citation_signature","submit_replication":"https://pith.science/pith/5KYPMR46DAJCNRMG2BM74UFJ5T/action/replication_record"}},"created_at":"2026-05-18T00:41:56.560727+00:00","updated_at":"2026-05-18T00:41:56.560727+00:00"}