{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7F7LFZSXDWXAQLKD3D4SAYMX2W","short_pith_number":"pith:7F7LFZSX","schema_version":"1.0","canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","source":{"kind":"arxiv","id":"1301.1585","version":1},"attestation_state":"computed","paper":{"title":"An Averaging Theorem for Perturbed KdV Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guan Huang","submitted_at":"2013-01-08T16:31:46Z","abstract_excerpt":"We consider a perturbed KdV equation:\n  [\\dot{u}+u_{xxx} - 6uu_x = \\epsilon f(x,u(\\cdot)), \\quad x\\in \\mathbb{T}, \\quad\\int_\\mathbb{T} u dx=0.]\n  For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\\in\\mathbb{R}_+^{\\infty}$ be the vector, formed by the KdV integrals of motion, calculated for the potential $u(x)$. Assuming that the perturbation $\\epsilon f(x,u(\\cdot))$ is a smoothing mapping (e.g. it is a smooth function $\\epsilon f(x)$, independent from $u$), and that solutions of the perturbed equation satisfy some mild a-priori assumptions, we prove that for solutions $u(t,x)$ wit"},"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":"1301.1585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T16:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"293555a0063992127c6def37321bce23db691a7d799c3707ba571553eedd2bcd","abstract_canon_sha256":"854d613e04ec1364a8079cc4f4dbe40066e68aee27fdc20ccecc4492ee097f5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:57.107720Z","signature_b64":"nrGKlmQghsH2gDUdYx1vnBpBrqmO3GJAbjIbHclc6/n6LgdN3Jm22X1NDPDzQv05oUKS94qpl8MKleMVasXjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","last_reissued_at":"2026-05-18T03:36:57.107243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:57.107243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Averaging Theorem for Perturbed KdV Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guan Huang","submitted_at":"2013-01-08T16:31:46Z","abstract_excerpt":"We consider a perturbed KdV equation:\n  [\\dot{u}+u_{xxx} - 6uu_x = \\epsilon f(x,u(\\cdot)), \\quad x\\in \\mathbb{T}, \\quad\\int_\\mathbb{T} u dx=0.]\n  For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\\in\\mathbb{R}_+^{\\infty}$ be the vector, formed by the KdV integrals of motion, calculated for the potential $u(x)$. Assuming that the perturbation $\\epsilon f(x,u(\\cdot))$ is a smoothing mapping (e.g. it is a smooth function $\\epsilon f(x)$, independent from $u$), and that solutions of the perturbed equation satisfy some mild a-priori assumptions, we prove that for solutions $u(t,x)$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1585","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":"1301.1585","created_at":"2026-05-18T03:36:57.107298+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.1585v1","created_at":"2026-05-18T03:36:57.107298+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1585","created_at":"2026-05-18T03:36:57.107298+00:00"},{"alias_kind":"pith_short_12","alias_value":"7F7LFZSXDWXA","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7F7LFZSXDWXAQLKD","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7F7LFZSX","created_at":"2026-05-18T12:27:36.564083+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/7F7LFZSXDWXAQLKD3D4SAYMX2W","json":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W.json","graph_json":"https://pith.science/api/pith-number/7F7LFZSXDWXAQLKD3D4SAYMX2W/graph.json","events_json":"https://pith.science/api/pith-number/7F7LFZSXDWXAQLKD3D4SAYMX2W/events.json","paper":"https://pith.science/paper/7F7LFZSX"},"agent_actions":{"view_html":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W","download_json":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W.json","view_paper":"https://pith.science/paper/7F7LFZSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.1585&json=true","fetch_graph":"https://pith.science/api/pith-number/7F7LFZSXDWXAQLKD3D4SAYMX2W/graph.json","fetch_events":"https://pith.science/api/pith-number/7F7LFZSXDWXAQLKD3D4SAYMX2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/action/storage_attestation","attest_author":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/action/author_attestation","sign_citation":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/action/citation_signature","submit_replication":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/action/replication_record"}},"created_at":"2026-05-18T03:36:57.107298+00:00","updated_at":"2026-05-18T03:36:57.107298+00:00"}