{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HLVJHWXVG5F5OE7SBW54OOARZQ","short_pith_number":"pith:HLVJHWXV","schema_version":"1.0","canonical_sha256":"3aea93daf5374bd713f20dbbc73811cc382f1c8d07e5b1eb6147a08821f27fdb","source":{"kind":"arxiv","id":"1607.02583","version":1},"attestation_state":"computed","paper":{"title":"Quasi-periodic solutions for quasi-linear generalized KdV equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Giuliani","submitted_at":"2016-07-09T08:15:03Z","abstract_excerpt":"We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash-Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iterat"},"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":"1607.02583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-09T08:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"270df7c00d72458f9ab1847d06cc4c3c00774ab2dc32d6ce3d29821420a66275","abstract_canon_sha256":"885a85d20f4916e7ed164e1b13aaf35e142c246f5874b6f137e2feca9a71ddf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:16.755013Z","signature_b64":"EnWM02WSeKXE3kfdsUhUQ/XgJsQ4AXia5AjJ/hzxmJQlz759voVTTKP22e0n9EvfnRi0QrDrHRAEcdfYFq3rCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3aea93daf5374bd713f20dbbc73811cc382f1c8d07e5b1eb6147a08821f27fdb","last_reissued_at":"2026-05-18T01:11:16.754501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:16.754501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-periodic solutions for quasi-linear generalized KdV equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Giuliani","submitted_at":"2016-07-09T08:15:03Z","abstract_excerpt":"We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The proof is based on an iterative Nash-Moser algorithm. To initialize this scheme, we need to perform a bifurcation analysis taking into account the strongly perturbative effects of the nonlinearity near the origin. In particular, we implement a weak version of the Birkhoff normal form method. The inversion of the linearized operators at each step of the iterat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02583","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":"1607.02583","created_at":"2026-05-18T01:11:16.754588+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02583v1","created_at":"2026-05-18T01:11:16.754588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02583","created_at":"2026-05-18T01:11:16.754588+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLVJHWXVG5F5","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLVJHWXVG5F5OE7S","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLVJHWXV","created_at":"2026-05-18T12:30:19.053100+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/HLVJHWXVG5F5OE7SBW54OOARZQ","json":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ.json","graph_json":"https://pith.science/api/pith-number/HLVJHWXVG5F5OE7SBW54OOARZQ/graph.json","events_json":"https://pith.science/api/pith-number/HLVJHWXVG5F5OE7SBW54OOARZQ/events.json","paper":"https://pith.science/paper/HLVJHWXV"},"agent_actions":{"view_html":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ","download_json":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ.json","view_paper":"https://pith.science/paper/HLVJHWXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02583&json=true","fetch_graph":"https://pith.science/api/pith-number/HLVJHWXVG5F5OE7SBW54OOARZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/HLVJHWXVG5F5OE7SBW54OOARZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ/action/storage_attestation","attest_author":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ/action/author_attestation","sign_citation":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ/action/citation_signature","submit_replication":"https://pith.science/pith/HLVJHWXVG5F5OE7SBW54OOARZQ/action/replication_record"}},"created_at":"2026-05-18T01:11:16.754588+00:00","updated_at":"2026-05-18T01:11:16.754588+00:00"}