{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HFJXHSG2PYIHPHUM5HTIEWFRRW","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":"e72bdd149af20aaf0439bb252406a4607d9b60e9edabb725ba79484921c65108","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-11T23:07:06Z","title_canon_sha256":"cd82a3d8e383cf4509d20770df26f2de45ecc039f3667a100e3ce11f3d490385"},"schema_version":"1.0","source":{"id":"1212.2674","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2674","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2674v3","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2674","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"HFJXHSG2PYIH","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HFJXHSG2PYIHPHUM","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HFJXHSG2","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:d7c18fcff27c9e964c1eb60da9540ce2c75078da6b93c705a9fd759a3d42c675","target":"graph","created_at":"2026-05-18T01:16:33Z","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 consider the KdV equation $$ \\partial_t u +\\partial^3_x u +u\\partial_x u=0 $$ with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence and uniqueness, in the class of functions which have an expansion with exponentially decaying Fourier coefficients, of a solution on a small interval of time, the length of which depends on the given data and the frequency vector involved. For a Diophantine frequency vector and for small quasi-periodic data (i.e., when the Fourier coefficients obey $|c(m)| \\le \\varepsilon \\exp(-\\kappa_0 |m|)$ with $\\varepsilon > 0$ ","authors_text":"David Damanik (Rice University), Michael Goldstein (University of Toronto)","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-11T23:07:06Z","title":"On the Existence and Uniqueness of Global Solutions for the KdV Equation with Quasi-Periodic Initial Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2674","kind":"arxiv","version":3},"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:c0af0431bbb042138c484ecf5f6f577b273b9eeccdc4ad866f134ed2fa67c001","target":"record","created_at":"2026-05-18T01:16:33Z","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":"e72bdd149af20aaf0439bb252406a4607d9b60e9edabb725ba79484921c65108","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-11T23:07:06Z","title_canon_sha256":"cd82a3d8e383cf4509d20770df26f2de45ecc039f3667a100e3ce11f3d490385"},"schema_version":"1.0","source":{"id":"1212.2674","kind":"arxiv","version":3}},"canonical_sha256":"395373c8da7e10779e8ce9e68258b18d8143c7afaf7b7f384b6e4b7d9cd1d713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"395373c8da7e10779e8ce9e68258b18d8143c7afaf7b7f384b6e4b7d9cd1d713","first_computed_at":"2026-05-18T01:16:33.682971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.682971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DIjTENNvnb2PKBjfQfKRbdyawq10hmHG9joP57CUTBP8jJlS9lFEa3PVhHnZmm3CgBfOEAW4QTZYP0TOWH0ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.683635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2674","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0af0431bbb042138c484ecf5f6f577b273b9eeccdc4ad866f134ed2fa67c001","sha256:d7c18fcff27c9e964c1eb60da9540ce2c75078da6b93c705a9fd759a3d42c675"],"state_sha256":"b463922dcc39bf1fb69481b327b88ffa12020b086cfe9cfae9b3c9f60b46364c"}