{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VMLVWONXE2ATXNENCYY3TKDVEM","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":"9f0dcf41807d26194c3d1761e426b61c741791f25007102cc86373fb09a6b864","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-02-01T09:23:41Z","title_canon_sha256":"16b8ad916115171dcefc285c7b9199d139913d062dee0cbc7b85ddab075541e4"},"schema_version":"1.0","source":{"id":"math/0702015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702015","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702015v2","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702015","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"VMLVWONXE2AT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VMLVWONXE2ATXNEN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VMLVWONX","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:2a5321ea564c4c93d44858a718988f45140d284914b8ce3f0d6bd97c3fb74440","target":"graph","created_at":"2026-05-18T01:19:31Z","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 rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore f","authors_text":"Borys Alvarez-Samaniego (IMB), David Lannes (IMB)","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-02-01T09:23:41Z","title":"Large time existence for 3D water-waves and asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702015","kind":"arxiv","version":2},"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":"sha256:96dedc087f4500122b3b9885dd42b8af7d37a92c539609a6015085c8322f77a4","target":"record","created_at":"2026-05-18T01:19:31Z","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":"9f0dcf41807d26194c3d1761e426b61c741791f25007102cc86373fb09a6b864","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-02-01T09:23:41Z","title_canon_sha256":"16b8ad916115171dcefc285c7b9199d139913d062dee0cbc7b85ddab075541e4"},"schema_version":"1.0","source":{"id":"math/0702015","kind":"arxiv","version":2}},"canonical_sha256":"ab175b39b726813bb48d1631b9a875231b08d46fa82516950be904012142e362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab175b39b726813bb48d1631b9a875231b08d46fa82516950be904012142e362","first_computed_at":"2026-05-18T01:19:31.194718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:31.194718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSVrETpOwQrxnKZZuHwm7FRscOLNldQGCukxfHcOIEuSlFfHeUaHzTqet3tmhbXn/DpGkoLc6mCMVThu4/dhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:31.195348Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96dedc087f4500122b3b9885dd42b8af7d37a92c539609a6015085c8322f77a4","sha256:2a5321ea564c4c93d44858a718988f45140d284914b8ce3f0d6bd97c3fb74440"],"state_sha256":"6c82bd542b746276228e75a33d76e2ec6cd10f49d22ad78885bc6f17e11e5f85"}