{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5V7I3UYHQPC7O2Z6BQBR5KEX55","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":"17f836f6f8aef2458659f815ce7d2113ca63e59dfe0b803228466177797509f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:05:57Z","title_canon_sha256":"091856c81d32828b98ad5b25e4cd2eb6a47dae5d1d9961c9da6fc1f60f6933a9"},"schema_version":"1.0","source":{"id":"1110.5155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5155","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5155v1","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5155","created_at":"2026-05-18T01:22:44Z"},{"alias_kind":"pith_short_12","alias_value":"5V7I3UYHQPC7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5V7I3UYHQPC7O2Z6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5V7I3UYH","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:0e1448ece6ae01a73a4fd4832edd8e4309a6ede22627a256ac218f5d53dcb9e5","target":"graph","created_at":"2026-05-18T01:22:44Z","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":"This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem of homogenization theory. In this setting we derive a new model system of equations, consisting of the classical shallow water equations coupled with nonlocal evolution equations for a periodic corrector term. We also exhibit a new resonance phenomenon between surface waves and a periodic bottom. This resonance, which gives rise to secular growth of surface ","authors_text":"Catherine Sulem, David Lannes, Walter Craig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:05:57Z","title":"Water waves over a rough bottom in the shallow water regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5155","kind":"arxiv","version":1},"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":"sha256:0f27e298609e697ff79980eb1e8ba59ac7e6a9d2ff76887b5ade4d28850ad63e","target":"record","created_at":"2026-05-18T01:22:44Z","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":"17f836f6f8aef2458659f815ce7d2113ca63e59dfe0b803228466177797509f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:05:57Z","title_canon_sha256":"091856c81d32828b98ad5b25e4cd2eb6a47dae5d1d9961c9da6fc1f60f6933a9"},"schema_version":"1.0","source":{"id":"1110.5155","kind":"arxiv","version":1}},"canonical_sha256":"ed7e8dd30783c5f76b3e0c031ea897ef6f782e58a2e3bcd002d9ab5ed720e0b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed7e8dd30783c5f76b3e0c031ea897ef6f782e58a2e3bcd002d9ab5ed720e0b9","first_computed_at":"2026-05-18T01:22:44.157576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:44.157576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kYNbl8IYdGcUgaSoNGUjlfXVRaCbBK+MbMpB0PIThispGvTCRCW3M6IcdGgfDlhiP8YeSOK1nrWQ4QIuWJcUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:44.158145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f27e298609e697ff79980eb1e8ba59ac7e6a9d2ff76887b5ade4d28850ad63e","sha256:0e1448ece6ae01a73a4fd4832edd8e4309a6ede22627a256ac218f5d53dcb9e5"],"state_sha256":"37fcd0b030b89d7af05c55dfac7fccf22f7c7d9e9b9dca04b84e88ff129a03f7"}