{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QCIHLA6KVMV63RVM3SRTXPJERM","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":"f68d07bcc65558acff1728a04a90631a9bf483fb0e5d3d8d800b6c82a2d3fd31","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-30T14:46:26Z","title_canon_sha256":"0df9f6d3b80ef8462c867d29e9c4bf23269b2e3d322b87a6c1080d62956fb6e4"},"schema_version":"1.0","source":{"id":"1310.8174","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8174","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8174v2","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8174","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"QCIHLA6KVMV6","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QCIHLA6KVMV63RVM","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QCIHLA6K","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:034cba308e57a35db8c2e043ef29c73fe7b61b46cc90bff7aecbd36ee2c52fcc","target":"graph","created_at":"2026-05-18T02:19:06Z","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 two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.","authors_text":"Marco Sammartino, Maria E. Schonbek, Vincenzo Sciacca","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-30T14:46:26Z","title":"Long time behavior for a dissipative shallow water model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8174","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":"sha256:7407f8dfcc3690e79139c11613e115098489f59e61def22a95b73ed8f0b84b93","target":"record","created_at":"2026-05-18T02:19:06Z","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":"f68d07bcc65558acff1728a04a90631a9bf483fb0e5d3d8d800b6c82a2d3fd31","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-30T14:46:26Z","title_canon_sha256":"0df9f6d3b80ef8462c867d29e9c4bf23269b2e3d322b87a6c1080d62956fb6e4"},"schema_version":"1.0","source":{"id":"1310.8174","kind":"arxiv","version":2}},"canonical_sha256":"80907583caab2bedc6acdca33bbd248b09b7ffa78f89eaa4431ec76d1a5c188c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80907583caab2bedc6acdca33bbd248b09b7ffa78f89eaa4431ec76d1a5c188c","first_computed_at":"2026-05-18T02:19:06.273838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:06.273838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQ7jM6oU+ESgIiJHTWqhP1imNHjO7Gt7f1HYTe1gdcEW4UF4+Rhar2kWIIXHuC6E2q+V4LGXLjmtQHREu6iNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:06.274331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8174","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7407f8dfcc3690e79139c11613e115098489f59e61def22a95b73ed8f0b84b93","sha256:034cba308e57a35db8c2e043ef29c73fe7b61b46cc90bff7aecbd36ee2c52fcc"],"state_sha256":"8292cf8791fd6964259a0f3d36b134b22492eed1bd911ca7f390864733471683"}