{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RXS7D6ZYJXDG54BOVDMAPDK6P7","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":"0d48b586b903198bba220e5d01feb4e168058944c38656e5a796d372da5fb15f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-01T16:58:07Z","title_canon_sha256":"e127cc6f2d9098da9a77bcc74c82ff5c8ef13255e3491fb975423ec1e8311feb"},"schema_version":"1.0","source":{"id":"1902.00454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00454","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00454v2","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00454","created_at":"2026-05-17T23:47:58Z"},{"alias_kind":"pith_short_12","alias_value":"RXS7D6ZYJXDG","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RXS7D6ZYJXDG54BO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RXS7D6ZY","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:bec56c4b327fc50abe2db7b73a4c5f84d55707becf2591024a08615b1063ce1a","target":"graph","created_at":"2026-05-17T23:47:58Z","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":"Consider the Hamiltonian $abcd$ system in one dimension, with data posed in the energy space $H^1\\times H^1$. This model, introduced by Bona, Chen and Saut, is a well-known physical generalization of the classical Boussinesq equations. The Hamiltonian case corresponds to the regime where $a,c<0$ and $b=d>0$. Under this regime, small solutions in the energy space are globally defined. A first proof of decay for this $2\\times 2$ system was given by the two authors and Poblete and Pozo, in a strongly dispersive regime, i.e. under essentially the conditions \\[ b=d > \\frac29, \\quad a,c<-\\frac1{18}.","authors_text":"Chulkwang Kwak, Claudio Mu\\~noz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-01T16:58:07Z","title":"Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00454","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":"sha256:3b37c2e8b4a0854f17096897650d98d7c0203ac5b99de83352c89da26ff7f0c9","target":"record","created_at":"2026-05-17T23:47:58Z","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":"0d48b586b903198bba220e5d01feb4e168058944c38656e5a796d372da5fb15f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-01T16:58:07Z","title_canon_sha256":"e127cc6f2d9098da9a77bcc74c82ff5c8ef13255e3491fb975423ec1e8311feb"},"schema_version":"1.0","source":{"id":"1902.00454","kind":"arxiv","version":2}},"canonical_sha256":"8de5f1fb384dc66ef02ea8d8078d5e7ffe2860dcb59cf5ca2be0e14cd9f8def2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8de5f1fb384dc66ef02ea8d8078d5e7ffe2860dcb59cf5ca2be0e14cd9f8def2","first_computed_at":"2026-05-17T23:47:58.235872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:58.235872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YQPjPB21cdr46aJag97zYuHeXnTc34e+xrPrwjyxQ/PnJB9Ax8LL/xkJIW6y07E6tcC+r+CjXYfooZEsEy8aCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:58.236273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b37c2e8b4a0854f17096897650d98d7c0203ac5b99de83352c89da26ff7f0c9","sha256:bec56c4b327fc50abe2db7b73a4c5f84d55707becf2591024a08615b1063ce1a"],"state_sha256":"5accb9fc00add9dc5abb41536283e2afa1b3b415cf53c7db7d020a0d970fc42e"}