{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MU5DV3VH2UYCU6CZLL6TIDWWJZ","short_pith_number":"pith:MU5DV3VH","schema_version":"1.0","canonical_sha256":"653a3aeea7d5302a78595afd340ed64e7b8ec130915d2630b1553acc292152b8","source":{"kind":"arxiv","id":"1411.0963","version":2},"attestation_state":"computed","paper":{"title":"An optimal decay estimate for the linearized water wave equation in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aynur Bulut","submitted_at":"2014-11-04T16:51:21Z","abstract_excerpt":"We obtain a decay estimate for solutions to the linear dispersive equation $iu_t-(-\\Delta)^{1/4}u=0$ for $(t,x)\\in\\mathbb{R}\\times\\mathbb{R}$. This corresponds to a factorization of the linearized water wave equation $u_{tt}+(-\\Delta)^{1/2}u=0$. In particular, by making use of the Littlewood-Paley decomposition and stationary phase estimates, we obtain decay of order $|t|^{-1/2}$ for solutions corresponding to data $u(0)=\\varphi$, assuming only bounds on $\\lVert \\varphi\\rVert_{H_x^1(\\mathbb{R})}$ and $\\lVert x\\partial_x\\varphi\\rVert_{L_x^2(\\mathbb{R})}$. As another application of these ideas, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.0963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-04T16:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"98da82bf9a0564ffa9ff9223501f79b471e4a74ce8d3304145e16f30f3d40073","abstract_canon_sha256":"e36e2e484670fc51c69aff7748bae6e50446b2cae83439d472a39a286d9abead"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:19:06.168403Z","signature_b64":"nq/yr8WrrrbbzplWYgf1aTAqI1kMrA6cR4gl6I07yb2fIyrarNDGO9cCrfH9Hn6gpoqm+DStTAPznFdO7r7oAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"653a3aeea7d5302a78595afd340ed64e7b8ec130915d2630b1553acc292152b8","last_reissued_at":"2026-07-05T08:19:06.167993Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:19:06.167993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An optimal decay estimate for the linearized water wave equation in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aynur Bulut","submitted_at":"2014-11-04T16:51:21Z","abstract_excerpt":"We obtain a decay estimate for solutions to the linear dispersive equation $iu_t-(-\\Delta)^{1/4}u=0$ for $(t,x)\\in\\mathbb{R}\\times\\mathbb{R}$. This corresponds to a factorization of the linearized water wave equation $u_{tt}+(-\\Delta)^{1/2}u=0$. In particular, by making use of the Littlewood-Paley decomposition and stationary phase estimates, we obtain decay of order $|t|^{-1/2}$ for solutions corresponding to data $u(0)=\\varphi$, assuming only bounds on $\\lVert \\varphi\\rVert_{H_x^1(\\mathbb{R})}$ and $\\lVert x\\partial_x\\varphi\\rVert_{L_x^2(\\mathbb{R})}$. As another application of these ideas, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0963","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1411.0963/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.0963","created_at":"2026-07-05T08:19:06.168051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0963v2","created_at":"2026-07-05T08:19:06.168051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0963","created_at":"2026-07-05T08:19:06.168051+00:00"},{"alias_kind":"pith_short_12","alias_value":"MU5DV3VH2UYC","created_at":"2026-07-05T08:19:06.168051+00:00"},{"alias_kind":"pith_short_16","alias_value":"MU5DV3VH2UYCU6CZ","created_at":"2026-07-05T08:19:06.168051+00:00"},{"alias_kind":"pith_short_8","alias_value":"MU5DV3VH","created_at":"2026-07-05T08:19:06.168051+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ","json":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ.json","graph_json":"https://pith.science/api/pith-number/MU5DV3VH2UYCU6CZLL6TIDWWJZ/graph.json","events_json":"https://pith.science/api/pith-number/MU5DV3VH2UYCU6CZLL6TIDWWJZ/events.json","paper":"https://pith.science/paper/MU5DV3VH"},"agent_actions":{"view_html":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ","download_json":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ.json","view_paper":"https://pith.science/paper/MU5DV3VH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0963&json=true","fetch_graph":"https://pith.science/api/pith-number/MU5DV3VH2UYCU6CZLL6TIDWWJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/MU5DV3VH2UYCU6CZLL6TIDWWJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ/action/storage_attestation","attest_author":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ/action/author_attestation","sign_citation":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ/action/citation_signature","submit_replication":"https://pith.science/pith/MU5DV3VH2UYCU6CZLL6TIDWWJZ/action/replication_record"}},"created_at":"2026-07-05T08:19:06.168051+00:00","updated_at":"2026-07-05T08:19:06.168051+00:00"}