{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:G5P7K5ZP6TBIJTYGIOWOQJFXGF","short_pith_number":"pith:G5P7K5ZP","schema_version":"1.0","canonical_sha256":"375ff5772ff4c284cf0643ace824b7316b9fb86b46ad5209a465053bc5dc9793","source":{"kind":"arxiv","id":"1908.00607","version":2},"attestation_state":"computed","paper":{"title":"Pointwise decay for semilinear wave equations in $\\mathbb{R}^{!+3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shiwu Yang","submitted_at":"2019-08-01T20:09:51Z","abstract_excerpt":"In this paper, we use Dafermos-Rodnianski's new vector field method to study the asymptotic pointwise decay properties for solutions of energy subcritical defocusing semilinear wave equations in $\\mathbb{R}^{1+3}$. We prove that the solution decays as quickly as linear waves for $p>\\frac{1+\\sqrt{17}}{2}$, covering part of the sub-conformal case, while for the range $2<p\\leq \\frac{1+\\sqrt{17}}{2}$, the solution still decays with rate at least $t^{-\\frac{1}{3}}$. As a consequence, the solution scatters in energy space when $p>2.3542$. We also show that the solution is uniformly bounded when $p>\\"},"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":"1908.00607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-01T20:09:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"439b5bef66c566b00c98f5a03385210de03a72649bf936a73c3befb66bb3d02f","abstract_canon_sha256":"ba4b590e5490cea9bdedba38ee49822e81cdf682f61f54106889c09572f298e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:18:13.924744Z","signature_b64":"mZwKf8U+845Efm898NhLq78aOheFUUQrQcJh4PFihwt8m7qK+eUqLx1wWYKPeTXU2mI+bjCZ3hXZ0WYMF9Q2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"375ff5772ff4c284cf0643ace824b7316b9fb86b46ad5209a465053bc5dc9793","last_reissued_at":"2026-07-05T02:18:13.924303Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:18:13.924303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pointwise decay for semilinear wave equations in $\\mathbb{R}^{!+3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shiwu Yang","submitted_at":"2019-08-01T20:09:51Z","abstract_excerpt":"In this paper, we use Dafermos-Rodnianski's new vector field method to study the asymptotic pointwise decay properties for solutions of energy subcritical defocusing semilinear wave equations in $\\mathbb{R}^{1+3}$. We prove that the solution decays as quickly as linear waves for $p>\\frac{1+\\sqrt{17}}{2}$, covering part of the sub-conformal case, while for the range $2<p\\leq \\frac{1+\\sqrt{17}}{2}$, the solution still decays with rate at least $t^{-\\frac{1}{3}}$. As a consequence, the solution scatters in energy space when $p>2.3542$. We also show that the solution is uniformly bounded when $p>\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00607","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/1908.00607/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":"1908.00607","created_at":"2026-07-05T02:18:13.924368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.00607v2","created_at":"2026-07-05T02:18:13.924368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00607","created_at":"2026-07-05T02:18:13.924368+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5P7K5ZP6TBI","created_at":"2026-07-05T02:18:13.924368+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5P7K5ZP6TBIJTYG","created_at":"2026-07-05T02:18:13.924368+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5P7K5ZP","created_at":"2026-07-05T02:18:13.924368+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/G5P7K5ZP6TBIJTYGIOWOQJFXGF","json":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF.json","graph_json":"https://pith.science/api/pith-number/G5P7K5ZP6TBIJTYGIOWOQJFXGF/graph.json","events_json":"https://pith.science/api/pith-number/G5P7K5ZP6TBIJTYGIOWOQJFXGF/events.json","paper":"https://pith.science/paper/G5P7K5ZP"},"agent_actions":{"view_html":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF","download_json":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF.json","view_paper":"https://pith.science/paper/G5P7K5ZP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.00607&json=true","fetch_graph":"https://pith.science/api/pith-number/G5P7K5ZP6TBIJTYGIOWOQJFXGF/graph.json","fetch_events":"https://pith.science/api/pith-number/G5P7K5ZP6TBIJTYGIOWOQJFXGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF/action/storage_attestation","attest_author":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF/action/author_attestation","sign_citation":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF/action/citation_signature","submit_replication":"https://pith.science/pith/G5P7K5ZP6TBIJTYGIOWOQJFXGF/action/replication_record"}},"created_at":"2026-07-05T02:18:13.924368+00:00","updated_at":"2026-07-05T02:18:13.924368+00:00"}