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It is known that, under a suitable condition on the nonlinearity, the solution is global-in-time for compactly supported Cauchy data. We prove in this paper that the result holds even when data are not compactly supported but just decaying as $\\langle x \\rangle^ {--1}$ at infinity, combining t"},"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":"1507.02035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-08T06:07:36Z","cross_cats_sorted":[],"title_canon_sha256":"b3bd3675d84b93ee95cedac03ae7b3bcd806bd72fc88e62f75bfb5931ca80276","abstract_canon_sha256":"3598d979a3da8f2df60ff5be4c86fd32b048c01ab54c597fe517b06a0d5438d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:12.657332Z","signature_b64":"C0MYSlnTLZ2xzB3j9vU59tCnYMPX85uI+MZBLUGKbpW56i1RN6cu2bKmKrkp9sgIpcj9vlO6m+cpqSXPIoPzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8b53bcd4328d40d7f2f0fc853870a6926afdff42d6ab6e569a8e7c0e72add9d","last_reissued_at":"2026-05-18T01:34:12.656587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:12.656587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global existence and asymptotics for quasi-linear one-dimensional Klein-Gordon equations with mildly decaying Cauchy data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Annalaura Stingo","submitted_at":"2015-07-08T06:07:36Z","abstract_excerpt":"Let u be a solution to a quasi-linear Klein-Gordon equation in one-space dimension, $\\Box u + u = P (u, $\\partial$\\_t u, $\\partial$\\_x u; $\\partial$\\_t $\\partial$\\_x u, $\\partial$^2\\_x u)$ , where P is a homogeneous polynomial of degree three, and with smooth Cauchy data of size $\\epsilon \\rightarrow 0$. It is known that, under a suitable condition on the nonlinearity, the solution is global-in-time for compactly supported Cauchy data. We prove in this paper that the result holds even when data are not compactly supported but just decaying as $\\langle x \\rangle^ {--1}$ at infinity, combining t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02035","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1507.02035","created_at":"2026-05-18T01:34:12.656711+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.02035v1","created_at":"2026-05-18T01:34:12.656711+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02035","created_at":"2026-05-18T01:34:12.656711+00:00"},{"alias_kind":"pith_short_12","alias_value":"7C2TXTKDFDKA","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"7C2TXTKDFDKA27ZP","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"7C2TXTKD","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.03516","citing_title":"Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE","json":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE.json","graph_json":"https://pith.science/api/pith-number/7C2TXTKDFDKA27ZPB7EFHBYKNE/graph.json","events_json":"https://pith.science/api/pith-number/7C2TXTKDFDKA27ZPB7EFHBYKNE/events.json","paper":"https://pith.science/paper/7C2TXTKD"},"agent_actions":{"view_html":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE","download_json":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE.json","view_paper":"https://pith.science/paper/7C2TXTKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.02035&json=true","fetch_graph":"https://pith.science/api/pith-number/7C2TXTKDFDKA27ZPB7EFHBYKNE/graph.json","fetch_events":"https://pith.science/api/pith-number/7C2TXTKDFDKA27ZPB7EFHBYKNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE/action/storage_attestation","attest_author":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE/action/author_attestation","sign_citation":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE/action/citation_signature","submit_replication":"https://pith.science/pith/7C2TXTKDFDKA27ZPB7EFHBYKNE/action/replication_record"}},"created_at":"2026-05-18T01:34:12.656711+00:00","updated_at":"2026-05-18T01:34:12.656711+00:00"}