{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JECDWCZRQDRKFFQF46D2PCIADN","short_pith_number":"pith:JECDWCZR","schema_version":"1.0","canonical_sha256":"49043b0b3180e2a29605e787a789001b5b574f6118567981db95b24417fb1031","source":{"kind":"arxiv","id":"2605.01814","version":2},"attestation_state":"computed","paper":{"title":"Large data global well-posedness for a one-dimensional quasilinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The quasilinear wave equation u_tt = c(u)^2 u_xx has globally smooth solutions for large initial data when c is positive, bounded, monotonically increasing, and has bounded derivative.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuusuke Sugiyama","submitted_at":"2026-05-03T10:46:49Z","abstract_excerpt":"In this paper, we prove global well-posedness with large initial data for the one-dimensional quasilinear wave equation $$\n  u_{tt}=c(u)^2u_{xx},\n  \\qquad (t,x)\\in (0,T)\\times\\R, $$ where \\(c\\) is a positive, bounded, monotonically increasing function with bounded derivative. This result gives a partial resolution of an open problem posed by Glassey, Hunter and Zheng on the global existence of smooth solutions to this equation for large initial data. Our proof is based on upper and lower estimates for the Riemann variables via a new comparison principle."},"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":"2605.01814","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-03T10:46:49Z","cross_cats_sorted":[],"title_canon_sha256":"fff148f9812ecd7a17a9eb528f02d8f09ee3a8eb25bb797b133f81fd8bee2152","abstract_canon_sha256":"14b9bd6db9d45496cefea94935aa25743a4c7bcb95c5d2cbe1161bfd89cbc3a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:15.158481Z","signature_b64":"3c/j1ZWh6P8EQBn954kXqM9BjXelepVtAqCvinUgXZq12UbhSvBWYWfeWhwWOp4YTeXYIX0+7eYuO5V9ufz4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49043b0b3180e2a29605e787a789001b5b574f6118567981db95b24417fb1031","last_reissued_at":"2026-05-20T01:05:15.157879Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:15.157879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large data global well-posedness for a one-dimensional quasilinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The quasilinear wave equation u_tt = c(u)^2 u_xx has globally smooth solutions for large initial data when c is positive, bounded, monotonically increasing, and has bounded derivative.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuusuke Sugiyama","submitted_at":"2026-05-03T10:46:49Z","abstract_excerpt":"In this paper, we prove global well-posedness with large initial data for the one-dimensional quasilinear wave equation $$\n  u_{tt}=c(u)^2u_{xx},\n  \\qquad (t,x)\\in (0,T)\\times\\R, $$ where \\(c\\) is a positive, bounded, monotonically increasing function with bounded derivative. This result gives a partial resolution of an open problem posed by Glassey, Hunter and Zheng on the global existence of smooth solutions to this equation for large initial data. Our proof is based on upper and lower estimates for the Riemann variables via a new comparison principle."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we prove global well-posedness for the one-dimensional quasilinear wave equation u_tt = c(u)^2 u_xx, where c is a positive, bounded, monotonically increasing function with bounded derivative. This result gives a partial resolution of an open problem posed by Glassey, Hunter and Zheng on the global existence of smooth solutions to this equation for large initial data.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proof relies on upper and lower estimates for the Riemann variables via a new comparison principle that exploits the monotonicity and boundedness of c; if this comparison principle fails to hold under the stated assumptions on c, the global existence claim does not follow.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Global well-posedness is proved for the quasilinear wave equation u_tt = c(u)^2 u_xx under the stated conditions on c, partially resolving an open problem on large-data global existence.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The quasilinear wave equation u_tt = c(u)^2 u_xx has globally smooth solutions for large initial data when c is positive, bounded, monotonically increasing, and has bounded derivative.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9f78e1880ee28c2133f46d39f23294e7dfadd6256ce60009244f83d9b2af7e90"},"source":{"id":"2605.01814","kind":"arxiv","version":2},"verdict":{"id":"4a0b609c-191b-4ca0-ae6d-eac8594db9d8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T16:54:40.123790Z","strongest_claim":"we prove global well-posedness for the one-dimensional quasilinear wave equation u_tt = c(u)^2 u_xx, where c is a positive, bounded, monotonically increasing function with bounded derivative. This result gives a partial resolution of an open problem posed by Glassey, Hunter and Zheng on the global existence of smooth solutions to this equation for large initial data.","one_line_summary":"Global well-posedness is proved for the quasilinear wave equation u_tt = c(u)^2 u_xx under the stated conditions on c, partially resolving an open problem on large-data global existence.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proof relies on upper and lower estimates for the Riemann variables via a new comparison principle that exploits the monotonicity and boundedness of c; if this comparison principle fails to hold under the stated assumptions on c, the global existence claim does not follow.","pith_extraction_headline":"The quasilinear wave equation u_tt = c(u)^2 u_xx has globally smooth solutions for large initial data when c is positive, bounded, monotonically increasing, and has bounded derivative."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01814/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T16:57:52.384712Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"487aa3c2bbd0d7d0a466e3cbf6e4f6e4b4d2a78130c0b1f3b71e2ed42f673918"},"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":"2605.01814","created_at":"2026-05-20T01:05:15.157977+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.01814v2","created_at":"2026-05-20T01:05:15.157977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.01814","created_at":"2026-05-20T01:05:15.157977+00:00"},{"alias_kind":"pith_short_12","alias_value":"JECDWCZRQDRK","created_at":"2026-05-20T01:05:15.157977+00:00"},{"alias_kind":"pith_short_16","alias_value":"JECDWCZRQDRKFFQF","created_at":"2026-05-20T01:05:15.157977+00:00"},{"alias_kind":"pith_short_8","alias_value":"JECDWCZR","created_at":"2026-05-20T01:05:15.157977+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/JECDWCZRQDRKFFQF46D2PCIADN","json":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN.json","graph_json":"https://pith.science/api/pith-number/JECDWCZRQDRKFFQF46D2PCIADN/graph.json","events_json":"https://pith.science/api/pith-number/JECDWCZRQDRKFFQF46D2PCIADN/events.json","paper":"https://pith.science/paper/JECDWCZR"},"agent_actions":{"view_html":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN","download_json":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN.json","view_paper":"https://pith.science/paper/JECDWCZR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.01814&json=true","fetch_graph":"https://pith.science/api/pith-number/JECDWCZRQDRKFFQF46D2PCIADN/graph.json","fetch_events":"https://pith.science/api/pith-number/JECDWCZRQDRKFFQF46D2PCIADN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN/action/storage_attestation","attest_author":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN/action/author_attestation","sign_citation":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN/action/citation_signature","submit_replication":"https://pith.science/pith/JECDWCZRQDRKFFQF46D2PCIADN/action/replication_record"}},"created_at":"2026-05-20T01:05:15.157977+00:00","updated_at":"2026-05-20T01:05:15.157977+00:00"}