{"paper":{"title":"Gauge symmetry and uniqueness in inverse problems for the JMGT equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The nonlinear acoustic coefficient β in the JMGT equation is uniquely determined by the all-boundary measurement map on a simple Riemannian manifold.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Qiu, Ting Zhou, Xiang Xu, Yeqiong Ye","submitted_at":"2026-04-30T15:42:01Z","abstract_excerpt":"In this paper, we study an inverse boundary value problem for the Jordan--Moore--Gibson--Thompson equation on a simple Riemannian manifold. We consider an all boundary measurement map that maps Dirichlet boundary data and initial data to the corresponding Neumann-type boundary data and final-time data. Our main result shows that the nonlinear acoustic coefficient $\\beta$ is uniquely determined by this measurement map, and the linear damping coefficients $\\alpha$ and $q$, along with the internal source term $F$, can be recovered up to a gauge symmetry. As a corollary, we also establish a specif"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result shows that the nonlinear acoustic coefficient β is uniquely determined by this measurement map, and the linear damping coefficients α and q, along with the internal source term F, can be recovered up to a gauge symmetry.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The construction of geometric optics solutions works for the linearized MGT equation on the simple Riemannian manifold, and the first- and second-order linearization procedure fully captures the nonlinear effects without hidden dependencies.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The nonlinear coefficient β in the JMGT equation is uniquely determined from boundary measurements, while α, q, and F are recovered up to gauge symmetry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The nonlinear acoustic coefficient β in the JMGT equation is uniquely determined by the all-boundary measurement map on a simple Riemannian manifold.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"204019607ea60b06a6bf1c6f4ca03d58fdf0f0739f63b65aa63583cb5ff2720a"},"source":{"id":"2604.28023","kind":"arxiv","version":2},"verdict":{"id":"c382bea7-dc5f-43cd-a407-5942de7f2e70","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T07:55:30.620410Z","strongest_claim":"Our main result shows that the nonlinear acoustic coefficient β is uniquely determined by this measurement map, and the linear damping coefficients α and q, along with the internal source term F, can be recovered up to a gauge symmetry.","one_line_summary":"The nonlinear coefficient β in the JMGT equation is uniquely determined from boundary measurements, while α, q, and F are recovered up to gauge symmetry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The construction of geometric optics solutions works for the linearized MGT equation on the simple Riemannian manifold, and the first- and second-order linearization procedure fully captures the nonlinear effects without hidden dependencies.","pith_extraction_headline":"The nonlinear acoustic coefficient β in the JMGT equation is uniquely determined by the all-boundary measurement map on a simple Riemannian manifold."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.28023/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T20:42:09.833760Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:41:30.496909Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e19d4c3ebf7f1440765a799d14951ffcd9be6c5aa48384739f923c1b15859781"},"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"}