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The speed function is allowed to have discontinuities along locally finitely many curves. Through the TASEP height-function representation, the process is coupled to an inhomogeneous directed last-passage percolation model whose exponential rates vary discontinuously in the two macroscopic LPP coordinates. 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The speed function is allowed to have discontinuities along locally finitely many curves. Through the TASEP height-function representation, the process is coupled to an inhomogeneous directed last-passage percolation model whose exponential rates vary discontinuously in the two macroscopic LPP coordinates. Combining "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Combining the law of large numbers for this last-passage model with an extension of the variational coupling method, we prove a hydrodynamic limit for the height function and for the associated particle density.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The speed function is allowed to have discontinuities along locally finitely many curves; the proof relies on this local finiteness to control the variational coupling and the envelope formulation at jumps.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A height-dependent TASEP with space-time discontinuous jump rates has a hydrodynamic limit given by a Lax-Oleinik variational formula for the current.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0ad9d71fad14ed420cf21c06aeecfbda0a1e7447edc169213f21628ca31cb03f"},"source":{"id":"2605.13512","kind":"arxiv","version":1},"verdict":{"id":"b734d5f0-697e-44f1-8a50-70787540bbf5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:20:57.503836Z","strongest_claim":"Combining the law of large numbers for this last-passage model with an extension of the variational coupling method, we prove a hydrodynamic limit for the height function and for the associated particle density.","one_line_summary":"The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The speed function is allowed to have discontinuities along locally finitely many curves; the proof relies on this local finiteness to control the variational coupling and the envelope formulation at jumps.","pith_extraction_headline":"A height-dependent TASEP with space-time discontinuous jump rates has a hydrodynamic limit given by a Lax-Oleinik variational formula for the current."},"references":{"count":69,"sample":[{"doi":"10.1215/kjm/1250283740","year":2003,"title":"Adimurthi and G. 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