{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4FAJSATU6YU2BI7I5MGOH6LAXQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3f57e985af783c7744534a0bbd63555f5b130e6cf7929846dfaee7206b666275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-13T13:31:46Z","title_canon_sha256":"9f445496faff74fca8fdc8d48214be24e728b4bcfda8ad66ae6cda4825d44ed4"},"schema_version":"1.0","source":{"id":"2605.13512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13512","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13512v1","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13512","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"4FAJSATU6YU2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"4FAJSATU6YU2BI7I","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"4FAJSATU","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:93c0138e52e195ecbc78084bb645b7961e52133eb444b9d1a35c4ce88a0d5aa9","target":"graph","created_at":"2026-05-18T02:44:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","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."}],"snapshot_sha256":"0ad9d71fad14ed420cf21c06aeecfbda0a1e7447edc169213f21628ca31cb03f"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We develop a hydrodynamic theory for a height-dependent version of the totally asymmetric simple exclusion process in which the jump rate at a growth site is sampled from a macroscopic two-dimensional speed function evaluated at the spatial coordinate and the current height level. 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 ","authors_text":"Enrico Scalas, Jacob Butt, Nicos Georgiou","cross_cats":[],"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.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-13T13:31:46Z","title":"Hydrodynamic limits for TASEP with space-time discontinuities"},"references":{"count":69,"internal_anchors":1,"resolved_work":69,"sample":[{"cited_arxiv_id":"","doi":"10.1215/kjm/1250283740","is_internal_anchor":false,"ref_index":1,"title":"Adimurthi and G. D. Veerappa Gowda,Conservation law with discontinuous flux, J. Math. Kyoto Univ.43(2003), no. 1, 27–70. doi:10.1215/kjm/1250283740","work_id":"a8bc6b50-9171-4bf4-88c7-fa5526b71811","year":2003},{"cited_arxiv_id":"","doi":"10.1007/bf01204214","is_internal_anchor":false,"ref_index":2,"title":"D. Aldous and P. Diaconis. Hammersley’s interacting particle process and longest increasing subsequences.Probability Theory and Related Fields, 103:199–213, 1995. doi:10.1007/BF01204214","work_id":"8d7941c0-ab55-4dee-87f3-632e8a9c64f0","year":1995},{"cited_arxiv_id":"","doi":"10.1214/24-aihp1482","is_internal_anchor":false,"ref_index":3,"title":"G. Amir, C. Bahadoran, O. Busani, and E. Saada. Invariant measures for multilane exclusion process.Annales de l’Institut Henri Poincar´ e, Probabilit´ es et Statistiques, 61(3):2184–2234, 2025. doi:10","work_id":"bc44115c-04a4-42aa-bdba-c0bc5f41882b","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"G. Amir, C. Bahadoran, O. Busani, and E. Saada. Hydrodynamics and relaxation limit for multilane exclusion process and related hyperbolic systems.arXiv preprint, arXiv:2501.19355, 2025","work_id":"0cfc18b9-a9b5-43cc-a533-f3d483f19ee8","year":2025},{"cited_arxiv_id":"","doi":"10.1007/s00205-010-0389-4","is_internal_anchor":false,"ref_index":5,"title":"Archive for Rational Mechanics and Analysis , author =","work_id":"56c8fd29-33b6-46da-89fb-8b48556138a3","year":2011}],"snapshot_sha256":"2513b1febf64225e09f88b179b1121a8ee0b568f1881a1600e82b5f0791613f9"},"source":{"id":"2605.13512","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:20:57.503836Z","id":"b734d5f0-697e-44f1-8a50-70787540bbf5","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"b734d5f0-697e-44f1-8a50-70787540bbf5"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4dc7f7faa7f48b4f1bcf7245a7b60e7fd5344efcb3b337a93fd191dc93f191f0","target":"record","created_at":"2026-05-18T02:44:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3f57e985af783c7744534a0bbd63555f5b130e6cf7929846dfaee7206b666275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-13T13:31:46Z","title_canon_sha256":"9f445496faff74fca8fdc8d48214be24e728b4bcfda8ad66ae6cda4825d44ed4"},"schema_version":"1.0","source":{"id":"2605.13512","kind":"arxiv","version":1}},"canonical_sha256":"e140990274f629a0a3e8eb0ce3f960bc2c222796f5cf320b6b95df489ba03ab8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e140990274f629a0a3e8eb0ce3f960bc2c222796f5cf320b6b95df489ba03ab8","first_computed_at":"2026-05-18T02:44:24.545685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:24.545685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LA5I4/Hyqv1BKzwnQtuI+VbEg6pcCVyT0jhlOJ850DlGxzOpDQx5H/wiOd75e7FmHsejq/iQpS7XgWp+JnmOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:24.546089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dc7f7faa7f48b4f1bcf7245a7b60e7fd5344efcb3b337a93fd191dc93f191f0","sha256:93c0138e52e195ecbc78084bb645b7961e52133eb444b9d1a35c4ce88a0d5aa9"],"state_sha256":"3dc78eec4dab3a1ec78231db8887c2817db5b76d8d8fe92ea2da6876308fdf49"}