{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:VKN3QJCJQZLJL6KYXPZCLMGSMQ","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":"244f9851ec81d30c7b2d98b112f3c1c417279d2183dc5d43c3649db6bb485ac9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-04-10T21:36:22Z","title_canon_sha256":"663fd689485997059f8c27cad0d15171d5bba44261d9927ddac3d00bde21d531"},"schema_version":"1.0","source":{"id":"0804.1810","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.1810","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"0804.1810v2","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.1810","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"VKN3QJCJQZLJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"VKN3QJCJQZLJL6KY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"VKN3QJCJ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:0521eab41e357567fd3860f6dfa286849cc81ba5e689da138c4ebd05500d970b","target":"graph","created_at":"2026-05-18T01:04:50Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the deterministic limiting shape of the maximal path. We obtain a sufficient analytical condition for uniqueness of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.","authors_text":"Augusto Q. Teixeira, Leonardo T. Rolla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-04-10T21:36:22Z","title":"Last Passage Percolation in Macroscopically Inhomogeneous Media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1810","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:eb6a72ea3f6240099cea8a998d2919d2cc2f075539174ed72bd77aae54df1c09","target":"record","created_at":"2026-05-18T01:04:50Z","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":"244f9851ec81d30c7b2d98b112f3c1c417279d2183dc5d43c3649db6bb485ac9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-04-10T21:36:22Z","title_canon_sha256":"663fd689485997059f8c27cad0d15171d5bba44261d9927ddac3d00bde21d531"},"schema_version":"1.0","source":{"id":"0804.1810","kind":"arxiv","version":2}},"canonical_sha256":"aa9bb82449865695f958bbf225b0d26433617adb598f7abd189494285e896348","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa9bb82449865695f958bbf225b0d26433617adb598f7abd189494285e896348","first_computed_at":"2026-05-18T01:04:50.988247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.988247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVPLpz1EvLsjzZclHi1BFSwa1mtAHpG6PVWW1CxbC9mtwO0jLVEk4JpWlk5MAPookeGsjzqDL+Amz749ExE5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.988651Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.1810","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6a72ea3f6240099cea8a998d2919d2cc2f075539174ed72bd77aae54df1c09","sha256:0521eab41e357567fd3860f6dfa286849cc81ba5e689da138c4ebd05500d970b"],"state_sha256":"757064c48b32247e22790337a8ae5926060e663ee45940136554700d7650c176"}