{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3NKKFKXARJAN2OXDBPFSEZEXTM","short_pith_number":"pith:3NKKFKXA","schema_version":"1.0","canonical_sha256":"db54a2aae08a40dd3ae30bcb2264979b2655720505965171b45c2dff33af2816","source":{"kind":"arxiv","id":"1812.00309","version":7},"attestation_state":"computed","paper":{"title":"The directed landscape","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Balint Virag, Duncan Dauvergne, Janosch Ortmann","submitted_at":"2018-12-02T02:41:51Z","abstract_excerpt":"The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-2/3- continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape."},"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":"1812.00309","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2018-12-02T02:41:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a9feae7433b0d9b9400087ff7a1fe17c827ba3bc269cc6737353463665bff2ce","abstract_canon_sha256":"e76ef0ff588f78b54a67cb21e1cca8e9a65b36183eb0e1bbd522fb6e1450659b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:10:51.744089Z","signature_b64":"zikCV9XbNxXAGKVx16aCIxbcMb43uy9ebx3ru8NvdXCb3245aZs4TvUYckMNA/TLaQ8JlIn1OTQTIgA2C57UCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db54a2aae08a40dd3ae30bcb2264979b2655720505965171b45c2dff33af2816","last_reissued_at":"2026-07-05T08:10:51.743653Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:10:51.743653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The directed landscape","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Balint Virag, Duncan Dauvergne, Janosch Ortmann","submitted_at":"2018-12-02T02:41:51Z","abstract_excerpt":"The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-2/3- continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00309","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1812.00309/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1812.00309","created_at":"2026-07-05T08:10:51.743708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.00309v7","created_at":"2026-07-05T08:10:51.743708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00309","created_at":"2026-07-05T08:10:51.743708+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NKKFKXARJAN","created_at":"2026-07-05T08:10:51.743708+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NKKFKXARJAN2OXD","created_at":"2026-07-05T08:10:51.743708+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NKKFKXA","created_at":"2026-07-05T08:10:51.743708+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.10496","citing_title":"Dimension lower bounds in random geometry via Lipschitz functions","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2002.09459","citing_title":"Hidden invariance of last passage percolation and directed polymers","ref_index":22,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM","json":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM.json","graph_json":"https://pith.science/api/pith-number/3NKKFKXARJAN2OXDBPFSEZEXTM/graph.json","events_json":"https://pith.science/api/pith-number/3NKKFKXARJAN2OXDBPFSEZEXTM/events.json","paper":"https://pith.science/paper/3NKKFKXA"},"agent_actions":{"view_html":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM","download_json":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM.json","view_paper":"https://pith.science/paper/3NKKFKXA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.00309&json=true","fetch_graph":"https://pith.science/api/pith-number/3NKKFKXARJAN2OXDBPFSEZEXTM/graph.json","fetch_events":"https://pith.science/api/pith-number/3NKKFKXARJAN2OXDBPFSEZEXTM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM/action/storage_attestation","attest_author":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM/action/author_attestation","sign_citation":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM/action/citation_signature","submit_replication":"https://pith.science/pith/3NKKFKXARJAN2OXDBPFSEZEXTM/action/replication_record"}},"created_at":"2026-07-05T08:10:51.743708+00:00","updated_at":"2026-07-05T08:10:51.743708+00:00"}