{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VPQSORU2VKS5FK3ORNRQC3HRZO","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":"aec2c8ebf0148b471dcb29561fb9fc5669ee7b38bf4584781be39cb04ca2c19f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-16T15:09:21Z","title_canon_sha256":"d9e644497e3ccb40f72e82679fb665ec53ef64dcf04f58b1653b07ebb562d340"},"schema_version":"1.0","source":{"id":"2406.10971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.10971","created_at":"2026-07-05T11:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"2406.10971v2","created_at":"2026-07-05T11:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.10971","created_at":"2026-07-05T11:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"VPQSORU2VKS5","created_at":"2026-07-05T11:22:15Z"},{"alias_kind":"pith_short_16","alias_value":"VPQSORU2VKS5FK3O","created_at":"2026-07-05T11:22:15Z"},{"alias_kind":"pith_short_8","alias_value":"VPQSORU2","created_at":"2026-07-05T11:22:15Z"}],"graph_snapshots":[{"event_id":"sha256:df97c2d071b6ca9802bf6b020259bd77bf9b62aaa34fae5f4a33c96a92e78741","target":"graph","created_at":"2026-07-05T11:22:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.10971/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study planar first-passage percolation with independent weights whose common distribution is supported in $(0,\\infty)$ and is absolutely continuous with respect to Lebesgue measure. We prove that the passage time from $x$ to $y$ denoted by $T(x,y)$ satisfies $$\\max _{a\\ge 0} \\mathbb P \\big( T(x,y)\\in [a,a+1] \\big) \\le \\frac{C}{\\sqrt{\\log \\|x-y\\|}},$$ answering a question posed by Ahlberg and de la Riva. This estimate recovers earlier results on the fluctuations of the passage time by Newman--Piza, Pemantle--Peres, and Chatterjee.","authors_text":"Dor Elboim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-16T15:09:21Z","title":"Small ball probabilities for the passage time in planar first-passage percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10971","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":"sha256:977c92e7680bda01c6494e685ad299d86ad6cf99dae77f84d2a62b162d9c1cbc","target":"record","created_at":"2026-07-05T11:22:15Z","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":"aec2c8ebf0148b471dcb29561fb9fc5669ee7b38bf4584781be39cb04ca2c19f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-16T15:09:21Z","title_canon_sha256":"d9e644497e3ccb40f72e82679fb665ec53ef64dcf04f58b1653b07ebb562d340"},"schema_version":"1.0","source":{"id":"2406.10971","kind":"arxiv","version":2}},"canonical_sha256":"abe127469aaaa5d2ab6e8b63016cf1cbbdbffa7110eddf6762a70ac70d1544b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe127469aaaa5d2ab6e8b63016cf1cbbdbffa7110eddf6762a70ac70d1544b8","first_computed_at":"2026-07-05T11:22:15.980129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:15.980129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"apE3tX+OJKYFt9XGqMwHXdUOcyZ9qLs+iJfyeXCVFwzk92GBYNce/pKQZWCuUooZVxiwB1KVhVjhi4TNZ+KHBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:15.981276Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.10971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:977c92e7680bda01c6494e685ad299d86ad6cf99dae77f84d2a62b162d9c1cbc","sha256:df97c2d071b6ca9802bf6b020259bd77bf9b62aaa34fae5f4a33c96a92e78741"],"state_sha256":"9884a5a1291bab2a62cfca7ec2438c7729a98125a2f2ab8193d2b292a0d0ed07"}