{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AR37KOWDRVXPQP5PKLZB5H3JSA","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":"629d99db78724144a4f3e3f43d107649c8cb729534dc47a21d643750be1a0bea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-05T17:52:05Z","title_canon_sha256":"6b1986f1f8b21dd59dfe08d3d28d8be5421d961db92f01946db3b91fc5cfdc9a"},"schema_version":"1.0","source":{"id":"1401.0917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0917","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0917v2","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0917","created_at":"2026-05-18T02:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"AR37KOWDRVXP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AR37KOWDRVXPQP5P","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AR37KOWD","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:e68a3e1ef62643d454c7bc5b245ffd8292630068e395a23ed0a8c0ef3460c067","target":"graph","created_at":"2026-05-18T02:32:46Z","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":"We prove exponential concentration in i.i.d. first-passage percolation in $Z^d$ for all $d \\geq 2$ and general edge-weights $(t_e)$. Precisely, under an exponential moment assumption $E e^{\\alpha t_e}< \\infty$ for some $\\alpha>0$) on the edge-weight distribution, we prove the inequality $$ P(|T(0,x)-E T(0,x)| \\geq \\lambda \\sqrt{\\frac{|x|}{log |x|}}) \\leq ce^{-c' \\lambda}, |x|>1 $$ for the point-to-point passage time $T(0,x)$. Under a weaker assumption $E t_e^2(\\log t_e)_+< \\infty$ we show a corresponding inequality for the lower-tail of the distribution of $T(0,x)$. These results extend work o","authors_text":"Jack Hanson, Michael Damron, Philippe Sosoe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-05T17:52:05Z","title":"Subdiffusive concentration in first-passage percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0917","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":"sha256:44b2e5800a56379aa11e5794a89527bdddeeeb79426ea31e2ba53c05ff4d7fbb","target":"record","created_at":"2026-05-18T02:32:46Z","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":"629d99db78724144a4f3e3f43d107649c8cb729534dc47a21d643750be1a0bea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-05T17:52:05Z","title_canon_sha256":"6b1986f1f8b21dd59dfe08d3d28d8be5421d961db92f01946db3b91fc5cfdc9a"},"schema_version":"1.0","source":{"id":"1401.0917","kind":"arxiv","version":2}},"canonical_sha256":"0477f53ac38d6ef83faf52f21e9f69901a7b01d8980f57bf73283ba39c801358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0477f53ac38d6ef83faf52f21e9f69901a7b01d8980f57bf73283ba39c801358","first_computed_at":"2026-05-18T02:32:46.298000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:46.298000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"afmkXELewQLkL/PX9gTy77dK9aBfcHk/hEjijkmkVtgsOdhcAxUrbTygyf6sFh9fW0f4ia1wSXKUsT7Hl133CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:46.298421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44b2e5800a56379aa11e5794a89527bdddeeeb79426ea31e2ba53c05ff4d7fbb","sha256:e68a3e1ef62643d454c7bc5b245ffd8292630068e395a23ed0a8c0ef3460c067"],"state_sha256":"d8348313af428617efa1fda08011a74e735e85cb9433c4882beaee9e2d10f1af"}