{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:W5KALLMVHGNW56SE6L66KRKNSU","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":"bfd7908010e8d92e23bc26c16d7d11a478e67da6dd88e775852b71f865712b4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-06T10:08:56Z","title_canon_sha256":"4f033c9d49bb291e11d5842d3cc79f62942ce7353e0aec2bb020bf14f47816a0"},"schema_version":"1.0","source":{"id":"1007.0849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0849","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0849v2","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0849","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"W5KALLMVHGNW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"W5KALLMVHGNW56SE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"W5KALLMV","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:1598c5245b04a7d204cd3ec92588b2da36a99cd5215f324fbfc5b3288243bf92","target":"graph","created_at":"2026-05-18T03:58:14Z","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":"Let $E$ be the set of edges of the $d$-dimensional cubic lattice $\\mathbb{Z}^d$, with $d\\geq2$, and let $t(e),e\\in E$, be nonnegative values. The passage time from a vertex $v$ to a vertex $w$ is defined as $\\inf_{\\pi:v\\rightarrow w}\\sum_{e\\in\\pi}t(e)$, where the infimum is over all paths $\\pi$ from $v$ to $w$, and the sum is over all edges $e$ of $\\pi$. Benjamini, Kalai and Schramm [2] proved that if the $t(e)$'s are i.i.d. two-valued positive random variables, the variance of the passage time from the vertex 0 to a vertex $v$ is sublinear in the distance from 0 to $v$. This result was extend","authors_text":"Demeter Kiss, Jacob van den Berg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-06T10:08:56Z","title":"Sublinearity of the travel-time variance for dependent first-passage percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0849","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":"sha256:702e995d4e7c40c2620bb14d651d1cf82c1a409245a3c5c5643c62de806dfa37","target":"record","created_at":"2026-05-18T03:58:14Z","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":"bfd7908010e8d92e23bc26c16d7d11a478e67da6dd88e775852b71f865712b4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-06T10:08:56Z","title_canon_sha256":"4f033c9d49bb291e11d5842d3cc79f62942ce7353e0aec2bb020bf14f47816a0"},"schema_version":"1.0","source":{"id":"1007.0849","kind":"arxiv","version":2}},"canonical_sha256":"b75405ad95399b6efa44f2fde5454d9523bb3e3c55ab1f7535035e2575783863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b75405ad95399b6efa44f2fde5454d9523bb3e3c55ab1f7535035e2575783863","first_computed_at":"2026-05-18T03:58:14.233523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:14.233523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B4y/mg4nlmnbvVvBWECVSk+sOoYIdLY4QJ5oUD42Bob/sqixU1PrOgr94JMx8SdyEg0UOhLBV/eycMVoxB3VBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:14.234035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:702e995d4e7c40c2620bb14d651d1cf82c1a409245a3c5c5643c62de806dfa37","sha256:1598c5245b04a7d204cd3ec92588b2da36a99cd5215f324fbfc5b3288243bf92"],"state_sha256":"e83a9982e1f4f479e494cc564aad94d464cda9fa918c9983c35d5cdb360c81e7"}