{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KLXPGMGQNE7P4WXA6FUMIAXJGA","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":"318e576683edb5e8ca4716ccbf98e358f3c741b63702fef1811c6d1d9c40c822","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-18T20:38:23Z","title_canon_sha256":"e85b8a3604c3960b4b12e505161a04bd036da08eb6c649b706390c69ff8cd398"},"schema_version":"1.0","source":{"id":"1810.08270","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08270","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08270v2","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08270","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"KLXPGMGQNE7P","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KLXPGMGQNE7P4WXA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KLXPGMGQ","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:7be18d31ce69d8204ac319b5e706af1f3e6bf55774a2bd31965557b0cb409efa","target":"graph","created_at":"2026-05-17T23:43:09Z","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 first-passage percolation (FPP), one assigns i.i.d.~weights to the edges of the cubic lattice $\\mathbb{Z}^d$ and analyzes the induced weighted graph metric. If $T(x,y)$ is the distance between vertices $x$ and $y$, then a primary question in the model is: what is the order of the fluctuations of $T(0,x)$? It is expected that the variance of $T(0,x)$ grows like the norm of $x$ to a power strictly less than 1, but the best lower bounds available are (only in two dimensions) of order $\\log \\|x\\|$. This result was found in the '90s and there has not been any improvement since. In this paper, we","authors_text":"Chen Xu, Christian Houdr\\'e, Jack Hanson, Michael Damron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-18T20:38:23Z","title":"Lower bounds for fluctuations in first-passage percolation for general distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08270","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:a337c8a1129e82773915b96ec6002b3e889d6648732204c2ed781c32945b0a7e","target":"record","created_at":"2026-05-17T23:43:09Z","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":"318e576683edb5e8ca4716ccbf98e358f3c741b63702fef1811c6d1d9c40c822","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-18T20:38:23Z","title_canon_sha256":"e85b8a3604c3960b4b12e505161a04bd036da08eb6c649b706390c69ff8cd398"},"schema_version":"1.0","source":{"id":"1810.08270","kind":"arxiv","version":2}},"canonical_sha256":"52eef330d0693efe5ae0f168c402e9301f55ec47fbfe11fd53fce388bc997f44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52eef330d0693efe5ae0f168c402e9301f55ec47fbfe11fd53fce388bc997f44","first_computed_at":"2026-05-17T23:43:09.351903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:09.351903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CXWOMrvz0NlLX92dS26hx91SgL9jjc6a/dPHEsDLNUly5hwLk0YT7l24fd2mrMmYRU/xUa3U+xRJ1+o101mFCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:09.352438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08270","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a337c8a1129e82773915b96ec6002b3e889d6648732204c2ed781c32945b0a7e","sha256:7be18d31ce69d8204ac319b5e706af1f3e6bf55774a2bd31965557b0cb409efa"],"state_sha256":"d12786a74a69d1e5e682311f555b7369164c8e038d396d8e6255530076ef4d65"}