{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7A7KUDHYJ55GEADIGFD3DS43SW","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":"7625ce94c5a771d8d752c1487f73784c9707d3a5ec7d7ea3553a682cc2f4d2a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-13T14:23:28Z","title_canon_sha256":"b96f4f3eddeed53b37b666a9a8ba822f3e3366c99491e949620df8dd51719ba7"},"schema_version":"1.0","source":{"id":"1808.04261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04261","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04261v2","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04261","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"7A7KUDHYJ55G","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7A7KUDHYJ55GEADI","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7A7KUDHY","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:8295afbcb49f76f35f7d0e1369a1a618c0974e1ed4c4bf43621d0698130f2fc3","target":"graph","created_at":"2026-05-17T23:55:29Z","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 study tree-indexed random walks as introduced by Benjamini, H\\\"aggstr\\\"om, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conjecture of those authors that the distribution of the range for any such tree is dominated by that of a path on the same number of edges. The two main variants of this conjecture considered in the literature are the $\\textit{standard}$ walks, in which adjacent vertices must have labels differing by $\\textit{exactly}$ 1, and $\\textit{lazy}$ walks, in which adjacent vertices must have labels differing by $\\textit{at ","authors_text":"Aaron Berger, Caleb Ji, Erik Metz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-13T14:23:28Z","title":"On the Distribution of Range for Tree-Indexed Random Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04261","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":"sha256:7409222431238114d3646c62748e0cdfb516a7a3d421e1c33c130c4af1d252cd","target":"record","created_at":"2026-05-17T23:55:29Z","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":"7625ce94c5a771d8d752c1487f73784c9707d3a5ec7d7ea3553a682cc2f4d2a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-13T14:23:28Z","title_canon_sha256":"b96f4f3eddeed53b37b666a9a8ba822f3e3366c99491e949620df8dd51719ba7"},"schema_version":"1.0","source":{"id":"1808.04261","kind":"arxiv","version":2}},"canonical_sha256":"f83eaa0cf84f7a6200683147b1cb9b95a9f449083a84e3465dcf061558b47dd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f83eaa0cf84f7a6200683147b1cb9b95a9f449083a84e3465dcf061558b47dd6","first_computed_at":"2026-05-17T23:55:29.072367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:29.072367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i4h9WlEirIadUB21siZgI+o7IQ+PTuxUFkn3LxiHEKCTwX1JhgKLujWBmOBJwxwYi4lBSJUXFCB6CDuaDsgvAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:29.072721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7409222431238114d3646c62748e0cdfb516a7a3d421e1c33c130c4af1d252cd","sha256:8295afbcb49f76f35f7d0e1369a1a618c0974e1ed4c4bf43621d0698130f2fc3"],"state_sha256":"9df754630c057df1e63d8dae55b69eef797b56e14a752210d70d3ad46df96b0c"}