{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ATWAL3CYI4YF6XOCIPRUSYFQ5I","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":"322995bdae33de9a72afc8792b3ea65780e49012f6dbfc10dd56c56a7bf6a5fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-06T10:55:23Z","title_canon_sha256":"7d4050dcf0976d735f0b442c05059a8862551c8f12ece760fcb3b6a97bba9321"},"schema_version":"1.0","source":{"id":"1401.1036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1036","created_at":"2026-05-18T01:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1036v2","created_at":"2026-05-18T01:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1036","created_at":"2026-05-18T01:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"ATWAL3CYI4YF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"ATWAL3CYI4YF6XOC","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"ATWAL3CY","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:b1e0a75780bc360a804421201013bd413d5f0d760a2b33722a45cd8f4f5b8b7e","target":"graph","created_at":"2026-05-18T01:12:20Z","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 that vertex-reinforced random walk on the integers with weight of order k to the power alpha, for alpha in [0, 1/2), is recurrent. This confirms a conjecture of Volkov for alpha<1/2. The conjecture for alpha in [1/2, 1) remains open.","authors_text":"Gady Kozma, Jun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-06T10:55:23Z","title":"Vertex-reinforced random walk on Z with sub-square-root weights is recurrent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1036","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:d9f24c8c501af8abe1d7a87edcea3fc5bcfb916783597a5b793b09d68f69baf7","target":"record","created_at":"2026-05-18T01:12:20Z","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":"322995bdae33de9a72afc8792b3ea65780e49012f6dbfc10dd56c56a7bf6a5fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-06T10:55:23Z","title_canon_sha256":"7d4050dcf0976d735f0b442c05059a8862551c8f12ece760fcb3b6a97bba9321"},"schema_version":"1.0","source":{"id":"1401.1036","kind":"arxiv","version":2}},"canonical_sha256":"04ec05ec5847305f5dc243e34960b0ea27a3bfa05c0d4abc5f0093fa14d69df8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04ec05ec5847305f5dc243e34960b0ea27a3bfa05c0d4abc5f0093fa14d69df8","first_computed_at":"2026-05-18T01:12:20.138419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:20.138419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CZezOSNYE3h8jsYX/iPwgulAYBBHpaummBWFfFHrgYmP0GuvgBMBVKT8ZFjjDScUStHLuCo6WbcKBgypTe36Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:20.138751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f24c8c501af8abe1d7a87edcea3fc5bcfb916783597a5b793b09d68f69baf7","sha256:b1e0a75780bc360a804421201013bd413d5f0d760a2b33722a45cd8f4f5b8b7e"],"state_sha256":"242bbf5d1bc1b52726d3517b945f0b2ff744fe286769072e776b95f46d5f3751"}