{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:46236K6R6YZVXAVJIWXPLOJPDC","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":"9c3e0e34153f2b92889bd26222a09fb0e5472d96199051ea2dde8d7bf4743d7c","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-04-05T14:44:22Z","title_canon_sha256":"35849c3566e0e1889871039a86e46425b849e8e228969b6ffd29dfa843e8765c"},"schema_version":"1.0","source":{"id":"math/0404085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404085","created_at":"2026-07-04T14:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404085v1","created_at":"2026-07-04T14:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404085","created_at":"2026-07-04T14:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"46236K6R6YZV","created_at":"2026-07-04T14:38:30Z"},{"alias_kind":"pith_short_16","alias_value":"46236K6R6YZVXAVJ","created_at":"2026-07-04T14:38:30Z"},{"alias_kind":"pith_short_8","alias_value":"46236K6R","created_at":"2026-07-04T14:38:30Z"}],"graph_snapshots":[{"event_id":"sha256:9b0bd02b64ad211df07d6a9e16208ded31a4070ab24d342384c807135ff8365d","target":"graph","created_at":"2026-07-04T14:38:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0404085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two symmetric step distributions of bounded support.","authors_text":"Itai Benjamini, Robin Pemantle, Yuval Peres","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2004-04-05T14:44:22Z","title":"Random Walks in Varying Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404085","kind":"arxiv","version":1},"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:f31eba1ab2d0bf293d8d0deaa76b7d619cb214ee418c2f391a0723d26914ac8b","target":"record","created_at":"2026-07-04T14:38:30Z","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":"9c3e0e34153f2b92889bd26222a09fb0e5472d96199051ea2dde8d7bf4743d7c","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-04-05T14:44:22Z","title_canon_sha256":"35849c3566e0e1889871039a86e46425b849e8e228969b6ffd29dfa843e8765c"},"schema_version":"1.0","source":{"id":"math/0404085","kind":"arxiv","version":1}},"canonical_sha256":"e7b5bf2bd1f6335b82a945aef5b92f189abe5e6724ed00f8bd5bdcdf1782dd9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7b5bf2bd1f6335b82a945aef5b92f189abe5e6724ed00f8bd5bdcdf1782dd9b","first_computed_at":"2026-07-04T14:38:30.085359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:30.085359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuLhijlMgTzRKic+BMaCDoNeuTOOYs4UK+gsnVBLxvPFKm9iQfrLI4HjMVs6wdM24pYqa0EoVCNXpdw3z+FuAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:30.085728Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f31eba1ab2d0bf293d8d0deaa76b7d619cb214ee418c2f391a0723d26914ac8b","sha256:9b0bd02b64ad211df07d6a9e16208ded31a4070ab24d342384c807135ff8365d"],"state_sha256":"b4c221899f22b574b9c8fb0dfbc6eec9e8c61ac933e1a4b167cc474abd89fc85"}