{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UP7ECYMHUYTNDIN3QVFADZGYVF","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":"b1a0c90def4bdfdabbf33c96e42aca91d5a9295dcd0085c84a3c29663680baea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-20T17:01:24Z","title_canon_sha256":"5337c4145e9e2d2e95e51b0777f84fb3975836262aef7bf4acd3f30510221b2f"},"schema_version":"1.0","source":{"id":"1504.05124","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05124","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05124v2","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05124","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"UP7ECYMHUYTN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UP7ECYMHUYTNDIN3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UP7ECYMH","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:c0f59f26956f9b6575c26d89046034f048eaf218c291b8e37186665c7e671cfd","target":"graph","created_at":"2026-05-18T01:12:38Z","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 $W$ be an integer valued random variable satisfying $E[W] =: \\delta \\geq 0$ and $P(W<0)>0$, and consider a self-interacting random walk that behaves like a simple symmetric random walk with the exception that on the first visit to any integer $x\\in \\mathbb{Z}$ the size of the next step is an independent random variable with the same distribution as $W$. We show that this self-interacting random walk is recurrent if $\\delta\\leq 1$ and transient if $\\delta>1$. This is a special case of our main result which concerns the recurrence and transience of excited random walks (or cookie random walk","authors_text":"Burgess Davis, Jonathon Peterson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-20T17:01:24Z","title":"Excited random walks with non-nearest neighbor steps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05124","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":"sha256:85d65eb2680a87acc4c54f2b518ecb7dc3d802da56b6cd08a5269d6463e65252","target":"record","created_at":"2026-05-18T01:12:38Z","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":"b1a0c90def4bdfdabbf33c96e42aca91d5a9295dcd0085c84a3c29663680baea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-20T17:01:24Z","title_canon_sha256":"5337c4145e9e2d2e95e51b0777f84fb3975836262aef7bf4acd3f30510221b2f"},"schema_version":"1.0","source":{"id":"1504.05124","kind":"arxiv","version":2}},"canonical_sha256":"a3fe416187a626d1a1bb854a01e4d8a959246db6c338a14d6c56110a62192109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3fe416187a626d1a1bb854a01e4d8a959246db6c338a14d6c56110a62192109","first_computed_at":"2026-05-18T01:12:38.089249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:38.089249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Vg2T8KdgZdXnrmRmnRsbjSG+04+49YuWj8Ux9IHzJLhCAQ4AzDmeIIHOEw6ta774B3oABMnvS5g26nwfY3zBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:38.089641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05124","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85d65eb2680a87acc4c54f2b518ecb7dc3d802da56b6cd08a5269d6463e65252","sha256:c0f59f26956f9b6575c26d89046034f048eaf218c291b8e37186665c7e671cfd"],"state_sha256":"0e8a0adc89052a68ac59cd792ef84a248a5349bbfb6d1f81b989a531a043cd09"}