{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7UEVWI3Q46MTF5BCWZORSQS55M","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":"44f4928590bd6f724a1a00950a8e88735c5f3db597a75dcc886909e3e6e0000e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-23T21:59:55Z","title_canon_sha256":"05e0ca08c5fa5c73847a964f889c5eb6a1dec3e7897d147bcbf8ebc517a68c51"},"schema_version":"1.0","source":{"id":"1408.5533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5533","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5533v1","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5533","created_at":"2026-05-18T02:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"7UEVWI3Q46MT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7UEVWI3Q46MTF5BC","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7UEVWI3Q","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:e94d765c19e09b690f3888a36f5afacee0a453ad0518f2b0f91bfaedf656da71","target":"graph","created_at":"2026-05-18T02:44:24Z","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 a \\emph{rotor walk} the exits from each vertex follow a prescribed periodic sequence. On an infinite Eulerian graph embedded periodically in $\\R^d$, we show that any simple rotor walk, regardless of rotor mechanism or initial rotor configuration, visits at least on the order of $t^{d/(d+1)}$ distinct sites in $t$ steps. We prove a shape theorem for the rotor walk on the comb graph with i.i.d.\\ uniform initial rotors, showing that the range is of order $t^{2/3}$ and the asymptotic shape of the range is a diamond. Using a connection to the mirror model and critical percolation, we show that r","authors_text":"Laura Florescu, Lionel Levine, Yuval Peres","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-23T21:59:55Z","title":"The range of a rotor walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5533","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:e060a9d4a570c42d22394ad56c851a1f0d1cc7efffc2edfa948d4fa480beec5a","target":"record","created_at":"2026-05-18T02:44:24Z","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":"44f4928590bd6f724a1a00950a8e88735c5f3db597a75dcc886909e3e6e0000e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-23T21:59:55Z","title_canon_sha256":"05e0ca08c5fa5c73847a964f889c5eb6a1dec3e7897d147bcbf8ebc517a68c51"},"schema_version":"1.0","source":{"id":"1408.5533","kind":"arxiv","version":1}},"canonical_sha256":"fd095b2370e79932f422b65d19425deb0d0aed2d8fe90b00f8d1a057d9b07738","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd095b2370e79932f422b65d19425deb0d0aed2d8fe90b00f8d1a057d9b07738","first_computed_at":"2026-05-18T02:44:24.889462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:24.889462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Pr+lov4rGQul+suN1NXlxW0czDau3yMhfdJNom5TwZOf8kL7ZD5vKDtcLtJ0qpIKC96mIILnh55/SHyEt2MDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:24.889816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e060a9d4a570c42d22394ad56c851a1f0d1cc7efffc2edfa948d4fa480beec5a","sha256:e94d765c19e09b690f3888a36f5afacee0a453ad0518f2b0f91bfaedf656da71"],"state_sha256":"4fcdde6772d921d00ff9cd7a867586574a98fcf300a9765741920bc4842789e2"}