{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z33VGTCOU3H7BD4WY6KRU2OA42","short_pith_number":"pith:Z33VGTCO","schema_version":"1.0","canonical_sha256":"cef7534c4ea6cff08f96c7951a69c0e6956599fc790dadf55009949ab53fbada","source":{"kind":"arxiv","id":"1412.5330","version":2},"attestation_state":"computed","paper":{"title":"Rotor-routing on Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ecaterina Sava-Huss, Sebastian Mueller, Wilfried Huss","submitted_at":"2014-12-17T10:54:04Z","abstract_excerpt":"A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is routed to the neighbor the rotor is now pointing at. In the current work we make a step toward in understanding the behavior of rotor-router walks on random trees. More precisely, we consider random i.i.d. initial configurations of rotors on Galton-Watson trees, i.e. on a family tree arising from a Galton-Watson process, and give a classification in recurrence "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.5330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T10:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"408f4013b4a07bec96237b312f1989e70b5cf32a41d09270e627c1c7b6ae2a0b","abstract_canon_sha256":"a360f61162a83c69ff56825da8aaff0a79d3b646939bf5b409a40b3f8029738b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:47.873521Z","signature_b64":"wD0EWySP9Z/sP/zt+Ao61uTot9A3YIWlTsCsumJ2HK/ZCIdAizs2KWOixrluRliJ8tMvDg5kQGLrUm/F6rxxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cef7534c4ea6cff08f96c7951a69c0e6956599fc790dadf55009949ab53fbada","last_reissued_at":"2026-05-18T01:42:47.872776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:47.872776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotor-routing on Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ecaterina Sava-Huss, Sebastian Mueller, Wilfried Huss","submitted_at":"2014-12-17T10:54:04Z","abstract_excerpt":"A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is routed to the neighbor the rotor is now pointing at. In the current work we make a step toward in understanding the behavior of rotor-router walks on random trees. More precisely, we consider random i.i.d. initial configurations of rotors on Galton-Watson trees, i.e. on a family tree arising from a Galton-Watson process, and give a classification in recurrence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5330","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.5330","created_at":"2026-05-18T01:42:47.872885+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5330v2","created_at":"2026-05-18T01:42:47.872885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5330","created_at":"2026-05-18T01:42:47.872885+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z33VGTCOU3H7","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z33VGTCOU3H7BD4W","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z33VGTCO","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42","json":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42.json","graph_json":"https://pith.science/api/pith-number/Z33VGTCOU3H7BD4WY6KRU2OA42/graph.json","events_json":"https://pith.science/api/pith-number/Z33VGTCOU3H7BD4WY6KRU2OA42/events.json","paper":"https://pith.science/paper/Z33VGTCO"},"agent_actions":{"view_html":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42","download_json":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42.json","view_paper":"https://pith.science/paper/Z33VGTCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5330&json=true","fetch_graph":"https://pith.science/api/pith-number/Z33VGTCOU3H7BD4WY6KRU2OA42/graph.json","fetch_events":"https://pith.science/api/pith-number/Z33VGTCOU3H7BD4WY6KRU2OA42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42/action/storage_attestation","attest_author":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42/action/author_attestation","sign_citation":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42/action/citation_signature","submit_replication":"https://pith.science/pith/Z33VGTCOU3H7BD4WY6KRU2OA42/action/replication_record"}},"created_at":"2026-05-18T01:42:47.872885+00:00","updated_at":"2026-05-18T01:42:47.872885+00:00"}