{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ULYYL2A4HEE3EI4EVKSUB2N7R3","short_pith_number":"pith:ULYYL2A4","schema_version":"1.0","canonical_sha256":"a2f185e81c3909b22384aaa540e9bf8ecd63d10e269a1c0f276671f6d6270321","source":{"kind":"arxiv","id":"1404.6238","version":6},"attestation_state":"computed","paper":{"title":"Recurrence and transience for the frog model on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christopher Hoffman, Matthew Junge, Tobias Johnson","submitted_at":"2014-04-24T19:34:45Z","abstract_excerpt":"The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase transition, finding it recurrent for $d=2$ and transient for $d\\geq 5$. Simulations suggest strong recurrence for $d=2$, weak recurrence for $d=3$, and transience for $d\\geq 4$. Additionally, we prove a 0-1 law for all $d$-ary trees, and we exhibit a graph on which a 0-1 law does not hold.\n  To prove recurrence when $d=2$, we construct a recursive distribution"},"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":"1404.6238","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T19:34:45Z","cross_cats_sorted":[],"title_canon_sha256":"e0a0a59bb6f1e61eb21c7f018a0a75d485e1272bc4de78db782776cd473d5124","abstract_canon_sha256":"8c0c6aadb942f1e98f0cae7e610a98647da2ee9e41f7ebd6721a9cdd27431dbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:10.675554Z","signature_b64":"bezcfpidqo6m4pN05ky1n7EvZl/zXCTkbCwF2IMUIHPu6JAwonm6FNbixXv+YV5YDJLphPvKSCXLZ17d/ONtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2f185e81c3909b22384aaa540e9bf8ecd63d10e269a1c0f276671f6d6270321","last_reissued_at":"2026-05-18T00:24:10.674648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:10.674648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recurrence and transience for the frog model on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christopher Hoffman, Matthew Junge, Tobias Johnson","submitted_at":"2014-04-24T19:34:45Z","abstract_excerpt":"The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase transition, finding it recurrent for $d=2$ and transient for $d\\geq 5$. Simulations suggest strong recurrence for $d=2$, weak recurrence for $d=3$, and transience for $d\\geq 4$. Additionally, we prove a 0-1 law for all $d$-ary trees, and we exhibit a graph on which a 0-1 law does not hold.\n  To prove recurrence when $d=2$, we construct a recursive distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6238","kind":"arxiv","version":6},"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":"1404.6238","created_at":"2026-05-18T00:24:10.674817+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6238v6","created_at":"2026-05-18T00:24:10.674817+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6238","created_at":"2026-05-18T00:24:10.674817+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULYYL2A4HEE3","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULYYL2A4HEE3EI4E","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULYYL2A4","created_at":"2026-05-18T12:28:52.271510+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/ULYYL2A4HEE3EI4EVKSUB2N7R3","json":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3.json","graph_json":"https://pith.science/api/pith-number/ULYYL2A4HEE3EI4EVKSUB2N7R3/graph.json","events_json":"https://pith.science/api/pith-number/ULYYL2A4HEE3EI4EVKSUB2N7R3/events.json","paper":"https://pith.science/paper/ULYYL2A4"},"agent_actions":{"view_html":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3","download_json":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3.json","view_paper":"https://pith.science/paper/ULYYL2A4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6238&json=true","fetch_graph":"https://pith.science/api/pith-number/ULYYL2A4HEE3EI4EVKSUB2N7R3/graph.json","fetch_events":"https://pith.science/api/pith-number/ULYYL2A4HEE3EI4EVKSUB2N7R3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3/action/storage_attestation","attest_author":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3/action/author_attestation","sign_citation":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3/action/citation_signature","submit_replication":"https://pith.science/pith/ULYYL2A4HEE3EI4EVKSUB2N7R3/action/replication_record"}},"created_at":"2026-05-18T00:24:10.674817+00:00","updated_at":"2026-05-18T00:24:10.674817+00:00"}