{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FHQWYUMTZQHMYJQK6KUT5SP3LY","short_pith_number":"pith:FHQWYUMT","schema_version":"1.0","canonical_sha256":"29e16c5193cc0ecc260af2a93ec9fb5e12c6400c9b5a921a3037925e3d7c5da9","source":{"kind":"arxiv","id":"1707.07749","version":1},"attestation_state":"computed","paper":{"title":"The nonhomogeneous frog model on $\\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Josh Rosenberg","submitted_at":"2017-07-24T20:59:03Z","abstract_excerpt":"We examine a system of interacting random walks with leftward drift on $\\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become activated when landed on by other particles, and all particles beginning at the same point posses equal leftward drift. Once activated, the trajectories of distinct particles are independent. This system belongs to a broader class of problems involving interacting random walks on rooted graphs, referred to collectively as the frog model. Additional conditions "},"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":"1707.07749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-24T20:59:03Z","cross_cats_sorted":[],"title_canon_sha256":"87b08fe144bdef0fe338527ec0be0c4a2eaacebe36f8019c5db460520305105d","abstract_canon_sha256":"7deb6e93d4ee9d69cfae1518b216b179d42da0529773a9451c9804ca84a19900"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:30.521755Z","signature_b64":"y3Iu6ifQQIKa7Hd86VGStGxwzdtDqQrPigXwazQEpmgmfkqOTSutmtd2JlxnakqveLEAyAY9Z6MFXsnYpAgSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29e16c5193cc0ecc260af2a93ec9fb5e12c6400c9b5a921a3037925e3d7c5da9","last_reissued_at":"2026-05-18T00:39:30.521185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:30.521185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The nonhomogeneous frog model on $\\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Josh Rosenberg","submitted_at":"2017-07-24T20:59:03Z","abstract_excerpt":"We examine a system of interacting random walks with leftward drift on $\\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become activated when landed on by other particles, and all particles beginning at the same point posses equal leftward drift. Once activated, the trajectories of distinct particles are independent. This system belongs to a broader class of problems involving interacting random walks on rooted graphs, referred to collectively as the frog model. Additional conditions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07749","kind":"arxiv","version":1},"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":"1707.07749","created_at":"2026-05-18T00:39:30.521263+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07749v1","created_at":"2026-05-18T00:39:30.521263+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07749","created_at":"2026-05-18T00:39:30.521263+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHQWYUMTZQHM","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHQWYUMTZQHMYJQK","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHQWYUMT","created_at":"2026-05-18T12:31:15.632608+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/FHQWYUMTZQHMYJQK6KUT5SP3LY","json":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY.json","graph_json":"https://pith.science/api/pith-number/FHQWYUMTZQHMYJQK6KUT5SP3LY/graph.json","events_json":"https://pith.science/api/pith-number/FHQWYUMTZQHMYJQK6KUT5SP3LY/events.json","paper":"https://pith.science/paper/FHQWYUMT"},"agent_actions":{"view_html":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY","download_json":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY.json","view_paper":"https://pith.science/paper/FHQWYUMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07749&json=true","fetch_graph":"https://pith.science/api/pith-number/FHQWYUMTZQHMYJQK6KUT5SP3LY/graph.json","fetch_events":"https://pith.science/api/pith-number/FHQWYUMTZQHMYJQK6KUT5SP3LY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY/action/storage_attestation","attest_author":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY/action/author_attestation","sign_citation":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY/action/citation_signature","submit_replication":"https://pith.science/pith/FHQWYUMTZQHMYJQK6KUT5SP3LY/action/replication_record"}},"created_at":"2026-05-18T00:39:30.521263+00:00","updated_at":"2026-05-18T00:39:30.521263+00:00"}