{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DEAHHTGONMZAFMN243KBV4O7NH","short_pith_number":"pith:DEAHHTGO","schema_version":"1.0","canonical_sha256":"190073ccce6b3202b1bae6d41af1df69ef984aa8a2c2a252aa787d702fffe535","source":{"kind":"arxiv","id":"1310.1583","version":1},"attestation_state":"computed","paper":{"title":"Random Walk with Long-Range Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Peled, Yinon Spinka","submitted_at":"2013-10-06T13:10:01Z","abstract_excerpt":"We consider a model of a random height function with long-range constraints on a discrete segment. This model was suggested by Benjamini, Yadin and Yehudayoff and is a generalization of simple random walk. The random function is uniformly sampled from all graph homomorphisms from the graph P_{n,d} to the integers Z, where the graph P_{n,d} is the discrete segment {0,1,..., n} with edges between vertices of different parity whose distance is at most 2d+1. Such a graph homomorphism can be viewed as a height function whose values change by exactly one along edges of the graph P_{n,d}. We also con"},"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":"1310.1583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-06T13:10:01Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"e31697da2aa51a7c197d42dafbdb1f26ec226a20a3114628300d84d8273c9a35","abstract_canon_sha256":"91bcc2bb2bbbaa5332ebe0f516d56ad83635b352cb24b42706f1ab393d7271f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.407780Z","signature_b64":"GeYLOSO1Wl2CKhBQz/3LS9vB+SmutVIdjLC0ipgXZM2a3xf2gnll6jE+cR6qn8ZToIha+ysZvcUcSXG3FpIhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"190073ccce6b3202b1bae6d41af1df69ef984aa8a2c2a252aa787d702fffe535","last_reissued_at":"2026-05-18T00:48:55.406722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.406722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Walk with Long-Range Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Peled, Yinon Spinka","submitted_at":"2013-10-06T13:10:01Z","abstract_excerpt":"We consider a model of a random height function with long-range constraints on a discrete segment. This model was suggested by Benjamini, Yadin and Yehudayoff and is a generalization of simple random walk. The random function is uniformly sampled from all graph homomorphisms from the graph P_{n,d} to the integers Z, where the graph P_{n,d} is the discrete segment {0,1,..., n} with edges between vertices of different parity whose distance is at most 2d+1. Such a graph homomorphism can be viewed as a height function whose values change by exactly one along edges of the graph P_{n,d}. We also con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1583","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":"1310.1583","created_at":"2026-05-18T00:48:55.407227+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.1583v1","created_at":"2026-05-18T00:48:55.407227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1583","created_at":"2026-05-18T00:48:55.407227+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEAHHTGONMZA","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEAHHTGONMZAFMN2","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEAHHTGO","created_at":"2026-05-18T12:27:43.054852+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/DEAHHTGONMZAFMN243KBV4O7NH","json":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH.json","graph_json":"https://pith.science/api/pith-number/DEAHHTGONMZAFMN243KBV4O7NH/graph.json","events_json":"https://pith.science/api/pith-number/DEAHHTGONMZAFMN243KBV4O7NH/events.json","paper":"https://pith.science/paper/DEAHHTGO"},"agent_actions":{"view_html":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH","download_json":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH.json","view_paper":"https://pith.science/paper/DEAHHTGO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.1583&json=true","fetch_graph":"https://pith.science/api/pith-number/DEAHHTGONMZAFMN243KBV4O7NH/graph.json","fetch_events":"https://pith.science/api/pith-number/DEAHHTGONMZAFMN243KBV4O7NH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH/action/storage_attestation","attest_author":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH/action/author_attestation","sign_citation":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH/action/citation_signature","submit_replication":"https://pith.science/pith/DEAHHTGONMZAFMN243KBV4O7NH/action/replication_record"}},"created_at":"2026-05-18T00:48:55.407227+00:00","updated_at":"2026-05-18T00:48:55.407227+00:00"}