{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E4C4XDNV2P4ITWA2RKWOZTPXYV","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":"4c0e7ad3d76616fc4986682281aa3986d6aa8106a556b15d89d03da93f8defb1","cross_cats_sorted":["cond-mat.stat-mech","math.CA","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-04T06:46:12Z","title_canon_sha256":"e64b7f61531d62c142f9e2ce7f7d99135cd691462c85416e88f3b3b4a97bdfab"},"schema_version":"1.0","source":{"id":"1608.01438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01438","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01438v1","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01438","created_at":"2026-05-18T00:39:52Z"},{"alias_kind":"pith_short_12","alias_value":"E4C4XDNV2P4I","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E4C4XDNV2P4ITWA2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E4C4XDNV","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:6218256904fbe6e173bf7ef3ce1b21d7a6f85ff4984e2e22bb2158d69e8bf0b9","target":"graph","created_at":"2026-05-18T00:39:52Z","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":"More than 15 years ago Guttmann and V\\\"oge [J. Statist. Plann. Inference, {\\bf 101}, 107 (2002)], introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model, originally introduced by Tsuchiya and Katori [J. Phys. Soc. Japan {\\bf 67}, 1655 (1988)], which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and","authors_text":"Iwan Jensen","cross_cats":["cond-mat.stat-mech","math.CA","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-04T06:46:12Z","title":"Three friendly walkers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01438","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":"sha256:9cb55d26f31d2de78f8210f4172b7dd4c841d1a0bd59fb5af0d552bec2b19c51","target":"record","created_at":"2026-05-18T00:39:52Z","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":"4c0e7ad3d76616fc4986682281aa3986d6aa8106a556b15d89d03da93f8defb1","cross_cats_sorted":["cond-mat.stat-mech","math.CA","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-04T06:46:12Z","title_canon_sha256":"e64b7f61531d62c142f9e2ce7f7d99135cd691462c85416e88f3b3b4a97bdfab"},"schema_version":"1.0","source":{"id":"1608.01438","kind":"arxiv","version":1}},"canonical_sha256":"2705cb8db5d3f889d81a8aaceccdf7c54f3fab04575b3b7b46cba3a2462433b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2705cb8db5d3f889d81a8aaceccdf7c54f3fab04575b3b7b46cba3a2462433b4","first_computed_at":"2026-05-18T00:39:52.963410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:52.963410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jxknHRqpbxnt6FuF5rcU6yroJNETlMgEqBUT+r3v0Ib8C2D1evqx5QBSXZZwLcRJ5+XpvKyQuyEBSgSxtmaTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:52.964042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cb55d26f31d2de78f8210f4172b7dd4c841d1a0bd59fb5af0d552bec2b19c51","sha256:6218256904fbe6e173bf7ef3ce1b21d7a6f85ff4984e2e22bb2158d69e8bf0b9"],"state_sha256":"f9964a5045e86e4ac4a4c531d17a4ab15fb91a6ebae6c0af0e7f3e8569d490d6"}