{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5ZYVASFUUOQ2JZ55RLR75AZM2A","short_pith_number":"pith:5ZYVASFU","schema_version":"1.0","canonical_sha256":"ee715048b4a3a1a4e7bd8ae3fe832cd0115dcf53a1b1f8a2bb6c1095ab20de61","source":{"kind":"arxiv","id":"2605.21744","version":1},"attestation_state":"computed","paper":{"title":"Return Probability for the Switch--Walk--Switch Lamplighter Walk on a Regular Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenyang An, Minghao Pan","submitted_at":"2026-05-20T21:12:57Z","abstract_excerpt":"We derive the sharp return-probability asymptotic for the switch--walk--switch lamplighter walk with lamp group $\\mathbb Z_2$ over the infinite $d$-regular tree: \\[\n  p_{2n}(e,e)\n  =\n  \\rho_d^{2n}\n  \\exp\\left[\n  -\\left(\\pi^2(\\log(d-1))^2+o(1)\\right)\n  \\frac{n}{\\log^2 n}\n  \\right]. \\] The proofs were generated by QED, a multi-agent system co-developed by the authors, without human intervention beyond the specification of the problem. This provides a test case for the ability of AI systems to produce rigorous mathematical proofs."},"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":"2605.21744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-20T21:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"e32809f7d026dcecb40c1b8dba54aa7c5110523e4e0607e88572c8f846ac0d2b","abstract_canon_sha256":"9f138aaa0d209e45d812363af41dc6bce44e5841ff1e5cfe71cb4e706b6cded6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:30.267667Z","signature_b64":"qI8uA/eXFwcsnfodJOdQuNWa7Npb7sSR/pAw/cL4wvu3NbKNM/MkDf5IsPdGujB77Ew3PdlqxuAswwUIqrulCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee715048b4a3a1a4e7bd8ae3fe832cd0115dcf53a1b1f8a2bb6c1095ab20de61","last_reissued_at":"2026-05-22T01:03:30.267105Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:30.267105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Return Probability for the Switch--Walk--Switch Lamplighter Walk on a Regular Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenyang An, Minghao Pan","submitted_at":"2026-05-20T21:12:57Z","abstract_excerpt":"We derive the sharp return-probability asymptotic for the switch--walk--switch lamplighter walk with lamp group $\\mathbb Z_2$ over the infinite $d$-regular tree: \\[\n  p_{2n}(e,e)\n  =\n  \\rho_d^{2n}\n  \\exp\\left[\n  -\\left(\\pi^2(\\log(d-1))^2+o(1)\\right)\n  \\frac{n}{\\log^2 n}\n  \\right]. \\] The proofs were generated by QED, a multi-agent system co-developed by the authors, without human intervention beyond the specification of the problem. This provides a test case for the ability of AI systems to produce rigorous mathematical proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21744","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.21744/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.21744","created_at":"2026-05-22T01:03:30.267216+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21744v1","created_at":"2026-05-22T01:03:30.267216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21744","created_at":"2026-05-22T01:03:30.267216+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZYVASFUUOQ2","created_at":"2026-05-22T01:03:30.267216+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZYVASFUUOQ2JZ55","created_at":"2026-05-22T01:03:30.267216+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZYVASFU","created_at":"2026-05-22T01:03:30.267216+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/5ZYVASFUUOQ2JZ55RLR75AZM2A","json":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A.json","graph_json":"https://pith.science/api/pith-number/5ZYVASFUUOQ2JZ55RLR75AZM2A/graph.json","events_json":"https://pith.science/api/pith-number/5ZYVASFUUOQ2JZ55RLR75AZM2A/events.json","paper":"https://pith.science/paper/5ZYVASFU"},"agent_actions":{"view_html":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A","download_json":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A.json","view_paper":"https://pith.science/paper/5ZYVASFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21744&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZYVASFUUOQ2JZ55RLR75AZM2A/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZYVASFUUOQ2JZ55RLR75AZM2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A/action/storage_attestation","attest_author":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A/action/author_attestation","sign_citation":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A/action/citation_signature","submit_replication":"https://pith.science/pith/5ZYVASFUUOQ2JZ55RLR75AZM2A/action/replication_record"}},"created_at":"2026-05-22T01:03:30.267216+00:00","updated_at":"2026-05-22T01:03:30.267216+00:00"}