{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:EK66AYT3ADZWZHJY43QDQUBQEV","short_pith_number":"pith:EK66AYT3","schema_version":"1.0","canonical_sha256":"22bde0627b00f36c9d38e6e0385030257eeb7caf867daf105640d626cd061f58","source":{"kind":"arxiv","id":"0910.0069","version":7},"attestation_state":"computed","paper":{"title":"Directed polymers and the quantum Toda lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Neil O'Connell","submitted_at":"2009-10-01T10:30:24Z","abstract_excerpt":"We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence."},"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":"0910.0069","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-01T10:30:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fe3739285cb73e109aa78df9f29258ab7d9f9d1b6f10d21a84090f6d8c9ab6b7","abstract_canon_sha256":"e10e743acadea1e7761016a77c253880ef57d00795e9550f96deb090c510f875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:12.468360Z","signature_b64":"MfQfI5hsotDWfbAgGS5gvcJM7oghtGmYDO8gJ9aL9/SE29Wre612nJq/K6ADp/gjL0AWtloGwJPpHAUjhIf/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22bde0627b00f36c9d38e6e0385030257eeb7caf867daf105640d626cd061f58","last_reissued_at":"2026-05-18T03:59:12.467886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:12.467886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Directed polymers and the quantum Toda lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Neil O'Connell","submitted_at":"2009-10-01T10:30:24Z","abstract_excerpt":"We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0069","kind":"arxiv","version":7},"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":"0910.0069","created_at":"2026-05-18T03:59:12.467945+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.0069v7","created_at":"2026-05-18T03:59:12.467945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0069","created_at":"2026-05-18T03:59:12.467945+00:00"},{"alias_kind":"pith_short_12","alias_value":"EK66AYT3ADZW","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"EK66AYT3ADZWZHJY","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"EK66AYT3","created_at":"2026-05-18T12:25:59.703012+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/EK66AYT3ADZWZHJY43QDQUBQEV","json":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV.json","graph_json":"https://pith.science/api/pith-number/EK66AYT3ADZWZHJY43QDQUBQEV/graph.json","events_json":"https://pith.science/api/pith-number/EK66AYT3ADZWZHJY43QDQUBQEV/events.json","paper":"https://pith.science/paper/EK66AYT3"},"agent_actions":{"view_html":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV","download_json":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV.json","view_paper":"https://pith.science/paper/EK66AYT3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.0069&json=true","fetch_graph":"https://pith.science/api/pith-number/EK66AYT3ADZWZHJY43QDQUBQEV/graph.json","fetch_events":"https://pith.science/api/pith-number/EK66AYT3ADZWZHJY43QDQUBQEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV/action/storage_attestation","attest_author":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV/action/author_attestation","sign_citation":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV/action/citation_signature","submit_replication":"https://pith.science/pith/EK66AYT3ADZWZHJY43QDQUBQEV/action/replication_record"}},"created_at":"2026-05-18T03:59:12.467945+00:00","updated_at":"2026-05-18T03:59:12.467945+00:00"}