{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ARZGJJOHQCC6UIDETC7M4BIRIO","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":"9eff34c2fe3d5be2a874e00d714bdf973b641efbd9a507e558da8b557f7deae2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-06-02T17:09:43Z","title_canon_sha256":"f7b940aebcfde903598bbad183ca09c34984895d58141618d8866fafc34cb096"},"schema_version":"1.0","source":{"id":"2506.01879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01879","created_at":"2026-07-05T11:14:20Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01879v1","created_at":"2026-07-05T11:14:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01879","created_at":"2026-07-05T11:14:20Z"},{"alias_kind":"pith_short_12","alias_value":"ARZGJJOHQCC6","created_at":"2026-07-05T11:14:20Z"},{"alias_kind":"pith_short_16","alias_value":"ARZGJJOHQCC6UIDE","created_at":"2026-07-05T11:14:20Z"},{"alias_kind":"pith_short_8","alias_value":"ARZGJJOH","created_at":"2026-07-05T11:14:20Z"}],"graph_snapshots":[{"event_id":"sha256:1bc6a041b157e4ad058485b9995036ccc263666764d7914ad1ded6a193cdf856","target":"graph","created_at":"2026-07-05T11:14:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.01879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of $\\mathbb{Z}^2$ has a unique stationary measure. Building on this, Barraquand arXiv:2409.08927 derived explicit contour integral formulas for the model's multipoint probability generating function. In this paper, we introduce free Askey--Wilson functionals and use them to extend these generating function formulas. Our framework yields explicit expressions valid over a broader range of boundary parameters than previously accessible. This generalization allows us to determine the ","authors_text":"Jacek Wesolowski, Kamil Szpojankowski, Wlodek Bryc","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-06-02T17:09:43Z","title":"Free Askey--Wilson functionals and geometric last passage percolation on a strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01879","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":"sha256:87692bd4c0923b9f426bfc24ef74c6a0e272aca6dac5c4c58840a2ecdc77503b","target":"record","created_at":"2026-07-05T11:14:20Z","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":"9eff34c2fe3d5be2a874e00d714bdf973b641efbd9a507e558da8b557f7deae2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-06-02T17:09:43Z","title_canon_sha256":"f7b940aebcfde903598bbad183ca09c34984895d58141618d8866fafc34cb096"},"schema_version":"1.0","source":{"id":"2506.01879","kind":"arxiv","version":1}},"canonical_sha256":"047264a5c78085ea206498bece051143853ade435cfd7269987f936a803b54fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"047264a5c78085ea206498bece051143853ade435cfd7269987f936a803b54fa","first_computed_at":"2026-07-05T11:14:20.800708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:20.800708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gecmIVWSvAH1WjAD4M8/kfuJirIZYv0nEzgL20HkCfcnczwRM9GQVYuhMsx/Aev+ea8PNLz9o45qDx7iMeCyBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:20.801104Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87692bd4c0923b9f426bfc24ef74c6a0e272aca6dac5c4c58840a2ecdc77503b","sha256:1bc6a041b157e4ad058485b9995036ccc263666764d7914ad1ded6a193cdf856"],"state_sha256":"f097e77765f90acd6ff01c6f92dc1b02fe242b34885c62a69a57785b03edc80a"}