{"paper":{"title":"On the small-step quarter plane lattice walks with a non D-finite univariate generating function","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Juan Pulido, Marni Mishna","submitted_at":"2026-05-15T22:52:05Z","abstract_excerpt":"We report on the status of the conjecture of Bousquet-M\\'elou and Mishna that the univariate counting generating function of a small-step quarter-plane lattice model is D-finite if and only if the group of the walk is finite. While the finite-group case is fully resolved, the infinite-group case remains incomplete. We list the arguments for the non-D-finiteness for 21 of the 56 infinite-group models: the five singular models, three models with zero drift and thirteen models with polar interior drift. The proof of the latter two families uses asymptotic results of Bostan--Raschel--Salvy combine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16688","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/2605.16688/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.376463Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.497201Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"395d7ddce8fcdc075a07d1758003507a9cfb67f1c2346760546cc8059698d9b1"},"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"}