{"paper":{"title":"Explicit classes in Habiro cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT"],"primary_cat":"math.AG","authors_text":"Campbell Wheeler, Stavros Garoufalidis","submitted_at":"2025-05-26T12:14:08Z","abstract_excerpt":"We propose a cycle description of the Habiro cohomology of a smooth variety $X$\n  over the spectrum $B$ of an \\'etale $Z[\\lambda]$-algebra and construct explicit\n  nontrivial cycles using either the Picard-Fuchs equation on $X/B$\n  of a hypergeometric motive, or a push-forward of elements\n  of the Habiro ring of $X/B$. In particular, we give explicit classes for\n  1-parameter Calabi--Yau families.\n  The $q$-hypergeometric origin of our cycles imply\n  that they generate $q$-holonomic modules that define $q$-deformations of the\n  classical Picard-Fuchs equation. We illustrate our theorems with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19885","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/2505.19885/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"}