{"paper":{"title":"Dold-Gauss Congruences, Norm Descent, and Rational Rigidity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Hartosh Singh Bal","submitted_at":"2025-09-29T16:56:20Z","abstract_excerpt":"We develop a Witt--Hadamard calculus for Euler products that unifies the classical Gauss congruences with their modern refinement, the Dold congruences. Within this framework we prove \\emph{norm descent}: Dold congruences are functorial under finite extensions and preserved by prime--ideal norms $N_{K/\\mathbb{Q}}$, yielding integer ghosts from algebraic ones. We extend the theory from $\\mathbb{Z}$ to Dedekind domains, and show that integrality is stable under both Hadamard and Witt products. Two rigidity theorems lie at the core: a \\emph{cyclotomic residues theorem}, asserting that if the loga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.25038","kind":"arxiv","version":2},"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/2509.25038/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"}