{"paper":{"title":"Iterated extensions and the ramification dichotomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mugurel Barcau, Vicen\\c{t}iu Pa\\c{s}ol","submitted_at":"2026-06-28T10:09:21Z","abstract_excerpt":"Let $K/\\mathbb Q_p$ be finite and let $f\\in\\mathcal O_K[X]$ be monic, of degree at least two, with $f'(X)\\in\\mathfrak m_K\\mathcal O_K[X]$, equivalently $\\bar f\\in k[X^p]$. For a compatible inverse branch $f(t_{n+1})=t_n$ with $t_0\\in\\mathcal O_K$, put $K_n=K(t_n)$ and $K_\\infty=\\bigcup_nK_n$. We prove that $K_\\infty/K$ is either unramified or deeply ramified. More precisely, once ramification appears, the ramification indices over the maximal unramified subfields tend to infinity and the finite-level differents are unbounded. In the Frobenius-type case $f(X)\\equiv X^{p^a}\\pmod{\\mathfrak m_K}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29310","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/2606.29310/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"}