{"paper":{"title":"Iwasawa-Type Spectral Resultant Growth Laws for Grover Walks on Graph Towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jir\\^o Akahori, Ryoichi Suzuki, Taro Hayashi","submitted_at":"2026-07-02T10:45:43Z","abstract_excerpt":"Let $X_0\\leftarrow X_1\\leftarrow\\cdots$ be a $\\mathbb Z_p^d$-tower of finite graphs, and let $U_n$ be the Grover transition matrix on $X_n$. We study Iwasawa-type $p$-adic growth laws for the polynomial spectral quantities \\[ \\det P(U_n), \\] where $P(A)$ is a monic polynomial. The basic object is the spectral resultant \\[ \\mathcal R_{X,P}(T)=\\operatorname{Res}_A(\\mathcal F_X(A,T),P(A)), \\] where $\\mathcal F_X(A,T)$ is the universal Grover--Ihara spectral polynomial of the tower. In the integral setting, this resultant generates the zeroth Fitting ideal of a natural finite module over the Iwasa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02011","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/2607.02011/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"}