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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.02011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-02T10:45:43Z","cross_cats_sorted":[],"title_canon_sha256":"d1130013697f2ba2983d8c7a7ff6334cba5dcf28276d011370688de87eada268","abstract_canon_sha256":"add11814297bd8da76838491b467aa02bbffcb2183cbbedc3f9a48f512a5e858"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:37.005196Z","signature_b64":"Z7mutjHGM5rbg/LdGmJdMCrtf174CtuXL7mfLoja5WApbfWJfJsHUj9lKsp52vZ5/QUYDLh5tcNDIRHQMQ3OAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4cab0b9b24c0432d7745105a44b77e39d4e9410198e3778abc579f87fc7008a","last_reissued_at":"2026-07-03T01:17:37.004767Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:37.004767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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