Sequence Systems, h-Patterns, EFU Assembly, and Transfer Kernels

Sequence Systems, h-Patterns, EFU Assembly, and Transfer Kernels | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 April 2026 V1 Latest version Share on Sequence Systems, h-Patterns, EFU Assembly, and Transfer Kernels Author : Sergey Kotikov 0009-0009-4367-7859 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177575369.98890570/v1 59 views 39 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This article develops a structural theory of symbolic objects in which syntactic realization, semantic interpretation, admissible transformation, and assembly structure are treated inside a common formal framework. The structural core begins with the category SEq of symbolic structures and its sequence-theoretic refinement SeqSEq, then passes through h-patterns, EFU decomposition, pattern-valued and assembly-valued generating series, transfer-kernel factorization, moment stability, and singular/spectral control. The basic word model on {S, P } is retained as a laboratory in which these layers are constructed explicitly and in theorem-proof form. The second half extends this structural core to an arithmetic and analytic route. We introduce a prime-transfer package, a completion theorem, and then specialize to the completed model Z sym. From there we pass to the heat-flow reduction governed by Λ SEq, the sharp-pair and tail-rigidity reduction, the Fourier/edge transport, and the edge phase rigidity theorem implying the Riemann hypothesis. Section 2 states the main result in standard analytic language with no internal terminology. Every step of the proof chain is formalized in Lean 4 without sorry and without axioms beyond the standard Lean/mathlib foundation. The de Bruijn-Newman bridge is used as a separately formalized theorem, not as an axiom; the companion repository is https://github.com/catman77/SymStructures-RH. Appendices include a full dependency table, a Lean module map, and a discussion of possible failure modes. Supplementary Material File (symstructures-rh_v1.pdf) Download 1.17 MB Information & Authors Information Version history V1 Version 1 09 April 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords categorical semantics completion efu decomposition h-patterns heat flow rigidity riman hypothesis sequence objects structural equivalence symbolic structures transfer kernels Authors Affiliations Sergey Kotikov 0009-0009-4367-7859 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 59 views 39 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Sergey Kotikov. Sequence Systems, h-Patterns, EFU Assembly, and Transfer Kernels. Authorea . 09 April 2026. 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