Composition and Quadratic Recombination of Dyadic Shell Triples: Homogeneous-Class Closure, Two-Adic Filters, and Stress-Test Diagnostics

Description This Zenodo record contains Version 7.1.5 of the manuscript: Composition and Quadratic Recombination of Dyadic Shell Triples: Homogeneous-Class Closure, Two-Adic Filters, and Stress-Test Diagnostics This version develops the dyadic shell framework as a structural and diagnostic approach for studying odd composite numbers, congruence classes, CRT sign patterns, two-adic filters, and recombination mechanisms. The manuscript is not presented as a general-purpose integer factorization algorithm. Instead, it studies algebraic constraints, closure phenomena, and failure modes of a specific dyadic-shell and gcd-trigger framework. Version 7.1.5 includes the following refinements: a clarified periodicity statement for dyadic square residues; a formal description of how CRT sign patterns behave under multiplicative composition; a clearer distinction between exact shell triples and modular shell pairs; a representative-invariance remark for the gcd test; a careful treatment of homogeneous-class closure as a diagnostic result rather than as a factorization claim; stress-test diagnostics on RSA-110, RSA-260, RSA-270, RSA-896, and ROCA-style 1024-bit inputs; an explicit caveat that the observed closure and zero non-trivial gcd events reflect the tested constructive homogeneous generator and do not constitute lower bounds for general integer factorization algorithms; an expanded bibliography relating the framework to classical congruence-of-squares methods, the quadratic sieve, the number field sieve, lattice reduction, Coppersmith-type small-root techniques, and structured RSA-key attacks. The stress-test section reports that constructive homogeneous seeds remain confined to the global-plus CRT branch under multiplicative composition. These experiments are interpreted as a negative-control diagnostic: the implemented homogeneous generator does not accidentally leak into mixed CRT classes. The observed two-adic survival rates and product-collision patterns are treated as implementation-level and sample-family-dependent phenomena, not as universal density theorems. This record may include the main PDF manuscript and selected companion files such as README documentation, stress-test summaries, logs, and reproducibility metadata. The LaTeX source file is intentionally not included in this Zenodo deposit. Earlier related Zenodo versions of the dyadic shell project are: Version 4.0: DOI 10.5281/zenodo.20350133 Version 5.10.18: DOI 10.5281/zenodo.20484456 Version 6.5.7: DOI 10.5281/zenodo.20636900 Version 7.1.5 should be read as a continuation of this line of work, with the main emphasis shifted from obstruction theory alone toward composition, recombination, homogeneous-class closure, and stress-test diagnostics. Suggested citation Khachatryan, A. A. (2026). Composition and Quadratic Recombination of Dyadic Shell Triples: Homogeneous-Class Closure, Two-Adic Filters, and Stress-Test Diagnostics (Version 7.1.5). Zenodo. https://doi.org/10.5281/zenodo.20710574 Keywords dyadic shells; two-adic arithmetic; CRT sign patterns; integer factorization diagnostics; semiprime arithmetic; quadratic recombination; homogeneous-class closure; gcd-trigger models; modular square roots; RSA; ROCA; Coppersmith method; quadratic sieve; number field sieve; computational number theory