This preprint presents the fifth version of the dyadic shell framework for semiprime arithmetic. It continues the program initiated in the previous version, where exact dyadic triples were identified as structurally relevant objects for semiprime factorization. The present work turns that theoretical idea into a bounded public screening procedure designed to search for such triples without prior knowledge of the prime factors. The paper develops a polynomially bounded diagnostic screening framework based on visible two-adic representatives, including the original dyadic shell layer, square-multiplier extensions, and an additional inverse-trace prime-seed screening mode. The construction is accompanied by explicit algorithms, implementation notes, and reproducibility scripts. Computational experiments were performed on RSA-110, RSA-260, RSA-270, RSA-896, and a ROCA-style 1024-bit test modulus. The square-multiplier screening runs processed hundreds of thousands of tested pairs and more than 1. 7 million candidate roots in total. The inverse-trace prime-seed tests processed all prime seed values up to (10⁷) for each tested modulus. Across the reported experiments, no exact non-trivial dyadic triples and no non-trivial factors were found. The main conclusion is therefore deliberately limited. The dyadic triple framework can be operationalized as a polynomially bounded structural diagnostic, and positive outputs would be directly verifiable by exact arithmetic and gcd checks. However, the experiments reported here indicate that the tested visible-representative mechanisms do not provide a practical route to factoring large RSA-type semiprimes. In particular, the guaranteed hidden existence of non-trivial dyadic branches does not imply their public discoverability by the bounded screening methods studied in this work. The preprint includes the LaTeX source, screening scripts, test vector information, and references to the computational log corpus used to reproduce the aggregate statistics reported in the appendix.
Arsen KHACHATRYAN (Mon,) studied this question.