Base-Shell Diagnostics for Individual Congruences of Squares in Semiprime Arithmetic

This record contains Version 9. 2. 2 of the article “Base-Shell Diagnostics for Individual Congruences of Squares in Semiprime Arithmetic” by A. A. Khachatryan, together with a computational reproducibility archive. The article develops a structural and diagnostic framework for studying individual congruences of squares in semiprime arithmetic. The work is based on deterministic base-shell relations, finite-window representatives, public boundary observability, and hidden CRT-sign information. The framework is intended to clarify the algebraic and combinatorial structure behind Kraitchik-type square congruences and to distinguish between public-mode diagnostics and validation-mode analysis where the factors are known. The work is not presented as a factorization attack, not as a replacement for classical algorithms such as QS or GNFS, and not as a universal weak-key or ROCA detector. The public statistic used in the article is interpreted as a calibrated boundary observable. It may indicate structural anomalies under specified bases, height windows, and calibration populations, but such an anomaly is not by itself evidence of cryptanalytic vulnerability. The computational part of the article reports reproducibility tests, positive-control finite-window checks, public-window sparsity experiments, validation-mode CRT-sign controls, legacy benchmark stress tests, and Weyl-profile calibration experiments. The reported results support the internal consistency of the finite-window counting implementation and demonstrate strong empirical sparsity of public strict-window events under the tested parameters. Validation-mode controls confirm that mixed hidden CRT-sign representatives produce the expected nontrivial gcd outcomes when the factors are known. The accompanying archive contains scripts, data, results, and figures used to support the computational section of the article. It is provided for transparency, inspection, and reproducibility of the reported experiments. The computational package should be understood as a diagnostic and research tool, not as an implementation of a practical factoring method. Files included in this record: KhachatryanAA₀009-0006-7629-3833Base-ShellDiagnosticsᵢnSemiprimeArithmetic. pdfFinal PDF version of the article. baseₛhellₜestsᵥ9₂₂ᵣeproducibility. zipReproducibility archive containing scripts, data, results, figures, requirements, and manifest files. README. mdDescription of the record, file structure, reproduction notes, citation information, license, and interpretation guidelines. License: Creative Commons Attribution Non Commercial 4. 0 International (CC BY-NC 4. 0). Author: A. A. KhachatryanORCID: 0009-0006-7629-3833Version: 9. 2. 2DOI: 10. 5281/zenodo. 20999427