Complete Dual Geometric Methodology: Source Code and Data Repository

This paper introduces the "Complete Dual Geometric Methodology," a topological framework to deconstruct complex scientific problems. It proposes a rigorous "Methodological Operating System" employing mechanisms like "synchronous alternation" to transform contradictions into stable outputs. This updated version introduces a rigorous 'Five-Fold Classification' of integers based on dual pairs (n, 1/n) and multiplicative order d = ord_n(10), proving that prime numbers are pure, indecomposable nuclei within a heptanuclear structure, governed by the Law of Nine and resonant with the golden ratio. The package includes a fully verifiable Python library (dual_methodology) and a master verification script (verify_all.py) that allows peer reviewers to independently reproduce the geometric proofs, 800-digit precision matrices, and extreme stress-testing protocols (10^±1000 asymptotic boundaries and stochastic perturbations) directly from the repository.