Verification code and results for Idempotents and decomposition maps for localized group rings

Exact verification materials accompanying the manuscript Idempotents and decomposition maps for localized group rings by Chatchawan Panraksa. The archive contains Python standard-library programs, canonical outputs, reproduction instructions, computational and AI-assisted research methods, and SHA-256 checksums. The order-twelve program enumerates all 4096 elements of the modular group algebra, verifies the explicit primitive idempotent, radical and quotient matrices, and checks rational quaternion relations. It finds 52 idempotents in the whole algebra and 26 in the nontrivial component, including 24 primitive idempotents. The arithmetic program tests all 499 odd moduli from 3 through 999, finding 210 admissible moduli, and checks 18 exponents in the proved 3^r 5^s family. These are exact finite verification checks; the general mathematical statements are proved in the manuscript independently of program output. The programs were tested with Python 3.9.6 and 3.12.13.