Computational Verification Data for the OMARWA Sequence: Period Tables, Digital Root Maps, and GCD Matrices

Computational verification data for the OMARWA sequence T_k = 6*2^k + 1 (OEIS A004119). Includes: period tables P(m) for m=1..1000, digital root maps DR(T_k) for k=0..100, GCD matrices up to 50x50, fractal period verification for prime powers, palindrome structure verification, Lucas number bridges, Grand Synthesis v25 data, and super-period/product theorem verification. All data generated by reproducible Python scripts.

本数据集为OMARWA序列T_k = 6×2^k + 1（在线整数序列百科，英文全称为Online Encyclopedia of Integer Sequences，缩写OEIS，编号A004119）的计算验证数据集。涵盖如下内容：当m取1至1000的整数时的周期表P(m)、当k取0至100的整数时的数字根映射DR(T_k)、最大尺寸为50×50的最大公约数（GCD, Greatest Common Divisor）矩阵、针对素数幂的分形周期验证、回文结构验证、卢卡斯数桥接项、Grand Synthesis v25数据集，以及超周期/乘积定理验证。所有数据均通过可复现的Python脚本生成。