Dynamic Matrix Logic (DML): Version 2 — Extension to Geometric Sequences with Invariant Noise

This work is an official extension of Dynamic Matrix Logic (DML) Version 1. While the previous version explored the Fibonacci sequence, Version 2 focuses on Geometric Sequences (r=2). In this version, we report a major discovery: the emergence of a scale-invariant noise behavior, which we define as the Adya Constant (η). By identifying this constant (η = 4096/4095), DML achieves 100% computational precision in target reconstruction through divergent paths (DML-4 and DML-8). The results presented in this paper prove that what was previously perceived as dynamic noise in binary systems can be quantified as a fixed structural residue, providing a new framework for data integrity, cryptography, and geometric deconstruction.