Collatz Conjecture 2026.1.10

This dataset presents the raw structural evidence supporting a modular reduction framework for the Collatz mapping. It documents a reproducible analysis of iterative behavior through modular classification, transition rules, and numerical verification, with emphasis on structural closure and existential convergence. The Excel file consists of four sections: 1. Mod 8 classification of even numbers, including transition rules between even-number sequences and the predicted structural form of maximum values. 2. Structural expression of numbers N ≡ 6 (mod 8) as a*2^n - 2 (with a odd), accompanied by numerical verification of the parameters a and n. 3. Convergence behavior of a*2^n - 2 under Collatz operations, with classification of resulting maximum values into 8m + k sequences. 4. Downward transition from N = 2(a*3^n - 1) to even numbers ≤ N/4, demonstrating the structural closure of the mapping and its reduction to predictable modular forms. This record serves as both a mathematical and philosophical documentation of Collatz-type structures, preserving the modular behavior, transition patterns, and structural invariants that underlie the dynamics of the mapping.