A Template-, Block-, and Coordinate-Based Framework for Constructing Magic Squares with Prescribed Line Sums

This public preprint documents a template-, block-, and coordinate-based framework for constructing, transforming, validating, and hierarchically combining magic squares with prescribed line sums. The method was developed independently by Mohammad Hossein Amir Mostofian over several decades. It combines positional templates, order-sized value blocks, quotient-and-remainder transformations, conditional manual repair, hierarchical composite construction, and large-order block decomposition. The note distinguishes established mathematical ingredients from the author's personal systematization and identifies open questions concerning composite structural preservation and distributed construction of very large squares.