Block-Wise Construction of Trimagic Squares with Trimagic Blocks of Orders 12 and 24 (20736)

Ordinary compounds of retained normal trimagic seeds produce large normal trimagic squares with translated trimagic blocks and distinct block constants. We give a complete moment proof, establish associativity in the explicit coordinate convention, and specialize the block constants to orders twelve and twenty-four. The recorded inventory comprises fourteen construction records, including seeds, auxiliary complementary products and final compounds through complete order 20736. The principal order-twelve block family is separated from order-twenty-four branches whose aligned order-twelve pieces fail magicity. Two auxiliary trimagic arrays explain the complete orders 10368 and 17280. A newly reconstructed order-144 example verifies the displayed order-twelve seed and compound rule, while the larger computational results are attributed to their retained records. Text and Excel files of complete work are attahced.