A short note on the Euclidean transport of multiplicative products under base change. It defines the quotient–remainder array Ad (n, q, r), proves a rank-independent transport map for fixed products, and decomposes the array at level n+1 into inherited interior mass and new boundary mass. The note extends the Euclidean decomposition framework and generalizes the transport viewpoint previously developed for the multiplication table. Version 2. This version corrects the transport formula in Proposition 1 and Corollary 1 for arbitrary multiplicative rank; the congruence R ≡ r−q (mod n+1) remains unchanged. Version 3. This version completes the transport picture by adding the reverse Euclidean re-expression for a fixed integer.
Frédéric D. W. Heidenthal-König (Sun,) studied this question.