The shared stage of Theorem 30 with batched band arrays, in every program beginning with base58B

For every $R$ and standard limits, the program base58B ++ R meets SharedSpecB lim (base58B ++ R) cShared30: the shared stage (procedure pSharedP) of the data structure of Theorem 30 with pruned encodings, run on a source $X\in\mathbb Z^{K_0N\times D}$ at aX and the transpose of $Y\in\mathbb Z^{D\times K_0N}$ at aY, returns within cShared30 * sharedShapeP p steps and leaves the shared data (tables, encodings of every band of the batched input arrays bArrayL, bArrayR) in place (SharedReadyA).

base58B is base58P (the 58 procedures of Theorem 30 with pruned encodings) with the body bandArrayBBody at the number of bandArray.

The batched layout (Batch/Tiling): the source of the left side is a $K_0N\times D$ matrix $X$ (row by row), that of the right side a $D\times K_0N$ matrix $Y$ (stored transposed); the slot $(g,h)$ of the band $\beta$ holds the row block number $(\beta K_0+g)K_0+h$ of the source, so one run of Theorem 30's data structure computes $K_0^2$ independent block products.