Use an eight-state profile dynamic program, where a mask records cells already
occupied from the preceding column.  Enumerating vertical placements within a
column and horizontal dominoes crossing its right boundary gives the submitted
transition matrix.  A missing top-left cell is therefore initial mask 001.

Rather than assuming an unproved period, binary exponentiation computes the
2021st matrix power modulo 19.  The certificate records the accumulator before
and after every set bit of 2021, namely bits 0, 2, 5, 6, 7, 8, 9, and 10.  The
empty outgoing profile has coefficient 1, so the requested remainder is 1,
not 4.  The proposed decomposition is invalid because its listed families do
not partition every legal tiling; the exact profile transition includes the
missing interactions automatically.
