Pair coloring
Bilocal pair conjugate links: rectangle diagonals and mono-digit pivot chains eliminate letter/digit options
How to use it
Within transversal's Symbol tables pass, this is the first recognition to try — a static rectangle shape, no hypothesis needed.
Two rules on bilocal pairs. First, rectangles: a pair with exactly two homes in different rows and columns spans a rectangle; whichever corner takes the pair, the two diagonal corners lose both its letter and its digit (the pair's row and column are consumed either way). Second, chains: a cell that offers one letter a single digit option can link two bilocal pairs into a pivot chain that forces a placement.
Harvest bilocal pairs first — pairs with exactly two homes — then read the diagonals and try to connect pairs through shared mono-option cells. The rules use only pair uniqueness plus the Latin lines, so they apply anywhere on the grid.
Why it is sound
If a pair can only go in two cells forming a rectangle (different rows and columns), the diagonal cells cannot have that pair's letter or digit: whichever corner holds the pair, both the row and the column of each diagonal are covered. Additionally, a mono-digit pivot chain forces a placement when a cell with a single digit option for a letter links two bilocal pairs. Both rules use only the orthogonality structure (pair uniqueness + Latin rows/columns) and are sound in every solution.