A General Logic for Sudoku

Rank 1 Double Loops with Rank 0 Branches

Points. Triplets affect the rank along the entire region belonging to its minor branch.

Rank 1 Double Loop with Rank 0 Branch

This rank 1 double loop is formed from a bifurcation at 5r7c6 and a linkset triplet at 1r5c8. The triplet lowers the rank along its minor branch to rank 0 eliminating candidate 8r7c5. All linksets that are rank 0 are highlighted in black. The rank 0 region ends at bifurcation 5r7c6 because it has two independent return paths to the triplet's 2 linksets.

Rank 1 Double Loop with Rank 0 Branch Loop

The second example is also a rank 1 double loop with a linkset triplet at 1r2c9. The triplet's minor branch travels through 4 sets and 4 linksets (highlighted black) until it reaches 1r1c5. The triplet lowers the rank along the entire path to rank 0. However, the (red) candidate in box 3 is not in this path but is eliminated by the overlap of two linksets, box set b31 and row set r21. The rank 0 path is just a nice example of a long minor branch.