Simple coloring
Conjugate links followed in two colors; a contradiction removes one color
How to use it
When a symbol has exactly two homes in a unit, exactly one of them is true: a conjugate pair. Chain conjugate pairs that share a cell into a graph and two-color it — each color class is an all-or-nothing scenario for the symbol. Two rules close deductions: if two same-colored cells see each other, that color is entirely false (both cannot hold the symbol) and the other color is true; if a candidate cell sees both colors, it cannot hold the symbol at all, whichever scenario holds.
Color one stubborn symbol at a time, on one layer at a time. Chains of four to six cells are the useful ones: long enough to reach eliminations, short enough to verify by eye.
Why it is sound
A conjugate pair (exactly two homes for a symbol in a unit) is a strong link: exactly one home is true. Chaining links partitions the visited cells into two color classes, exactly one of which is the true scenario. Two same-colored cells seeing each other would both hold the symbol — impossible — so that color is false and every cell of the other color holds the symbol. A candidate seeing cells of both colors is excluded by one or the other in either scenario. Both rules discard only impossible configurations.
A worked example
Color the digit 2. In row 1 it fits exactly two cells (r1c4, r1c5) — one of them is true; row 4 likewise (r4c4, r4c5); and column 4 chains the rows together (r1c4, r4c4). Following the links two-colors the four cells: r1c5 and r4c4 share one color, r1c4 and r4c5 the other. Cell r5c4 looks up column 4 onto r1c4 and r4c4 — one cell of each color — so whichever color is true, digit 2 cannot survive there; it dies at r5c4.