Three-Node Same-Digit AIC Ring
(3 Strong Links) X-Loop uses three single-digit strong-link nodes connected by valid weak inferences. The candidate propositions and links define the deduction; a count of highlighted cells or a familiar drawing does not.
What is a Three-Node Same-Digit AIC Ring?
A representative ring is (A=B)-(C=D)-(E=F) closed by a weak inference from the final side back to the first. Each equals sign marks a strong link (XOR) between two exhaustive positions of the digit, and each dash a weak inference (NAND) — not both. The closing weak inference must be verified independently of the path to form a continuous ring.
How to spot it
Choose one digit, list three strong nodes — each a strong link (XOR) between two positions of the digit — and verify both weak connections. Then verify the closing weak inference; geometric closure is insufficient.
The logic
If A is false, the strong link makes B true, the weak edge makes C false, and the propagation continues: D true, E false, F true. With the closing weak inference verified, the endpoint theorem supplies the missing strong inference between the closing pair, so every weak edge around the ring gains a complementary strong inference — eliminate the digit from any cell that sees both sides of one of those saturated pairs.