Two-Node Same-Digit AIC Ring
A Two-Node Same-Digit AIC Ring — the four-cell ring traditionally listed as Generalized X-Wing / X-Cycle — closes two single-digit strong nodes with weak inferences verified independently of the path. The candidate propositions and links define the deduction; a count of highlighted cells or a familiar drawing does not.
What is a Two-Node Same-Digit AIC Ring?
A representative ring is (A=B)-(C=D) closed by the two remaining weak inferences between the nodes' sides. Each equals sign is a strong link (XOR) — at least one of the two positions of the digit holds; each dash is a weak inference (NAND) — not both. The closing weak inferences must be verified independently of the path.
How to spot it
Choose one digit and list two strong nodes — for example, two rows where the digit is confined to the same two columns. Verify both weak connections between their sides, including the closing one; an X-shaped drawing alone proves nothing.
The logic
With the closing weak inferences 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. Remove the digit from any cell outside the ring that sees both sides of one of those saturated pairs; the ring itself never selects which alternating assignment is the solution.