Same-Digit AIC Ring
A Same-Digit AIC Ring — traditionally listed as Bidirectional X-Cycle — follows one digit through alternating strong and weak inferences and closes through a final weak inference 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 Same-Digit AIC Ring?
A representative ring is (A=B)-(C=D)-...-(Y=Z) closed by a weak inference from Z back to A. Each equals sign is a strong link (XOR) between two exhaustive positions of the digit; each dash is a weak inference (NAND) — not both. The closing weak inference must hold on its own; a drawing that closes geometrically proves nothing by itself.
How to spot it
Choose one digit, list its strong nodes — pairs of positions where the digit must occupy at least one — and connect consecutive nodes through weak inferences between occurrences that see each other. Then verify the closing weak inference from the last node back to the first.
The logic
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. Remove the digit from any cell that sees both sides of one of those saturated pairs; the ring itself never selects which alternating assignment is the solution.