Bivalue AIC Ring
A Bivalue AIC Ring — traditionally listed as Bidirectional Y-Cycle — is a closed AIC whose strong links all run through bivalue cells: each node is the pair of digits of one cell, joined to the next by weak inferences, with a final weak inference closing the loop. The candidate propositions and links define the deduction; a count of highlighted cells or a familiar drawing does not.
What is a Bivalue AIC Ring?
Each bivalue node is a strong link (XOR): its two digits cannot both be true and cannot both be false. A weak inference (NAND) from one node to the next is valid when the digit leaving the first cell conflicts with the digit entering the second — for example, two occurrences of the same digit in peer cells.
How to spot it
List the bivalue cells, choose for each node which digit exits and which enters, and verify every weak connection against the current candidate state — including the closing weak inference from the last node back to the first. Geometric closure alone proves nothing.
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 candidates that conflict with both sides of any weak edge; the ring itself never selects which alternating assignment is the solution.