Three-Node X-Chain
A Three-Node X-Chain — traditionally listed as 3 Strong Links and called an L(1)-Wing in strmckr's signature system — is the general length-3 same-digit AIC. Its signature is (A=B)-(C=D)-(E=F): three strong-inference nodes joined by two weak inferences. The chain proves the inclusive endpoint relation A OR F.
What is a Three-Node X-Chain?
Write the construction as (A=B)-(C=D)-(E=F). Each equals sign is a strong link (XOR) between exhaustive alternatives; each dash is a weak inference (NAND) whose connected sides cannot both be true. All length-3 same-digit chains of link types 0–3 are L(1)-Wings: parallel-line, alternating row-column and grouped forms belong to the same class. Named subclasses such as Dual Empty Rectangle, Rec't Kite and Bridged Empty Rectangle require specific ERi-link sequences; the house arrangement alone does not establish those names.
How to spot it
For one digit, identify three justified strong-inference nodes and verify the weak inferences B-C and D-E. The candidate propositions and relations define the chain; a familiar drawing does not. The outer sides A and F are the endpoints, and a target must see both.
The logic
If A is false, the alternating inferences make B true, C false, D true, E false, and F true. Therefore A OR F is true, possibly both. Any same-digit candidate seeing both endpoints can be removed. This is the Type 1 same-digit elimination; the theorem does not claim one unique internal assignment for the open chain.