Four+ Node X-Chain

A Four+ Node X-Chain is an open same-digit AIC with four or more strong-inference nodes — the general member of the X-Chain family beyond the two- and three-node forms. Write its alternating signature as (A=B)-(C=D)-...-(Y=Z): equals signs are strong inferences and dashes are weak inferences. The chain proves the inclusive endpoint relation A OR Z without assuming either endpoint first.

What is an X-Chain?

Every node concerns one digit and is a strong link (XOR) joining exhaustive alternatives: if one side is false, the other is true. Every edge is a weak inference (NAND): its connected sides cannot both be true. The chain may use singleton or properly justified grouped sides. Historical forcing-chain and Nice Loop descriptions are alternate frameworks, not the AIC proof taught here.

How to spot it

For one digit, list the strong-inference nodes and connect consecutive nodes only through independently valid weak inferences. Verify grouped edges against every represented candidate. The two unconnected outer sides are the endpoints; a target must conflict with every candidate represented by both.

The logic

If the first endpoint A is false, each strong link propagates false to true and each weak inference propagates true to false until the far endpoint Z is true. Therefore A OR Z holds, possibly with both endpoints true. A same-digit candidate conflicting with both endpoints can be removed; when the endpoints are distinct, this is the Type 1 same-digit elimination. An open chain does not select one unique internal assignment.