AIC Chains

Open alternating inference chains (AICs): exhaustive alternatives joined as strong-inference nodes, with consecutive nodes connected by weak inferences. This group covers same-digit X-Chains and bivalue-cell XY-Chains.

Skyscraper

A two-node X-Chain with parallel row or column strong inferences.

A row and a column strong link of one digit connected through a Sudoku box

2-String Kite

A two-node X-Chain with row and column strong inferences joined through a box.

Two strong-inference nodes of one digit joined by a weak inference in a Sudoku grid

Two-Node X-Chain (Empty Rectangle - minimal)

The general same-digit signature (A=B)-(C=D).

Empty Rectangle

A two-node X-Chain with an empty-rectangle (ERI) grouped strong link.

Three strong-inference nodes of one digit joined by weak inferences in a Sudoku grid

Three-Node X-Chain

The general L(1)-Wing signature (A=B)-(C=D)-(E=F).

Three strong-inference nodes of one digit with a grouped side in a Sudoku grid

Grouped Three-Node X-Chain

The general L(1)-Wing with one or more grouped sides.

An X-Chain of one digit in a Sudoku grid

Four+ Node X-Chain

An open single-digit alternating inference chain (AIC) of four or more strong-inference nodes.

XY-Chain

An open alternating inference chain through bivalue cells.

How an alternating inference chain proves an elimination

Write an open AIC as (A=B)-(C=D)-...-(Y=Z). Each equals sign is a strong inference between exhaustive alternatives: if one side is false, the other is true. Each dash is a weak inference: its connected sides cannot both be true. Alternating these relations proves the inclusive endpoint disjunction A OR Z; it does not choose one unique internal assignment.

A target can be removed only when it conflicts with every candidate represented by both endpoints. Grouped sides are disjunctions and require universal incompatibility at each weak inference. Skyscraper and 2-String Kite restrict the house signature of a two-node X-Chain; the length-3 same-digit chains are L(1)-Wings with signature (A=B)-(C=D)-(E=F), including parallel-line, alternating row-column and grouped forms. These are variants of one construct, not separate named techniques. ERi-based subclasses such as Dual Empty Rectangle, Rec't Kite and Bridged Empty Rectangle require their specific link signatures. XY-Chains use bivalue-cell nodes, while XY-Wing's equivalent AIC reading is taught in the ALS-XZ Wings group.

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