Empty Rectangle
An Empty Rectangle is a two-node same-digit AIC in which the second strong-inference node is a box's Empty Rectangle Intersection (ERI): every candidate for the digit inside the box lies on one row and one column, so the two arms act as a single grouped strong link. In strmckr's link typing the signature is type 0 (bilocal) joined to type 3 (ERI).
What is an Empty Rectangle?
Write the construction as (A=B)-(C=D). The first node is an ordinary bilocal strong link (XOR) for one digit in a row, column, or box. The second node is an ERI: all candidates for the digit inside one box sit in the intersection of a single row and a single column — a cross of two arms, where the corner cell may also hold the digit. One arm of the cross is weakly linked (NAND) to side B of the pair; the other arm is endpoint D. ERI is a grouped strong inference — a disjunction over box candidates — not a forcing-chain deduction, so it cannot be produced by on/off propagation over single candidates.
How to spot it
For one digit, look for a box whose remaining candidates all lie in one row and one column — the empty rectangle. Then find a bilocal pair for the same digit on the line that continues one arm beyond the box. If the pair's cell on that arm is false, the box must place the digit in the perpendicular arm. The digit can then be removed from the perpendicular line outside the box, in cells that also see the pair's far cell.
The logic
Let the bilocal pair be (A=B) and the ERI node (C=D), where C is the arm the pair's bridge cell sees and D is the other arm. If A is false, B is true; B eliminates every candidate in arm C, so the box forces the digit into arm D. Therefore A OR D is true. Any candidate on the far arm's line outside the box that also sees A can be removed — the Type 1 same-digit elimination with a type-3 ERI link. Larger ERI constructs (Dual ER, Bridged ER, n×ERI) embed the same link in longer chains and are outside this page's scope.