AIC Rings

Closed alternating inference chains: same-digit, bivalue, and mixed rings whose closing weak inference is verified independently of the path.

Two-Node Same-Digit AIC Ring

A four-cell single-digit AIC ring — the X-Wing loop — with a verified closing weak inference.

Three strong links of one digit closing into a ring in a Sudoku grid

Three-Node Same-Digit AIC Ring

Three single-digit strong nodes with a verified continuous-ring closure.

Three strong nodes of one digit, one grouped, closing into a ring in a Sudoku grid

Grouped Three-Node Same-Digit AIC Ring

Three strong nodes, including a grouped proposition, with a verified continuous-ring closure.

Same-Digit AIC Ring

A single-digit AIC ring whose alternating strong and weak links close into a continuous loop.

Bivalue AIC Ring

A ring whose strong inferences all run through bivalue cells, closed by a verified weak link.

Mixed AIC Ring

An AIC ring mixing bilocal and bivalue strong links, closed by a verified weak link.

Closed chains: when the last link bites the first

An AIC ring is an alternating inference chain whose ends connect: the closing weak inference between the last and first strong nodes is verified independently of the path itself. Because the loop has no free end, the endpoint theorem supplies the missing strong inference between the closing pair, every weak edge gains a complementary strong inference, and candidates that see both sides of a weak edge can be removed.

The guides here cover same-digit rings — from the four-cell X-Wing loop up through longer L(1)-Ring structures — plus bivalue and mixed rings built from cell and grouped strong nodes. Every ring on these pages is validated by the same rule: the closing weak link must exist independently of the path it closes.

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