Concept

Liberty — where it appears

An empty point next to a group of stones, and the thing a group must keep at least one of. In NoGo it is what makes a move’s legality a fact about the whole board rather than about the squares a stone touches.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Thickness is not the variable; the wall's own groups are. The same strips split by whether the wall is all one colour. A wall of one colour is a single group with liberties on both sides and it never separates them, at any thickness. A wall of two colours is two groups breathing in opposite directions and it nearly always does.

How thick a wall has to be

A single stone between two empty stretches of a NoGo board couples them, and the obvious repair is a thicker wall. Over 590 walled strips a thicker wall does help — and splitting the same 590 by the colour of the stones shows that thickness was never the variable. A wall of four one colour couples the sides exactly as one stone does.

positions · Nogo

A criterion that does not lift. The NoGo separation criterion run on strips and on three-row boards. On strips it holds on nine boards and explains all nine independent ones. On 227 three-row boards it holds on none at all.

A wall that bends

On a NoGo strip, two empty stretches add when no group breathes into both — a wall of two stones of different colours does it, and the criterion explains nine of ninety-three boards and all nine that it covers. On a three-row board it explains none of 227, and not because it is less accurate. A wall across a board has to bend, a stone at the bend sees empty squares on both sides by itself, and every one of the 227 has a group breathing into both regions. The condition is unsatisfiable.

positions · Nogo

Named alongside it

The objects these essays reach for when they reach for this one.

Counterexample Criterion Decomposition Enumeration Go Group Independence Nogo Region Board Canonical form Disjunctive sum

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