While I am intrigued that your two squares approach works as well as it does, I fear you may find yourself unable to complete it so that it is both useful and correct. It may be that it proves helpful in spite of that, though I think that is not yet clear. To some extent, I suppose it works because a ‘square’ is a ‘played out’ eye; in that sense it may be less original than it looks.

As things stand, it is a little unclear what your full definition is, so it is hard for us to provide counterexamples. There are various problems:

• Rather than stating your complete definition in one go, you first say one must have two squares, then add rules in a later section to say that:
  • omitting multiple corner stones is allowed, and
  • squares may go off the board.
• I have trouble making sense of:
  • My idea is to view living shape as a graph with edges and vertices instead of individual stones. A square is an edge, and connections between them are the vertices. A frequent appearing living graph has two edges (squares) with one vertex between them (one connection).
  • I get the idea that you mean to say that you consider a graph derived from the position by drawing a vertex for every square (as shewn in the previous section) and edges between vertices whose squares are connected, but in that case you have confused vertex and edge!
  • In practice, you do not actually refer to graphs again, so this formulation introduces redundant concepts and makes your approach harder to follow. If still you want to mention the graph, it might be better to observe after the basic definition that one can draw such a graph.
• You should also state explicitly (if it is what you mean) that by a living shape you mean one that has been ‘played out’, in the sense that there are no threats left and so no legal sequence of moves can capture it.

You also say that your 2x2 example is conceptually a two-headed dragon, but since you have not defined what you mean by that, this statement is unhelpful.

I also observe that several links to your page have been added, but I think this is premature until there is more consensus on how useful your approach is. I think that provisionally it is fair to link from very specific and theoretical pages; I am just not quite sure which.

To remove confusion, please move the chapter "Old section below" to a subpage.

To remove confusion, please move the chapter "Seki" to a subpage or clarify that it does not belong to the chapter "Old section below".

To remove confusion, please move the chapter "Applications" to a subpage or clarify that it does not belong to the chapter "Old section below".

In the case of the chapter "Seki" not belonging to the chapter "Old section below", please remove contradiction to your statement "Life is not dynamic." by deleting all diagrams showing move sequences or by deleting your statement.

In the case of the chapter "Applications" not belonging to the chapter "Old section below", please remove contradiction to your statement "Life is not dynamic." by deleting all diagrams showing move sequences or by deleting your statement.

Please clarify whether the draft of the method Two Squares applies to either a) each go position or b) each settled go position.

Please complete "two squares each with two connections to each other" as "two squares each with at least two connections to each other" (because examples with three or four connections are known on rectangular boards).

Without all these clarifications, the intention of the draft of the method Two Squares is ambiguous and unclear.