"On the subject of 4131, I consider the preamble to have been inadequate and misjudged, and I am fortified in that belief by its inordinate length. Ten-Four is to be congratulated on an ambitious puzzle that was clearly enjoyed and appreciated by many, and, as always, ultimate responsibility for ensuring fair play rests with the editors, rather than the composer. I studied graph theory (exam score 85%) as a final year option on my way to my first in maths — sorry if this sounds arrogant, but my point is: — if someone with that background is unable to divine the intended meaning of the preamble’s instructions, what chance do non-mathematicians stand? "
That comment rather makes my point that this puzzle did not require any knowledge of maths to solve it. Having read some comments by "mathematicians" elsewhere about this puzzle, i had to smile at how people tied themselves in knots with mathematical theory and ended up missing the point. A little knowledge a dangerous thing perhaps?
Now that the solution is out i can say what I wanted to say earlier: namely that the one aspect of multi-dimensionality which was relevant to the puzzle was the idea that rows and columns were continuous in two dimensions. This fact, however, was already obvious from the cyclic method of entry of certain answers. So the lines had to be cyclic as well. It was merely applying the principle already stated in the preamble. I had never even heard of graph theory before, and i found the preamble perfectly adequate. A little knowledge of maths perhaps a dangerous thing?
I am not saying the solution was easy to arrive at, far from it, but no way was any recondite mathematical knowledge required. Just logic and common sense from the recesses of one's own brain, like all the best puzzles.