Decide how a fan whose vertex lies on a folded edge closes around it #133

Follow-up to #52, #119, ADR 0040, ADR 0041 and ADR 0043.

#52 decided that flatten, reverse and squash are one operation in the kernel. #119 defined the reverse fold as a fan in the spec, but the kernel folds it by its opening and two blocks (ADR 0043), outside the flatten path. Moving it onto that path runs into a question the records leave open.

The vertex of a reverse fold lies where its axis meets the spine, on a folded edge. By ADR 0040 a fan sits at a table point and closes its motions around it (Kawasaki's condition in def-flatten); by ADR 0041 the condition drops when the vertex lies on the paper's edge, off the paper or at infinity. A vertex on a folded edge is none of these. On the paper, Kawasaki's condition holds around the paper point of each layer. On the table, every layer of the tip lies on one side of the spine's line, and the rays of a reverse fold satisfy the condition only when the axis is perpendicular to the spine.

To decide

• Where the closure condition of a fan is checked: around each layer's paper point, around the table point, or not at all for a vertex on a folded edge.
• What the sectors of a fan are at such a vertex: wedges around the table point, or the regions between the axis and the spine's line on each side.
• Whether the letters of a fan are one per ray, as flatten takes them today, or one per hinge, since the new crease of a reverse fold takes different letters in different layers.

The answer belongs in an ADR, since it changes def-flatten. The kernel work that follows, in steps that keep every output: the vertex and the sectors generalised with flatten unchanged; letters per hinge and the blocks of an opening as the units of the stacking; reverse routed through that path.