Global Chord Compatibility, Recursive Unfolding, and the Extreme-Concentration Endpoint Selection Problem on a Single Complex Plane

Taking the usual complex plane, its original complex addition and multiplication, and its modulus as fixed data, we construct d_c(x,y) = |x-y|^c (0 < c <= 1) and its limit d_0 for fixed pairs of points on the same underlying set. We make explicit the construction relating the normal plane, the concentration-sparsity distance structure, and the extremely sparse plane, and examine whether the full family of chords, inside-outside inversion, and affine recursion can determine an extreme-concentration output. The main theorem gives a unified account: actual pullbacks have global normalization one; every positive-parameter unfolding layer admits a surjective isometry onto the corresponding original layer; the distance readouts for fixed pairs of points of the original plane converge to d_0; and, for fixed unfolding labels within the class of contracting scales, the convergent endpoints are exactly alpha*d_0, 0 <= alpha <= 1. Every such endpoint is realizable, so the stated compatibility conditions do not uniquely select the zero endpoint. We further distinguish the zero readout, retained chord relations, and the quotient by the zero pseudometric, and explain the correspondence between this unfolding and the deformation to the normal cone of a point embedding. No concentration rule is added; established properties of the zero layer, classifications under additional assumptions, and unresolved questions about representing relations are identified separately. This is the complete English manuscript, version 0.2. The release includes the PDF and LaTeX source.