Two Limits of the Same Surface: Behavioural Correspondences Between Nucleon and Black Hole Closures in PDL

Sequel to D64. Document D64 established a structural correspondence between the proton's surface degeneracy theorem (D50) and the soft-hair programme of Hawking, Perry and Strominger, and reported that a naive nucleon-counting extrapolation fails the Bekenstein–Hawking value by 36.7 orders of magnitude, independently of black hole mass. This document asks a narrower question: independently of that gap, does PDL predict shared behaviours between its two most extreme closures — the isolated proton and the macroscopic black hole horizon? Five such behaviours are established or developed: (1) a topological necessity, verified by three independent methods including exact discrete Gauss–Bonnet computation and direct holonomy calculation in arbitrary precision, forcing exactly two coherence defects on any closed spherical PDL surface — a structural account of why no black hole has ever been observed with zero spin, related to but distinct from the Kerr/CFT correspondence of Guica, Hartman, Song and Strominger; (2) an exact curvature-migration law near extremality with asymptotic exponent 1, establishing an open tension with the third law of black hole thermodynamics; (3) a nucleon dissolution threshold, derived from the pre-existing saturation theorem Z_sat=20, giving a critical mass M*≈4.3 solar masses coinciding with the observed compact-object mass gap; (4) seven independently tested and excluded candidate mechanisms, each with a precisely stated structural cause; (5) a behaviour-versus-magnitude methodological principle organising all of the above. Three new open problems are introduced.