We retire three prior justifications for the auxetic brane Poisson ratio ν = −1 (a G₂ generator count, a 'z=6 → isostatic' claim, and a 'only ν=−1 gives Newton' claim), each shown to fail by direct verification, and replace them with a derivation. Given the genus-3 Klein-quartic brane (already postulated for the Standard-Model pants decomposition), three verified steps follow: (i) the G₂/Fano symmetry forces 2-D elastic isotropy; (ii) topological closure on a negative-curvature genus-3 surface forbids the flat z=6 lattice (the dense Fano truss = K₇ triangulates only the torus) and admits the z=4 kagome (medial of 7, 3) ; (iii) the z=4 isostatic conformal lattice gives ν = −1 exactly, for all twist angles. Thus ν = −1 is a theorem contingent on one independently-motivated postulate. The consequence K=0 predicts a dark sector with exactly zero bulk sound speed, distinguishing it from quintessence. Stated honestly: one postulate doing double duty (Standard-Model sector + auxetic mechanics), not 'zero free parameters. ' Eleven verification scripts (consolidated, 11/11 PASS) accompany the manuscript.
Bharathi Jagadeesan (Sat,) studied this question.