Realizable, not derivable: selection and obstruction for Coxeter-graded mass textures in finite real spectral triples

In the noncommutative-geometry derivation of the Standard Model, the fermion mass matrices are the free entries of the finite Dirac operator: the axioms constrain their form, not their values. Whether additional structure can fix the entries, rather than relate them, is the derivability question. This paper gives a complete derivability map for one unusually well-credentialed object: a two-base regularity \(m_f=K\,p^{D_f}q^{Q_f}\) of the nine charged-fermion masses, carrying three exact structural identities, and graded by the sixteen spinor weights of the root system \(B_4\). We prove that (i) the Weyl group acts transitively on the weights with stabilizer \(S_4\), so species distinction has no Weyl-invariant carrier; (ii) the depth function is a chain length whose step heights are the nested dual Coxeter numbers of \(B_4\supset B_3\supset B_2\supset B_1\), so all relative depths follow from root data up to two affine constants; (iii) the order-zero classification contains no selection point, and no diagonal depth operator at all is phenomenologically viable; and (iv) a trace invariant closes every same-template extension of the lepton derivation to the quark sector (required trace \(5/2\) incompatible with \(-17\) and 19). The quark offsets are tabulated with uncertainty bands as a requirement specification for any future structure. The texture's epistemic status is thereby pinned to one cell of a three-place taxonomy: realizable, not derivable.