2026/07/16 by Juan Bory-Reyes, Baruch Schneider, Diana Barseghyan Schneiderová +1 · 1 citation
#math.CV
We specialize the intrinsic right q-vector derivative on radial algebras to integral superdimension. The formal dimension is encoded by an independent coefficient Q, and formal radial superspace of superdimension M=m-2n is obtained by the coefficient specialization Q↦ qM. This gives a rigorous universal calculus and, on finite blocks containing at most m abstract vectors, a faithful coordinate realization on ℝm|2n. The localized exterior result is formulated as a Green decomposition by complementary projector images. Whenever the specialized finite determinant is nonzero, full left multiplication yields a determinant-localized right-monogenic Fischer decomposition. Beyond this base-change theory, we determine the exceptional one-vector calculus completely: for M=-2ℓ there is one additional singular monomial and one missing image monomial, whereas all other integral superdimensions give a surjective derivative with constants as its kernel. We then prove that the degree-zero Fischer operator is exactly diagonal on exterior blades, obtain its determinant explicitly, classify all support-resonance values in 0<q<1, and give an exact kernel-rank formula as a sum of support multiplicities. On a block with N auxiliary vectors, an even support rank p has pure multiplicity \binom Np on the support truncation. At an odd-support root, every lower odd factor is nonzero and any simultaneous lower resonance is unique, even, and characterized by one strictly monotone scalar equation. These results distinguish persistent nonpositive-even-superdimension defects from isolated support-dependent q-resonances. An appendix records that constant scalar projection of two independent orthogonal right q-vector derivatives does not descend to the Hermitian quotient.