A Cubic Pure Half-Spinor Approach to High Performance Photon-Counting Computerized X-ray Tomography – Transcendence of the Brauer Mirror Symmetry Functor –

The goal of this paper is to present a spectral theory of advanced photon-counting computerized X-ray tomography, which is a promising microelectronical semiconductor wafer X-ray technique on the verge of becoming clinically feasible and has the potential to dramatically alter the clinical application of computer-aided medical diagnosis in the upcoming decades. In analogy to the deep fact that any real division algebra has dimension 1, 2, 4 or 8, the isogeneous third Galois cohomological, mirror symmetrical approach to high spatial resolution spectral photon-counting computerized tomography establishes that the exceptional Lie group \(\textrm{Spin}(8,\mathbb {R})\) $\text{Spin}(8,\mathbb{R})$ is the only one of the spin group spectrum \(\{\textrm{Spin}(n,\mathbb {R})\mid n \ge 1\}\) $\{\text{Spin}(n,\mathbb{R})\mid n\ge 1\}$ to admit a triality automorphism. It is the exceptional phenomenon of triality which is able to produce by the spin representation theory of the exceptional Lie group of octonions \(\mathbb {O}\) $\mathbb{O}$ the spectral shaped digital signals of spectral photon-counting computerized X-ray tomography. Similarly to spin echo magnetic resonance tomography, the mathematical approach to spectral high performance computerized tomography is based on the isogeneously invariant, projectively weighted, symplectic coadjoint orbit picture \(\mathfrak {Lie}(\mathcal {N})^*/\textrm{CoAd}(\mathcal {N})\) $\mathfrak{Lie}{(\mathcal{N})}^{\ast }/\text{CoAd}(\mathcal{N})$ of the real 3-dimensional Heisenberg unipotent Lie group \(\mathcal {N}\) $\mathcal{N}$ of type \(\textrm{GL}(3,\mathbb {R})\) $\text{GL}(3,\mathbb{R})$ , and its solvable diamond toric Lie group extension.