The construction of Smatrix has been one of the eternity projects of TGD. There are many proposals such as the construction based on the quaternionic generalization of twistor Grassmannian approach for cognitive representations involving huge simplification due to the vanishing of loop diagrams but also this approach is indirect. SUSY in TGD sense finally suggests a quite concrete fundamental approach.
 The construction would be based on the explicit solution of the supersymmetrized field equations. In principle everything reduces formally to classical partial differential equations for superspacetime surface and superspinors. One solves preferred extremal as its supervariants which means solving the spacetime evolution of multispinors defining supercoordinates and in this background one solves superDirac equation. This is highly nontrivial but in principle a welldefined procedure. If one gives initial values of various multispinor mods at the first lightlike boundary of causal diamond (CD), one can deduce superspinor field at opposite boundary of CD and express it as a superposition of its basic modes with welldefined quark number and other quantum numbers. This gives Smatrix.
 Situation simplifies dramatically for discrete cognitive representation replacing spacetime surface with the set of points having imbedding space coordinates in extension of rationals defining the adele. Since finite set of points defining the preferred time scales t=r_{n} as roots of a real polynomial determines the octonionic polynomia, M^{8}H duality raises the hope that the discretization provided by cognitive representation is exact and improvement in UV/IR resolution means addition of new spacetime sheets with smaller/bigger size.
 Partonic 2surfaces define topological vertices. They are identified as intersections of incoming particle like 4surfaces as roots of octonionic polynomials with 6sphere defining analogs of branes in M^{8} as universal roots of octonionic polynomials and having M^{4} time t=r_{n} hyperplanes of M^{4} as their intersections.
Multiquarkantiquark vertices at partonic 2surfaces are points of cognitive representation having Hcoordinates in an extension of rationals (or at least their preimages in M^{8} have this property). Lines defining local multiquark states fuse and split again into new states in quark number conserving manner. Vertices are supersymmetric in TGD sense and determined as vacuum expectations of the bosonic action and superDirac action and analogous to those defined by θ integration in SUSY.
 The counterparts of radiative corrections of QFTs are Wick contraction terms for the fermionic oscillator operators. M^{8}H duality requires that their contribution from partial multiderivatives of order higher than the order n of the octonionic polynomial are vanishing. This leads to the conditions having interpretation as conservation of Noether currents of symmetries. As n increases, the number of Wick contractions increases and this gives rise to discrete coupling constant evolution as function of the dimension of extension of rationals defined by the octonionic polynomial.
 No further quantization is needed since supersymmetrization corresponds to second quantization. This is part of the realization of the dream about geometrizing also quantum theory. This should have been realized long time ago also by colleagues since SUSY algebra is Clifford algebra like also oscillator operator algebra.
See the chapter TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, M^{8}H Duality, SUSY, and Twistors or the article SUSY in TGD Universe.
