Both supersymmetry and superstring theory can be replaced as viable candidates of most advanced physical theories by a topological theory of supercomposition. This theory can demonstrate that all three generations of quarks and leptons as well as all fundamental high-energy elementary particle bosons: gluons, photons, W-bosons, Z-bosons, gravitons, Higgs bosons, as well as magnetic monopoles are all composites of space-time charges of H-pluses and H-minuses representing the quantum vacuum fluctuations of squares of zero-point energies. These can simply be described by square symmetric singular (SSS) Hadamard matrices of any order. However, for the sake of theoretical simplification, the proof sequence will be limited to discussing second order matrices that can be found embedded within a defined sieve of Diophantus.

This mathematical sieve is an infinite size square matrix repeatedly spanning all the whole numbers except unity. It is the simplest mathematical sieve that can determine by a process of matrix element rationalization the locations of all prime numbers. Consequently, any 2 by 2 submatrix can be proved invertible and each inverse is the Abelian composition of given fundamental irreducible matrices and the 1/6-multiples of the second order SSS Hadamard matrices. This irreducibility does not allow the matrices to form a group under the binary operation of matrix multiplication since every possible determinant is zero. On the other hand, they form a group under the binary operation of Abelian matrix addition if and only if the zero matrix of second order is defined as the identity of matrix addition but not non-Abelian matrix subtraction. By matrix rationalization, it can be shown that the matrix product of an H-plus and an H-minus, in certain cases, is equivalent to the non-Abelian binary subtraction of H-pluses and H-minuses.