Metric stability and Jacobi-Gauss periods

A spinor definition of matter is extended to simplest cycles in interval [0,1] and to permutations of quartic-cubic roots in elliptic curves. Minkowski spacetime and Mandelstam plane are linked with wave vectors due to rotation on real interval. Metrical geometry is discussed by rational triangles which are connected with modular invariants. An adiabatic solution in terms of cyclotomic units for constant elliptic invariants is derived and extended to iterated invariants. The pseudo-congruences allow to formulate coupling constants. Iterated invariants connect a scale factor with diagram expansions in different eras in bifurcating k-components.