Congruence and metaplectic covariance: rational biquadratic reciprocity and quantum entanglement

Abstract

The purpose of the paper is to elucidate the cyclotomographic applications of the coadjoint orbitmethodology to the Legendre-Hilbert-Artin symbolic tower of class field theory in the sense of the number field theories of Chevalley, Hasse, Weil and Witt. The Witt arithmetics concludes with the law of rational biquadratic reciprocityand quantum entanglement.Keywords: Third order principle of spinor triality, spaces of even and odd half-spinors, Hopf principal circle bundle,metaplectic Lie group Mp(2, R), the metaplectic coadjoint orbit model and spherical contact geometry, the first maximof the geometric quantization principle, half-spinor Maslov index, Witt quartic groups, cyclotomography, LegendreHilbert-Artin symbolic tower of class field theory, valuation and module function, adéles and idéles, differential idéles,rational quantum entanglement, pure spinor invariants of octonion geometry, magnetic resonance tomography andangiography, symplectic spectroscopy at molecular level.