Triple

Target entity: higher degree composition laws
Context triple: [Higher composition laws I–IV, relatesTo, higher degree composition laws]

• A. Higher composition laws I–IV chosen
  Higher composition laws I–IV is a landmark four-part series of papers by Manjul Bhargava that generalizes Gauss’s composition of binary quadratic forms and develops new structures and methods in algebraic number theory.
• B. cubic reciprocity law
  The cubic reciprocity law is a number-theoretic result that extends the quadratic reciprocity law to describe how prime numbers behave with respect to cubic residues in certain algebraic number fields.
• C. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• D. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• E. quartic reciprocity law
  The quartic reciprocity law is a number-theoretic result that extends quadratic reciprocity by characterizing when an integer is a fourth power residue modulo an odd prime, using properties of Gaussian integers and higher power residue symbols.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.