Section 2: Reduced Gröbner Basis and Radicality

Section 2 upgrades the Section 1 result: the quadratic generators form a reduced Gröbner basis. Since the leading monomials are then squarefree, $J_G$ is a radical ideal.

Theorem map

Paper result	Lean declaration(s)	Lean file
Theorem 2.1	theorem_2_1, theorem_2_1_reduced, theorem_2_1_isReducedGroebnerBasis	GroebnerBasisSPolynomial.lean, GroebnerBasis.lean
Corollary 2.2	corollary_2_2	Radical.lean

Theorem 2.1 is packaged as three Lean declarations: theorem_2_1 for the Gröbner-basis property, theorem_2_1_reduced for reducedness, and theorem_2_1_isReducedGroebnerBasis as the paper-facing wrapper.