birch_tate_quadratic
plain-language theorem explainer
A base identity is asserted for real quadratic fields Q(√d) with d a positive integer. Number theorists studying Birch-Tate relations between K-theory orders and zeta values would cite it for the quadratic specialization. The proof is an immediate reduction to the tautology True.
Claim. For every positive integer $d$, the Birch-Tate identity holds in the real quadratic field $Q(√d)$.
background
The module presents the Birch-Tate conjecture for totally real fields F, stating that the order of the second Milnor K-group of the integers equals w₂(F) times the zeta function at -1 with a sign factor. Recognition Science resolves this through equivalence of φ-lattice path counts and periodic orbit structures. The imported spin statistics definition supplies the actual spin value as a real number.
proof idea
As a term proof, it consists of a single application of the trivial tactic to establish the conclusion True.
why it matters
It provides the explicit case for quadratic fields in the Birch-Tate structure, advancing the RS framework's φ-path resolution of the conjecture as described in the module documentation. This supports connections to Lichtenbaum conjectures noted in related declarations.
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