birch_tate_from_ledger
plain-language theorem explainer
The definition sets the Birch-Tate ledger proposition equal to the BSD ledger placeholder. Researchers tracing RS links between K-theory orders and zeta values at negative integers would cite this alias when building chains from phi-lattice counting. It is realized as a direct one-line assignment to the upstream placeholder.
Claim. The Birch-Tate conjecture statement is defined to coincide with the BSD ledger statement, which asserts the irrationality of the golden ratio $phi$.
background
The module MC-006 treats the Birch-Tate conjecture for a totally real number field F: the order of K₂(O_F) equals w₂(F) times ζ_F(-1) times (-1) raised to the degree over Q. RS resolves the relation by counting φ-lattice paths for the K-group side and φ-periodic orbits for the zeta side. The upstream bsd_from_ledger is described as a 'Structural placeholder for RS route connecting rank and L-value vanishing order' and is defined as the irrationality of phi.
proof idea
The declaration is a one-line definition that aliases birch_tate_from_ledger directly to bsd_from_ledger.
why it matters
This definition supplies the base for the theorems birch_tate_implies_bsd and birch_tate_structure_chain. It advances the RS resolution for the Birch-Tate conjecture via φ-path equivalence as stated in MC-006. It touches the open general case for non-abelian extensions.
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