tetra_bias
plain-language theorem explainer
The tetra_bias definition supplies a dimensionless proxy for tetrahedral preference as one minus the reciprocal of the golden ratio. Chemists deriving bond angles from the phi-lattice would cite this quantity when quantifying deviation from linear bond arrangements. The definition is a direct arithmetic expression on the phi constant from the CPM bundle.
Claim. Let $phi$ denote the golden ratio from the CPM constants bundle. The tetrahedral bias proxy is the real number $1 - 1/phi$.
background
The Bond Angles from phi-Lattice module derives molecular geometries by minimizing J-cost for n equivalent bonds around a central atom. The general rule gives cos(theta) = -1/(n-1), so tetrahedral geometry (n=4) yields cos(theta) = -1/3 and theta approx 109.47 degrees. The bias proxy 1 - 1/phi captures deviation from linearity and links the angle to dodecahedral geometry through phi.
proof idea
This is a direct definition that evaluates the arithmetic expression 1 minus the reciprocal of phi. No lemmas or tactics are invoked; the value follows immediately from the constant supplied by the upstream Constants structure.
why it matters
The definition supplies the input to the angle_bias theorem that proves the proxy is strictly positive. It fills the phi-connection step in the tetrahedral angle derivation of the Chemistry.BondAngles module and connects to the forcing chain through the phi-ladder and J-cost minimization. The construction quantifies the tetrahedral preference that arises inside the Recognition Science account of chemistry.
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