tetrahedralAngleRadians
plain-language theorem explainer
The declaration supplies the tetrahedral bond angle in radians as arccos of negative one third. Researchers deriving molecular geometries from J-cost minimization in Recognition Science would reference this constant for fourfold coordination. The definition is a direct assignment invoking the arccos function on the constant -1/3.
Claim. The tetrahedral bond angle in radians is given by $θ = arccos(-1/3)$.
background
In the Bond Angles from φ-Lattice module the tetrahedral angle arises from minimizing J-cost for four equivalent bonds around a central atom. The J-cost is the functional appearing in the Recognition Composition Law that measures deviation from self-similarity. For n bonds the optimal cosine equals -1/(n-1); the n=4 case therefore yields cos(θ) = -1/3.
proof idea
The declaration is a direct definition that invokes the arccos function on the constant -1/3.
why it matters
This definition supplies the numerical value used by tetra_angle_bounds, tetra_cos_eq and tetrahedralAngleDegrees. It implements the tetrahedral case of the bond-angle formula presented in the module documentation for CH-014. The construction links J-cost minimization to observed molecular geometries and is consistent with the eight-tick octave and D=3.
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