ammoniaAnglePrediction
plain-language theorem explainer
ammoniaAnglePrediction supplies a numerical estimate for the NH3 bond angle by subtracting 2.5 degrees from the tetrahedral value. Chemists modeling geometries inside Recognition Science would cite this for lone-pair adjusted predictions consistent with the module's table. The definition is a direct arithmetic adjustment anchored in tetrahedralAngleDegrees.
Claim. The predicted bond angle for ammonia equals the tetrahedral angle in degrees minus 2.5, where the tetrahedral angle satisfies cos(θ) = -1/3.
background
The module derives bond angles from minimizing J-cost for n equivalent bonds around a central atom on the φ-lattice. For n bonds the optimal angle satisfies cos(θ) = -1/(n-1). Tetrahedral geometry (n=4) therefore yields cos(θ) = -1/3 and θ ≈ 109.47° via arccos(-1/3) converted to degrees. Ammonia (NH3) sits between water and methane because one lone pair reduces the angle from the pure tetrahedral case. The local setting is the φ-lattice derivation of geometry that also links the tetrahedral angle to the dodecahedron edge-center angle.
proof idea
One-line definition that subtracts the constant 2.5 from tetrahedralAngleDegrees.
why it matters
This definition completes the bond-angle prediction table for the ammonia case inside the φ-lattice framework. It directly implements the RS mechanism of J-cost minimization for n=4 bonds with a lone-pair correction, consistent with the observed 107° value listed in the module doc-comment. No downstream theorems yet reference it, leaving it as a leaf prediction that supports empirical falsification checks against the cosine formula and the CH4 > NH3 > H2O trend.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.