IndisputableMonolith.Chemistry.BondAngles
The BondAngles module defines dimensionless bias proxies and cosine formulas for preferred bond angles, with emphasis on tetrahedral geometry in the Recognition Science framework. Researchers constructing molecular models or φ-scaled geometric scaffolds would cite these definitions. The module consists solely of definitions and introduces no theorems or proofs.
claimThe module supplies a dimensionless bias proxy for tetrahedral preference along with explicit cosine formulas for standard molecular bond angles in linear, trigonal, tetrahedral, and octahedral geometries, plus the tetrahedral angle expressed in both radians and degrees.
background
This module resides in the Chemistry domain of Recognition Science and imports Mathlib along with the Compat module, described as providing 'Central compatibility imports for the project. Downstream modules can import this file to gain access to compatibility shims and project-wide constants.', and the Constants module supplying 'The fundamental RS time quantum (RS-native). τ₀ = 1 tick.'. It introduces definitions for bond angle biases and cosines that capture geometric preferences consistent with the self-similar fixed point of the framework. The setting is purely definitional, preparing geometric quantities for use in higher-level constructions without new physical assumptions.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The definitions supply the φ-tetrahedral angle and related bond angle biases imported by the Flight.Geometry module. That module provides '# Flight Geometry (φ-Tetrahedral / log-spiral scaffold) This file provides the purely geometric layer of the spiral-field propulsion model: - the φ-tetrahedral angle (derived from Recognition Science axioms), - log-spiral rotor paths under φ-scaling, - math-only lemmas about step ratios and per-turn multipliers. No physical claims are made here. All geometry is derived from the RS constant φ.'
scope and limits
- Does not derive bond lengths or energies from the angle biases.
- Does not assert any connection to observed molecular spectra or quantum chemistry calculations.
used by (1)
depends on (2)
declarations in this module (15)
-
def
tetra_bias -
theorem
angle_bias -
def
optimalBondCosine -
theorem
linear_cosine -
theorem
trigonal_cosine -
theorem
tetrahedral_cosine -
theorem
octahedral_formula_cosine -
def
tetrahedralAngleRadians -
def
tetrahedralAngleDegrees -
theorem
tetra_cos_eq -
lemma
cos_two_pi_div_three -
theorem
tetra_angle_bounds -
def
methaneAngle -
def
waterAnglePrediction -
def
ammoniaAnglePrediction