pith. sign in
module module moderate

IndisputableMonolith.Chemistry.BondAngles

show as:
view Lean formalization →

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

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (15)