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IndisputableMonolith.Chemistry.BondAngles

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The Chemistry.BondAngles module supplies dimensionless proxies and cosine definitions for molecular bond angles, with a central bias term that favors tetrahedral geometry under Recognition Science constraints. Modelers of molecular structures or φ-scaled propulsion geometries cite these when embedding RS-derived angles into geometric scaffolds. The module consists solely of definitions with no embedded proofs or theorems.

claimThe module defines a tetrahedral bias proxy together with cosine values for linear, trigonal, tetrahedral, and octahedral geometries, including the relation $cos(2π/3)$ and bounds on the tetrahedral angle in radians and degrees.

background

Recognition Science fixes spatial dimension D=3 and the self-similar fixed point φ via the forcing chain T0-T8. Bond angles enter as geometric constraints on the φ-ladder, expressed through the J-cost function and defect distances introduced in the Constants module. The present module imports those constants (with τ₀ = 1 tick) and Compat shims to define angle-specific cosines and a bias term that quantifies tetrahedral preference.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

These definitions supply the geometric primitives required by the downstream Flight.Geometry module, which builds the φ-tetrahedral and log-spiral scaffold for the spiral-field propulsion model. They instantiate the eight-tick octave and φ-forced fixed point inside a chemical setting, closing one link in the chain from T6 to concrete molecular geometry.

scope and limits

used by (1)

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depends on (2)

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declarations in this module (15)