IndisputableMonolith.Flight.Geometry
Flight.Geometry supplies the tetrahedral angle derived from RS cost minimization as a geometric primitive for spiral propulsion models. Engineers modeling φ-vortex drives or virtual rotors cite it to fix the 4-fold symmetry angle at arccos(-1/3). The module is a definition-only scaffold that imports BondAngles and SpiralField to expose the constant without internal proofs.
claimThe tetrahedral angle is $\theta = \arccos(-1/3) \approx 109.47^\circ$, obtained by minimizing J-cost over four equivalent bonds on the φ-lattice.
background
The module sits inside the Flight domain and imports BondAngles, which states that the tetrahedral angle arises from minimizing J-cost for four equivalent bonds around a central atom under the RS mechanism. It also imports SpiralField, whose variational ansatz treats logarithmic spiral fields under φ-scaling and eight-tick gating, and Constants, which fixes the RS time quantum at one tick. The supplied doc-comment identifies the angle as identical to the sp³ hybridization angle and notes its emergence from the φ-lattice structure.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the Flight facade, GravityBridge, Report, VirtualRotor, TeslaTurbine, and Searl candidate modules. It supplies the geometric constant required by any φ-spiral engine that invokes 4-fold symmetry, closing the link between the BondAngles derivation and downstream propulsion hypotheses.
scope and limits
- Does not derive the angle from J-cost minimization.
- Does not contain dynamics or time evolution.
- Does not address propulsion or lift calculations.
- Does not prove uniqueness of the angle under RS forcing.