pith. sign in
def

C_xi

definition
show as:
module
IndisputableMonolith.Gravity.GravityParameters
domain
Gravity
line
96 · github
papers citing
none yet

plain-language theorem explainer

Recognition Science sets the morphology coupling coefficient C_ξ to twice the golden ratio raised to the negative fourth power. Galaxy dynamics modelers cite this constant when fitting rotation curves under the RS gravity ansatz. The declaration is a direct real-arithmetic expression with no lemmas or hypotheses.

Claim. $C_ξ := 2 φ^{-4}$ where φ is the golden ratio.

background

The GravityParameters module derives seven galactic gravity parameters from Recognition Science. Three are marked DERIVED from φ, while C_ξ, p, and A carry an RS basis with explicit formulas. The module states that C_ξ follows the expression 2φ^{-4} and notes a 2% match to the fitted value 0.298 ± 0.015. Upstream imports supply the definition of φ together with positivity and structural predicates used elsewhere in the file.

proof idea

The declaration is a direct definition. It evaluates the real expression 2 multiplied by phi raised to the power of negative four.

why it matters

C_ξ supplies the morphology coupling coefficient required by the GravityParameters table. It is referenced by the downstream positivity theorem C_xi_pos. The numerical value 2/φ^4 ≈ 0.292 aligns with the RS prediction derived from φ as the self-similar fixed point (T6) and supports the eight-tick octave structure in the forcing chain.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.