Structural Constants

Status: CANONICAL

Primary Constants

Constant	Symbol	Value	Role in SSZ
Golden Ratio	φ	1.618033988749895	Fundamental segmentation constant
Pi	π	3.141592653589793	Division constant
Fine-structure	α	1/137.036	Geometric origin in SSZ
Coupling factor	φ/2	0.80902	Appears in coupling radius
Speed of light	c	299,792,458 m/s	Local invariant
Gravitational const.	G	6.67430×10⁻¹¹ m³/(kg·s²)	Mass→geometry
Planck constant	ℏ	1.054571817×10⁻³⁴ J·s	Quantum link
Solar mass	M☉	1.98892×10³⁰ kg	Reference mass

φ appears in SSZ as a structural constraint, not a fitted parameter:

Inner/decay Xi: Xi_A(x)=1-exp(-φ/x) — current global decay comparison, with x=r/r_s
Local saturation Xi: Xi_B(x)=min(1-exp(-φx), Xi_max) — paper/metric-pure saturation context
Horizon value: both forms give Ξ(r_s) = 1 - e^(-φ) = 0.80171
Coupling radius: r_φ = (φ/2) · r_s · [1 + β·Δ(M)] — φ/2 as coupling
Frequency grid: R = φ^N — discrete redshift scaling
Logarithmic spiral: b = ln(φ)/Δθ ≈ 0.306 — geometric growth

The claim: without φ-geometry, SSZ loses predictive sharpness.

Context	How π enters
Schwarzschild radius	r_s = 2GM/c² (implicitly via 3D geometry)
Perihelion precession	Δω = 6πGM/[a(1-e²)c²]
Curvature detection	Triangular frequency comparison
Fine-structure	α = e²/(4πε₀ℏc)

SSZ treats φ and π as the two fundamental geometric constants of segmented spacetime.

Quantity	Expression	Value
Ξ_max	1 - e^(-φ)	0.80171
D_min (at r_s)	1/(1 + Ξ_max)	0.55503
z_max (at r_s)	Ξ_max	0.80171
r*/r_s (decay/global D-intersection)	`D_SSZ = D_GR` with `Xi_A(x)=1-exp(-φ/x)`	1.594811
r*/r_s (saturation/local D-intersection)	`D_SSZ = D_GR` with `Xi_B(x)=1-exp(-φx)`	1.386562
D(r*)	depends on declared Xi form	0.610710 / 0.528007

Δ(M) = A · exp(-α / M^B)
A = 98.01
α = 2.7177 × 10⁴
B = 1.96

This correction is derived from φ-geometry, NOT from data fitting. It modulates the coupling radius for different mass scales.

Parameter	Value	Status
β	1	Exact in SSZ
γ	1	Exact in SSZ

Confirmed by Cassini (2003): γ = 1.000021 ± 0.000023

Constant	Symbol	Value	Unit
Speed of light	c	299,792,458.0	m/s
Gravitational constant	G	6.67430 × 10⁻¹¹	m³/(kg·s²)
Planck constant	ℏ	1.054571817 × 10⁻³⁴	J·s
Boltzmann constant	k_B	1.380649 × 10⁻²³	J/K
Solar mass	M☉	1.98892 × 10³⁰	kg
Electron mass	m_e	9.10938 × 10⁻³¹	kg
Elementary charge	e	1.60218 × 10⁻¹⁹	C