From Pure Lattice to Earth's Free Fall
The Universal Force of Time framework derives Earth's free-fall acceleration — what science calls gravity — from first principles without any empirical fitting. The chain starts from a pure lattice value and passes through five arithmetic operations, all of which use only the prime lattice {2, 3, 5, π}:
Step 2: × 4π²/10 → AU_G1 = 93.126... million miles
Step 3: × 5⁵/(2³×3⁵) → AU_G1 = 149.768... million km
Step 4: × 2 ÷ 360 ÷ 864 × 10⁵ → g² = 96.147...
g_G2 / g_G1 = √(1+δ_G) exactly
The G-bond step δ_G = 90.1506 ppm governs the separation between the G1 and G2 temporal registers. It is defined as the ratio of the two Moho radii:
Moho_G1 = 2⁹×3⁹×π²/5⁶ km × 1000
Since g ∝ √AU and AU(G2)/AU(G1) = (1+δ_G) exactly, the register ratio of free-fall accelerations follows algebraically:
g_G2 = 9.805929539... m/s²
Residual: < 10⁻¹⁵ (machine precision zero)
The Earth–Sun Distance in Two Registers
The AU itself is a dual-dimensional observable. The G1 and G2 starting values produce two register-conjugate Earth–Sun distances whose ratio is exactly (1+δ_G):
AU_G2 = 149.782... million km
Key Results
Earth surface free-fall is derived from a five-step pure lattice chain starting from G1_start = 3π/4 × 10 = 23.561944902... The chain uses only {2,3,5,π} arithmetic.
Step 3 of the chain uses km/miles = 5⁵/(2³×3⁵) = Sun×Mercury dimensional speed product. Planetary spacetime speeds are therefore embedded in Earth surface gravity.
The G1 register starting value 3π/4 × 10 simultaneously encodes Mercury quarter-orbit geometry (3π/4 = 135° in radians) and the AU scaling factor.
g_G2/g_G1 = √(1+δ_G) exactly. This is an algebraic identity following from g ∝ √AU and AU(G2)/AU(G1) = (1+δ_G). Residual is machine-precision zero.
AU(G2)/AU(G1) = (1+δ_G) exactly. The Earth–Sun distance exists in dual-dimensional form; their geometric mean equals the IAU 2012 standard AU.
G-bond step δ_G = 90.1506 ppm is the universal register separation constant. It appears identically in the equatorial radius split, the sidereal day split, the free-fall ratio, and the Mercury spin-orbit ratio.
g_G1 = 9.805487563... m/s² (G1 register, lower Moho anchor). g_G2 = 9.805929539... m/s² (G2 register, observed ground-level value). Deviation from ISO standard g (9.80665): 73.4 ppm.