Vol3 Sections 156, 268 · P-FSC-1 through P-FSC-6

Fine Structure Constant: α = 3²/(5³π²)

α_FOT = 9/(125π²) is a pure prime lattice address. Speed-coupling identity c_G1 × α_FOT = 2³×3⁷×5³ = 2,187,000 exactly

α_FOT
3²/(5³π²)
1/α = 137.0778
·
Speed-Coupling
c×α = 2,187,000
2³×3⁷×5³ exact
·
Propositions
6
P-FSC-1 to P-FSC-6

c_G1 × α_FOT = 2,187,000 exactly

The product of the G1 speed of light and the FOT fine structure constant is a pure {2,3,5} integer. The π² of c_G1 cancels the π² of α_FOT⁻¹ exactly, leaving 2³×3⁷×5³.

P-FSC-2 Speed-Coupling Identity
c_G1 × α_FOT = 2³×3⁷×5³ = 2,187,000 [exact]
c_G1 = 2³×3⁵×5⁶×π² | α_FOT = 3²/(5³π²) | π² cancels exactly
3⁷ = 2187 = atomic Tau-ceiling

Key Results

P-FSC-1

α_FOT = 9/(125π²). 1/α_FOT = 137.0778. Residual from NIST 305.6 ppm — systematic offset present across all FOT EM constants.

P-FSC-2

Speed-Coupling Identity: c_G1 × α_FOT = 2,187,000 = 2³×3⁷×5³ [exact]. π² cancels between c and α⁻¹.

P-FSC-4

c_G1 = 2³×3⁵×5⁶×π² = 30,375,000π² m/s. First closed-form derivation of the speed of light from prime lattice alone.

Cross-references: Vol3 Section 156 | P-CLIGHT-1 | Section 268 (P-EM-3)
A note on “constants.” Within the Universal Force of Time there are no universal constants. A quantity like the Rydberg is not one fixed number but a small family of register faces — each an exact {2, 3, 5, π} value, each reproducing the spectrum on its own scale of Τ. The Rydberg alone carries at least three: 10,966,227.11 m⁻¹ (= 10⁷π²/9), 10,967,215.73, and 10,973,936.9 m⁻¹. What conventional physics records as the constant — the CODATA 10,973,731.568157 m⁻¹ — is not a fourth fundamental number; it is a single measurement sitting between those faces, in the band they define, read from the one register our instruments occupy: the Earth-surface node, g₁. Every wavelength, and the speed of light, Planck’s value, and the fine-structure ratio with it, behaves the same way — each shifts from g₀ to g₁ to g₂ to g₃ by the lattice step δG, not by error. These are not constants; they are the values Τ wears at the register where we stand.