α⁻¹ Is the Universal Conversion Rate of Λ, G, H₀

McLean, Eric

doi:10.5281/zenodo.19365448

Bridge Line · April 2026

α⁻¹ Is the Universal Conversion Rate of Λ, G, H₀

G, H₀, and Λ — measured by three completely disconnected experimental programmes — are collinear in log-coupling space. The slope is α⁻¹ = 137.036, recovered independently from each sector. Four-constant constraint: G, Λ, α, and mₚ are not independent.

Eric McLean · Independent Researcher, Edinburgh · Pentagon Physics · 1 April 2026 · 10.5281/zenodo.19365448

Key Results

Three sectors, one slope

The gravitational constant (torsion balance), the Hubble rate (supernova distance ladders), and the cosmological constant (CMB) sit on a straight line in bridge space with slope α⁻¹ to 14 significant figures. Neither the slope nor the intercept is fitted — both are derived from the axiom σ = 1/(1+σ). The four-constant constraint G = mₚ²c⁴/(ρ_Λ ℏ² × 10^(α⁻¹φ⁻¹)) removes one degree of freedom from cosmology.

Bridge equation: depth = α⁻¹ × R + φ⁻². Slope α⁻¹ = 137.036 and intercept φ⁻² = 0.382 both derived. Neither fitted.

Exact identity: R(Λ) − R(G) = φ⁻¹. Three-line algebraic proof from R(Λ) = 2/√5 and R(G) = φ⁻¹/√5 using only (1+√5) = 2φ.

Four-constant constraint: G, Λ, α, mₚ are not independent. Given any three, the bridge determines the fourth. Zero free parameters.

Fifth bridge position at R = φ/√5, depth 99.54 — conjectured coupling between gravity and cosmic expansion. Character class 5A of 2I.

Kill Conditions

K1: G consensus above 6.674×10⁻¹¹ at 200 ppm → eigenmode derivation α_G = α¹⁸×12/7 falsified

K2: R(Λ) − R(G) ≠ φ⁻¹ at 100 ppm → bridge geometry falsified

K3: DESI DR2 w₀ ≠ −0.97 at 3σ → Friedmann constraint fails

K4: log(Λ/G) ≠ −α⁻¹φ⁻¹ beyond measurement precision → four-constant constraint fails

K5: Confirmed constant deeper than Λ → no-go theorem broken

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