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Bridge Structure · April 2026

All Fundamental Constants Lie on Two Bridge Lines

G, H₀, and Λ lie on a straight line in log-coupling space with slope α⁻¹. A second parallel line governs the electroweak constants with coupling formula φ^(−(φ(p−1)+4)) — no α anywhere. The two lines are dual: physics on one is a structural gap on the other.

Eric McLean · Independent Researcher, Edinburgh · Pentagon Physics · 3 April 2026 · 10.5281/zenodo.19402611
2Bridge lines
137.036Common slope α⁻¹
0.00085Geometric separation
6Kill conditions
Key Results

Two registers of one structure

The upper bridge (depths 23.8–123) and lower bridge (depths 0.55–1.17) are exactly parallel lines in (R, depth) space. Same slope α⁻¹ = 137.036. The perpendicular distance between them is 0.00085 — geometrically they are almost on top of each other. The sixty-decade apparent separation is an artefact of reading nearly-vertical lines in the vertical direction.

1
Upper bridge: depth = α⁻¹ × R + φ⁻². Positions {φ⁻², φ⁻¹, 1, φ, 2}/√5 give G, H₀, Λ, FDM, and floor. Slope and intercept both derived.
2
Lower bridge coupling: φ^(−(φ(p−1)+4)). No α in the formula. Three positions algebraically proved: p=φ⁻² gives sin²θ_W = φ⁻³ exactly.
3
Bridge duality: every physics position on the upper bridge is a structural gap on the lower, and vice versa. Exact across all five positions.
4
The "4" in the lower bridge formula encodes D=4 spacetime dimensions. In D=3: floor coupling φ⁻². In D=4: φ⁻³ = sin²θ_W. In D=5: φ⁻⁴.
Kill Conditions
K1: G consensus above 6.674×10⁻¹¹ at 200 ppm → eigenmode derivation fails
K2: R(Λ) − R(G) ≠ φ⁻¹ at 100 ppm independently → bridge geometry fails
K3: Weinberg angle deviates from φ⁻³ by >2% after scale matching → lower bridge floor fails
K4: Constants identified at p=φ⁻¹ (0.1964) or p=2 (0.0670) deviate >5% from prediction → lower bridge fails
K5: Fifth position coupling inconsistent with gravity-expansion coupling → fifth position fails
K6: Any confirmed constant deeper than Λ → no-go theorem broken
↗ Read on Zenodo doi:10.5281/zenodo.19402611