The Complete Running Changes Nothing Below the Wall: Two Loops, Thresholds, and the Third Coupling
Year: 2026
Type: preprint
Abstract: AF-5 ran the electromagnetic and strong couplings on declared one-loop lines to the frame's counting ceiling E_ind = 3.02×10⁹ GeV, found no meeting below the wall, and charged its own F1 as the price of the simplification: a two-loop, threshold-complete running that places a pairwise crossing below E_ind kills the verdict. This paper pays that charge. All three gauge couplings — the weak coupling α₂ added to the bench for the first time — are run with two-loop Machacek–Vaughn coefficients and the top threshold stepped at m_t = 172.69 GeV. At the ceiling the inverses stand at α₁⁻¹ = 47.571, α₂⁻¹ = 38.109, α₃⁻¹ = 28.150: no two within 9.46 of each other, no crossing anywhere below it. The first pairwise crossing of the complete running is α₁ = α₂ at ~10^13.05 GeV — four orders of magnitude above the ceiling, on the far side of the wall the frame owns. AF-5's verdict does not merely survive its own falsifier; the complete running sharpens its context: the couplings do converge toward each other far above the wall, and converge pairwise at three different addresses (10^13.05, 10^14.22, 10^16.41 GeV), so even the extrapolated record tells no single-meeting story. Below the wall there is no meeting. Above it, running is the thing this frame says saturates. Both halves now stand on the complete computation, not the declared simplification.
Author: Aldred, William Alexander
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225397756