Collider Reach for a Strong Transition: Portal Couplings That Deliver Alpha Above a Tenth, Checked Against the Ceiling

The target strength requires a portal coupling of 0.29. At that coupling the mixing proxy is 0.028, a value within reach of precision Higgs programmes and therefore a genuinely testable companion prediction: a portal strong enough for alpha of a tenth does not hide from colliders in this proxy. For orientation, a coupling of 0.5 gives a strength of 0.298, while a coupling of 1 gives 1.19. The ceiling maximum at this temperature exceeds the target strength by many orders of magnitude, so the density bound places no additional restriction on the collider-accessible region; the binding constraints on strong electroweak transitions come from Higgs measurements and perturbativity, not from the ceiling. This study is simulated and computed from stated assumptions; it is not a measurement.