The Stagger Is the Shadow: AF-10's Crossings Read Against the Ceiling

AF-10's complete running placed the first pairwise crossings of the three gauge couplings at three staggered addresses — α₁=α₂ at ~10^13.05 GeV, α₁=α₃ at ~10^14.22, α₂=α₃ at ~10^16.41 — all far above the frame's counting ceiling E_ind = 3.02×10⁹ GeV. This paper asks what those addresses are, read against the ceiling. First, they are exactly the linear shadow of the anchor: recomputing each crossing from AF-10's gaps at E_ind (9.462, 19.421, 9.959) and its trajectory's per-decade slopes (−1.516, +1.147, +2.587) returns log₁₀E = 13.03, 14.21, 16.39 — inside AF-10's printed brackets. The crossings contain no information beyond the anchor and the slopes; they are where the unsaturated lines, extended, would meet. Second, no saturation law at the ceiling returns them as predictions: under any common suppression factor f of the running above E_ind, every crossing address moves to log E_ind + (log E_cross − log E_ind)/f — f = ½ pushes them to 16.59/18.95/23.31, f = ¼ to 23.69/28.41/37.14, and the hard freeze (f = 0) abolishes them entirely. An address that takes every value in a family is not a prediction of the family. What is invariant — at every f > 0 — is the stagger itself: three distinct addresses, in a fixed order, with spacing ratios set by the Standard Model's slope ratios. The meeting story fails not because the couplings never converge, but because even the shadow they cast refuses to be a single point.