It from Bit, Measured: The Δ-Gate as Wheeler's Missing Coordinate

We identify the quantitative coordinate that Wheeler's "it from bit" program left unbuilt. Between Bekenstein's information ceiling and Landauer's erasure floor, a universal transition variable emerges: Δ = log₁₀(Eᵍ / Eᵍ,cr), measuring a system's perturbation immunity in Landauer units. Validated across 31 M₁₃ transition-metal nanoclusters (PBE data, Chaves et al. 2017), with Pd₁₃ as critical null point and a blind Pb₁₃ prediction accurate to 0.6 meV. The decay exponent α = 1 is derived algebraically, not fitted. A Lindblad decoherence bound maps Δ onto real qubit platforms (trapped ions, transmons, NV centers). The Δ-coordinate tracks material persistence across cosmic time via CMB cooling. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).