Big G as a Quantum-Coherence Readout: Parameter-Free Resolution of the Gravitational-Constant Discrepancy

The Newtonian gravitational constant G remains the most poorly determined fundamental constant: its CODATA-2022 recommendation, G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻², carries a relative uncertainty inflated by an expansion factor of 3.9 to absorb a Birge ratio of order five among mutually incompatible direct determinations. The 2026 NIST replication of the BIPM torsion balance reports G = 6.67387(38) × 10⁻¹¹ m³ kg⁻¹ s⁻², roughly 64 ppm below the consensus. We show that this offset is reproduced, with no experiment-level fit parameter, by a channel-selective Planck-unit bifurcation derived from the parameter-free finite-cell formulation of Mittermeier Attractor Theory (MAT). The Planck length is reconstructed before gravity is introduced, through an electron-to-Planck mass ratio fixed by a finite-support boundary action and the exact Rydberg identity R∞ℓP = (αX²/4π)(mₑ/MP), so that the resulting Newton coordinate is quartic in the selected electromagnetic carrier, G ∝ αX⁴. Coherent (N = 1) probes evaluate the electromagnetically healed atomic branch α₀,MAT and yield G_atomic = 6.674300 × 10⁻¹¹ m³ kg⁻¹ s⁻², on the CODATA central coordinate at 17.1 ppb (+0.0008σ). Decohered bulk matter (N → ∞) reverts to the bare support branch αM dressed by a calculable pairwise trace-anomaly penalty (2/3)εcl, yielding G_source = 6.673871 × 10⁻¹¹ m³ kg⁻¹ s⁻², within 0.166 ppm (+0.003σ) of the NIST/BIPM 2026 value. Every rational factor entering the construction (π/4, 5/2, 9/8, 2/3, 14, 28) is traced to a closed identity of the MAT support spine, and the entire 64 ppm split is shown to decompose exactly as 52.98 ppm (atomic→bare) + 11.30 ppm (bare→source). The single residue δα_chart,π that drives the bifurcation is determined by the finite-support geometry descended from the algebraic seed ρ; it is independently confirmed by the flow-side closure condition δ₃(Λ₀) = 0, which simultaneously fixes the cosmological constant Λ₀* = 2.817 × 10⁻¹²² — a quantity that ΛCDM leaves unexplained. The atomic fine-structure constant, the local and source values of G, the electron mass, the Planck/DESI matter fractions, and the vacuum energy are therefore all locked readouts of one upstream residue descended from ρ. The bifurcation is sharply falsifiable: purely macroscopic mass-to-mass experiments must converge to G_source, purely coherent measurements to G_atomic, and hybrid atom-interferometric set-ups to scattered intermediate values.