The Robertson Floor of the Vacuum: A CDT Derivation of the Cosmological Constant Scale from Dispersive Vacuum Physics

We derive a first-principles bracket on the minimum vacuum energy density required to maintain atomic structure in a dispersive dynamic vacuum. Building on White et al. (2026), we apply Conjugate Dimension Theory to the competition between vacuum energy extraction and Coulombic coherence, yielding:0.66 u_Λ ≤ u_floor ≤ 1.19 u_Λwith zero free parameters. The bracket collapses the vacuum catastrophe from 10¹²¹ to a factor of ~2.Key results: The extraction-coherence angle θ = α/π is derived geometrically from QED vacuum polarization (Uehling-Serber back-reaction) Quality factor Q = ω_*/4Γ_2P ≈ 8.2×10⁶ fixed by the Lamb shift (1947), predating dark energy discovery QCD, weak, and gravitational sectors proved to contribute zero or negligibly Two specific, calculable open questions remain: (1) the correct commutator power in the locked-energy fraction, (2) the exact coupling profile (Gaussian vs. Lorentzian). These are correlated—W₃ requires Gaussian, W₂ permits Lorentzian; W₃+Lorentzian fails by 3 orders of magnitude.Falsification conditions: Lamb shift remeasurement inconsistent with bracket; dark energy confirmed as exactly constant (w = −1.000...) at the floor value; vacuum energy extraction below floor without atomic disruption; DESI BAO evolution inconsistent with relaxation toward floor; sub-nm Casimir extraction without predicted spectral shifts.Status: Awaiting two zero-parameter calculations in dispersive QED to collapse bracket to single prediction or falsify framework. All equations, input inventory, and numerical verification provided.