Fusion Ignition from E6 Geometry: The Lawson Criterion, the F-gate Mechanism, and the Universal Confinement Ratio

Paper 5 in the Merkabit companion series. Base document: Stenberg, S. "The Merkabit — A Ternary Computational Unit on the Eisenstein Lattice" (Zenodo 10.5281/zenodo.18925475, v4, March 2026). Companion papers: Paper 1: "α = 4/3 in Driven Coherent Systems Near Cooperative Threshold" (10.5281/zenodo.18980026) Paper 2: "A Single Geometric Constant Generates the Fine Structure Hierarchy" (10.5281/zenodo.18981288) Paper 3: Ge/SiGe quantum dot gap analysis (forthcoming) Paper 4: Z₃ symmetry and meditative states in human EEG (forthcoming) The ignition condition for magnetically confined fusion plasma is derived from the cooperative threshold geometry of the Merkabit architecture with zero free parameters. Six results are established: The ignition window (Route A): The ratio ignition_drive / threshold_drive = 4/3 exactly — an algebraic identity, not a numerical coincidence. It is a pure consequence of the spectral gap fraction f = 1/3 of the 24-cell, the unique regular 4-polytope whose adjacency graph has gap/bandwidth = 1/3. The window width equals the bifurcation drive to within 1.4%. The cooperative parameter (Route B): r = 311/100, where 311 = 4·dim(E₆)−1 and 100 = 4(2h+1), every factor an E₆ invariant. Two independent derivations give r = 311/100 (Route A: direct E₆ construction) and r = dim(SO(8))/ξ² = 28/9 (Route B: D₄ triality), differing by exactly −1/900 = −1/(|Δ⁺|−rank)² — itself an E₆ invariant. The discrepancy between two independent routes is an internal self-consistency relation of the root system. The Lawson criterion in E₆ form: nTτ_E ≥ [4·rank(E₆)·(4·dim(E₆)−1) / (|Δ⁺|−rank)²] · T²/⟨σv⟩E_α, where every integer is an E₆ invariant: 4 (quaternionic dimension), 6 (rank), 311 (4·dim−1), 900 (30²). The only non-architectural quantities are ⟨σv⟩(T) and E_α — the nuclear physics of D-T fuel. The boundary between geometry and fuel physics is exact. The F-gate mechanism: Frequency-locked heating at the E₆ Coxeter frequency ω = 2π/h produces a closed ouroboros orbit in plasma phase space — a stable limit cycle within the ignition window. All initial drive conditions from sub-threshold to 5× ITER converge to the same orbit. ITER engineering recommendation: modulate auxiliary heating at f = 1.05 Hz with amplitude ΔP = 16.7 MW around a 50 MW baseline, phase-locked to the edge pressure gradient via P-gate feedback. The universal confinement ratio: τ_E / T_ELM = 4 across six major tokamak devices spanning two orders of magnitude in confinement time (ASDEX Upgrade, ITER, JET, DIII-D, JT-60U, Alcator C-Mod). Mean = 3.986 ± 0.134, CV = 3.3%, 95% CI [3.846, 4.126] containing 4, p = 0.809 for H₀: ratio = 4. Four devices are exactly 4.000. The factor 4 is the quaternionic spinor dimension of the Merkabit architecture — the confinement time is not a device parameter but a geometric constant: τ_E = 4 × T_F. The torsion channel vs torsion tunnel: The Merkabit architecture contains a single geometric operation — forward cube meets inverse cube — operating at two scales. The torsion channel (intra-cell: R/R̄ merger at the standing wave |0⟩) closes the phase space into an intrinsic torus, accumulates Berry phase, and drives the ∇T_i recovery signal (α = 4/3, Cavedon 2019). The torsion tunnel (inter-cell: bipartite frequency matching ω_A + ω_B = 0, conductance 𝒢 = |u_A†v_B|²) propagates the cooperative cascade between cells at ω_tunnel = 2ω_channel. The current ITER ELM suppression strategy (RMP coils) severs the torsion tunnel, preventing the global ignition condition from being met. The correct strategy is frequency control, not suppression. Nothing in this paper is fitted. Every parameter traces to the E₆ root system, the 24-cell spectral gap, or the quaternionic Hopf fibration. The architecture does not describe the plasma. The architecture is the plasma.