The Eleven Theorem: One Integer Governs Vacuum Geometry, Electromagnetism, Baryogenesis, Consciousness, Neutrinos, and Inflation

We prove that the integer 11 = |passive edges of Q₃| is the single combinatorial invariant from which six physically distinct phenomena derive simultaneously. Starting from the Recognition Composition Law (RCL) and the three-dimensional cube Q₃, we establish: (i) 11 is the passive mode count of the Q₃ vacuum, forcing Ω_Λ = 11/16 − α/π; (ii) 11 is the torsion gap Δτ₁₂ = 11 of the CKM filtration, forcing η_B = φ⁻⁴⁴ with 44 = 4 × 11; (iii) 11 is the integer part of φ⁵ = (11 + 5√5)/2, and φ⁵ is simultaneously the smallest φ-power exceeding 11 and the counterfactual consciousness threshold Z_cf; (iv) the solar neutrino mass splitting Δm²_⊙ sits at φ-rung 5, the same rung as Z_cf; (v) the number of inflationary e-foldings satisfies N_e = 44 + 11 = 55 = F₁₀ (the 10th Fibonacci number), giving n_s = 1 − 2/55 = 0.9636 (within 0.3% of Planck 2018). Taken together, these results show that the integer 11 is the universal coupling constant of the Recognition Science framework: it connects the electromagnetic fine structure, the baryon-to-photon ratio, the dark energy fraction, the consciousness threshold, the neutrino sector, and the primordial spectrum through a single geometric fact about the three-dimensional cube. All structural results are machine-verified in Lean 4 across four new modules (zero sorry, zero RS-specific axioms).