We demonstrate that the product modular tensor category SU (3) ₃ ⊗ SU (2) ₂ encodes the complete Standard Model vacuum structure. Using the Symmetry TFT (SymTFT) framework, we identify the SM vacuum as the Lagrangian algebra LSM = 1, 8, 10, 10̄ ⊗ 1, ψ with dimension 12 = Dₜotal, automatically reproducing the Z₆ gauge group center, quark confinement, and the Higgs mechanism. The Walker-Wang 3+1D model produces a unique gapped ground state (GSD=1) with TEE γ = ln (12), confined point excitations (quarks/leptons), and loop excitations (gauge flux tubes). We place this in the Décoppet-Yu classification with SPT twist (0, 1) ∈ Z₆, enforcing θQCD = 0 and the Witten anomaly. The hierarchy formula ρ_Λ/ρPl = D^Lx-1/C^Lx predicts log₁₀ (ρ_Λ/ρPl) = −122. 926 at Lx=82, within 1. 1σ of Planck 2018 (−122. 940 ± 0. 013). All quantum corrections (BTZ one-loop, Casimir, gravitational CS counterterms) are shown negligible. The parameter C acts as an RG invariant analogous to ΛQCD. Complete fermion condensation map: 4 Majoranas from SU (3) ₃ bosonization + 1 from SU (2) ₂ Ising ψ-condensation = 5 total (c = 5/2). Companion code includes: 16-paper synthesis resolving the 3π factor, fermion condensation analysis, SymTFT + Walker-Wang construction, and CC gap quantum corrections. Five new predictions derived: graviton mass bound, loop spectrum, ΛQCD dimensional transmutation, dark matter candidate, Ngen = 3. Scorecard: 12/12 observables match.
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Adam Bazih
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Adam Bazih (Wed,) studied this question.
www.synapsesocial.com/papers/69eb0b25553a5433e34b4eb3 — DOI: https://doi.org/10.5281/zenodo.19689327