Integer-Forced Identification of the Minimal Unification Extension: We did not choose this particle. The integers chose it.

Integer-Forced Identification of the Minimal Unification Extension: We did not choose this particle. The integers chose it. This paper is part of the HOWL research archive—a collection of physics papers exploring integer fraction derivations across multiple domains using exact arithmetic and automated comparison. Abstract The Standard Model has three gauge couplings — one for each factor of SU(3)×SU(2)×U(1). Grand unification predicts that these three couplings converge to a single value at high energy. Whether they converge depends on the particle content of the theory, which determines the rate at which each coupling changes with energy. These rates are exact rational numbers: b₁ = 41/10 for U(1), b₂ = −19/6 for SU(2), b₃ = −7 for SU(3). The ratio (b₁−b₂)/(b₂−b₃) = 218/115 = 1.896, compared to the value 1.358 measured from the three couplings at the Z boson mass scale, tests whether the couplings converge. They do not. The Standard Model overshoots by 40%. This paper asks: what single new particle, added to the Standard Model, would fix the convergence? An exhaustive enumeration of 15 candidate particles — every scalar and vector-like fermion with gauge representations up to dimension 8 in SU(3), 4 in SU(2), and hypercharge |Y| ≤ 2 — is tested by computing each candidate's modified convergence ratio in exact rational arithmetic. Twelve candidates are eliminated because their ratios are more than 0.15 from the measured 1.358. One more is eliminated by the existing proton decay bound from Super-Kamiokande. Two survive. The full supersymmetric extension of the Standard Model (MSSM), with ratio 7/5 = 1.400 (distance 0.042 from measured) and dozens of new particles. And a vector-like quark doublet in the (3,2,1/6) representation — a single new particle with the quantum numbers of the left-handed quark doublet — with ratio 38/27 = 1.407 (distance 0.049 from measured). The vector-like doublet achieves convergence quality comparable to the full MSSM with one particle instead of dozens, at a unification scale of 10^15.5 GeV testable by the Hyper-Kamiokande proton decay experiment. Falsification Criteria All papers in this archive are subject to falsification through direct comparison to published experimental measurements. Each derived value is tested against independent data with explicit PASS/FAIL criteria. Any derived value that fails its comparison is documented and published alongside the successes. Research Context This archive documents an ongoing research program in integer fraction physics. The methodology is: derive values from gauge group integers using exact fraction arithmetic, compare to published measurements, and document all results including failures. The archive spans multiple physics domains connected through the soliton boundary framework described in the constituent papers. Package Contents manuscript.md: The complete derivation and supporting analysis. README.md: Navigation, dependencies, and citation (Registry: HOWL-PHYS-15-2026). Dependencies: HOWL-PHYS-1-2026, HOWL-PHYS-10-2026, HOWL-PHYS-11-2026, HOWL-PHYS-12-2026, HOWL-PHYS-13-2026, HOWL-PHYS-2-2026, HOWL-PHYS-6-2026, HOWL-PHYS-7-2026, HOWL-PHYS-8-2026, HOWL-PHYS-9-2026 Motto: Derive. Compare. Publish.Status: Complete