From the Gap Ratio to the Cabibbo Doublet and Beyond: One mismatch. One particle. Sixteen findings. The integers spoke.

From the Gap Ratio to the Cabibbo Doublet and Beyond: One mismatch. One particle. Sixteen findings. The integers spoke. 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 Session 3 of the HOWL series began with a question — do the three SM gauge couplings unify? — and ended with a particle. The SM gap ratio 218/115 = 1.896 misses the measured 1.358 by 40%. The SM does not unify. Enumerating 15 single-multiplet extensions in exact Fraction arithmetic identified a unique minimal survivor: the Cabibbo Doublet (3,2,1/6), a vector-like quark doublet with gap ratio 38/27 = 1.407 and M_GUT = 10^15.5 at the proton decay boundary. Three independent experimental anomalies — CKM first-row unitarity deficit at 2.5-4 sigma, the LEP forward-backward b-quark asymmetry at ~3 sigma, and the Higgs signal strength excess at ~2 sigma — each independently point to the same (3,2,1/6) representation at 1.5-6 TeV. Two-loop corrections improve unification from Delta(1/alpha_3) = -1.17 (one-loop) to -0.40 (two-loop), with the residual within standard GUT threshold correction range. Session 3 produced 16 findings documented in 15 papers, verified 6 scripts with 98 total checks, identified 1 new particle, generated 3 experimental tests, closed 2 investigation paths, and extended the database to 146 entries with 38/38 checks. The integers identified a specific BSM particle. The universe has not yet confirmed it. 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-DISC-11-2026). Dependencies: HOWL-DISC-6-2026, HOWL-DISC-7-2026, HOWL-DISC-8-2026 Motto: Derive. Compare. Publish.Status: Complete