The No-Threshold Puzzle — More CD Running Means Better Predictions: No-threshold beats hard threshold by 12×. Soft threshold is worse. The CD contribution is needed at all scales.

The No-Threshold Puzzle — More CD Running Means Better Predictions: No-threshold beats hard threshold by 12×. Soft threshold is worse. The CD contribution is needed at all scales. 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 Cabibbo Doublet — a hypothetical vector-like quark doublet in the (3, 2, 1/6) representation — modifies the gauge coupling beta functions and enables precise unification predictions. The best αₛ prediction (PHYS-30: 0. 11838, miss 0. 33% from measured 0. 1180) uses the CD betas from MZ (91 GeV) to MGUT with no physical threshold. When a threshold is applied at MVL = 500 GeV (SM betas below, CD betas above), the miss worsens to 4. 0% — a factor of 12× degradation. This is puzzling because the CD has a physical mass and should decouple below it. This paper investigates the puzzle through three tests. First, a scan of 12 threshold positions from 200 GeV to 6 TeV: the miss increases monotonically with MVL, and no threshold position matches the no-threshold quality. The best hard threshold (MVL = 200 GeV, miss 1. 72%) is still 5. 3× worse. Second, a step sensitivity test at 200/500/1000/2000 Euler steps: the 12. 3× advantage is unchanged at every step count, ruling out numerical artifact. Third, a soft threshold test using a sigmoid transition f (μ) = 1/ (1+ (MVL/μ) ²): the soft threshold is WORSE than the hard threshold at every MVL, with misses of 7–13%. The pattern is clear and monotonic: more CD running = better prediction. The puzzle is documented with three possible explanations: virtual propagation below MVL, effective resummation, or cancellation of missing higher-order corrections. Future papers (PHYS-37: RK4 integrator, PHYS-38: three-loop estimate) will test which explanation holds. 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-35-2026). Dependencies: HOWL-PHYS-1-2026, HOWL-PHYS-13-2026, HOWL-PHYS-27-2026, HOWL-PHYS-30-2026 Motto: Derive. Compare. Publish. Status: Complete