Temporal Convergence Framework: Distinguishing Structure from Coincidence in High-Precision, Low-Dimensionality Parameter Spaces

Modern computational methods across scientific domains achieve precision through iterative refinement. This precision regime creates opportunities for refined evalua- tion methods: as measurement uncertainties decrease while parameter dimensionality remains fixed, statistical significance becomes more easily obtained through combinato- rial search. Traditional hypothesis testing could benefit from additional discrimination when nearly any simple relationship can achieve sub-sigma agreement by chance. We propose a seven-criteria framework emphasizing temporal convergence through pre-registration. The core innovation: patterns must be publicly registered before new data releases, then demonstrate directional convergence or stability as preci- sion improves. This requirement provides robust protection against retroactive fit- ting—reducing susceptibility to common biases including data selection and post-hoc hypothesis adjustment. Combined with six supporting criteria (scale invariance, com- pression, statistical agreement, mathematical simplicity, independent validation, theo- retical viability), temporal tracking enhances discrimination when statistical tests alone could benefit from additional tools. We demonstrate framework operation using lattice QCD quark mass ratios—deliberately selected as the hardest test case (N=3 parameters at 2% precision, maximum combi- natorial coincidence risk). The Diagnostic Pattern 2(md/mu)3 ≈ ms/md achieves 0.16σ statistical agreement yet self-falsifies through directional divergence: as uncer- tainties improved 37%, central values converged toward 2.162 rather than the predicted 2.154, with statistical significance doubling from 0.075σ to 0.16σ. This demonstrates successful filtering of numerical coincidence despite passing traditional validation. The framework’s discriminatory capability is validated through historical test cases: the Gell-Mann-Okubo relation correctly passes all criteria, demonstrating that physi- cally meaningful patterns survive multi-criteria evaluation. Framework value is methodology- independent—we demonstrate filtering through failed patterns, not to advocate specific 1 physics. Initial thresholds serve as community starting points; the contribution is es- tablishing systematic, pre-registration-based standards for pattern evaluation in any domain where computational precision outpaces dimensional growth.